We conducted field campaigns at three suburban sites, namely Wangdu (WD), Dianshan Lake (DL) and Taihu Lake (TL). WD is located in Baoding, Hebei, with farmlands, forests and two major roads nearby. DL is located in the southwest of Shanghai, surrounded by residential buildings, vegetation, a highway and a few industrial enterprises. Two campaigns were conducted at DL, one in winter (DLW) and the other in spring (DLS). TL is located in Wuxi, Jiangsu, surrounded by vegetation and a small number of settlements. The detailed information of these campaigns is given in Table 1. Furthermore, this study also involves ambient data previously reported from urban sites, namely Shanghai (SH, Yao et al., 2018) and Beijing (BJ, Cai et al., 2021; Qiao et al., 2021). The location of these five sites is shown in Fig. S1 in the Supplement.

A chemical ionization long time-of-flight mass spectrometer (CI-LToF-MS, Aerodyne Research, Inc.) was deployed to measure gaseous SA, OOMs, and molecular clusters at three suburban sites (Lu et al., 2020), using nitrate and its clusters to ionize neutral molecules and clusters. A calibration coefficient derived from SA and a mass-to-charge-dependent transmission efficiency of the instrument were used to obtain [OOMs], assuming that they share the same kinetically controlled collision rate with reagent ions as that of SA. The transmission efficiency was calibrated using a system coupling a high-resolution differential mobility analyzer (HR-DMA) with the mass spectrometer (Heinritzi et al., 2016). The calibrations of [SA] and transmission efficiency were performed before each campaign. A Vocus proton-transfer-reaction time-of-flight mass spectrometer (Vocus PTR-ToF-MS, Aerodyne Research Inc.) equipped with a focusing ion-molecular reactor (FIMR) was used at WD and DL, with modified instrument settings to measure DMA (Wang et al., 2020). A chemical ionization high-resolution time-of-flight mass spectrometer (CI-HToF-MS, Aerodyne Research Inc.) was used at TL, with protonated ethanol or its hydrated clusters as reagent ions, to measure DMA (Yao et al., 2016). Since mass spectrometer cannot distinguish among isomers, C₂-amine was taken as DMA. NH₃ concentration ([NH₃]) was measured using the ion chromatography (IC) method of Chinese Standard (HJ 1076-2019) at WD and DL. There was no measurement for [NH₃] at TL. The detailed measurement methods for these chemical species are given in the Supplement.

PSD ranging from 1 to 3 nm was measured by an Airmodus A10 particle size magnifier (PSM). The PSD of 3–736 nm particles was measured by two scanning mobility particle sizers (SMPS TSI Inc, USA), namely a nano-SMPS and a long-SMPS (Yao et al., 2018). Temperature was monitored by an automatic weather station (Vaisala AWS310).

A cluster dynamics-multicomponent sectional model was applied to simulate SA-DMA nucleation process (Li et al., 2023). The model is composed of one cluster dynamics module and one sectional module. The detailed description of these two modules is given in the Supplement. SA tetramers were treated as nucleated particles for simulating particle formation rate at 1.4 nm diameter, J1.4 (Larriba et al., 2011), and entered the sectional module as the smallest particles. Particle formation rate at 1.7 nm diameter, J1.7, was simulated by incorporating the initial growth on the basis of J1.4. However, in certain cases, this process could not be directly implemented in the model, because of data overflow (Fig. S2). Therefore, a survival probability approach was adopted as an alternative (Cai et al., 2022a): 1Jp1tJp2t=exp⁡∫dp2dp1-CoagSdpGRdpddp where dp1 is 1.7 nm, and dp2 is 1.4 nm, the corresponding particle size in calculating particle formation rates. The ratio J1.4/J1.7 is defined as the survival probability from 1.4 to 1.7 nm. GR is herein the simulated size-dependent growth rate, which is contributed by condensable vapors through the change of particle mass over time (Tröstl et al., 2016): 2dmpdt=∑imiαβiNi-βiNi,satexp⁡4viσdpkBTfi where mp is the mass of particle; i represents each condensable species; mi is the mass of molecules or clusters; α is the accommodation coefficient; βi is the collision constant between species i and the particle; Ni,sat is the saturation concentration; vi is the molecular volume; σ is the surface tension of the particle; kB is the Boltzmann constant; fi is the molar fraction in the particle. In calculations, the fragmentation of SA-DMA clusters from particles was taken to be negligible, i.e., clusters did not return to the gas phase after coagulating onto a particle.

The uncertainty of SA monomer concentration ([SA₁]) was estimated to be +100 % / -50 % (Cai et al., 2021). The uncertainty of [DMA] was +150 % / -60 % taking into account systematic and calibration uncertainties among campaigns (Freshour et al., 2014). The uncertainty of [OOMs] was expected to be greater than that of [SA₁], because it was quantified by the calibration factor of SA. Li et al. (2023) reported that [OOMs] with a scaling factor of 1.35-4 could explain the measured new particle growth. Hence, the uncertainty of OOMs was estimated to be +200 % / -66 %. In terms of the volatility estimation of OOMs, the logarithm of saturation mass concentration (logC^∗) had an uncertainty of ±1 (Stolzenburg et al., 2018). The uncertainties of CS and measured particle formation rate were ±10 % and +100 % / -50 %, respectively (Cai et al., 2021). All uncertainties of these parameters are listed in Table S1.

The uncertainties of simulated values, like the SA dimer concentration ([SA₂]) and the particle formation rate, were obtained by inputting the uncertainty ranges of measured data into the model. For example, the measured value of [SA₁], [DMA] and CS were scaled by factors of 2, 2.5, and 1.1 (according to their uncertainty) were input to calculate the upper boundary of the uncertainty range of simulated [SA₂] ([SA₂]_sim) and simulated J1.4 (J1.4,sim) and the lower boundary of simulated value was calculated in a similar way to the upper boundary, except that scale factors of 2, 2.5 and 1.1 were replaced by 0.5, 0.4 and 0.9, respectively.

To quantitatively characterize the effects of [SA₁] and temperature on [SA₂] and particle formation rate, we normalized the effects of CS and [DMA] by scaling the measured values to consistent conditions based on simulation. Here, the scaling of measured [SA₂] ([SA₂]_meas) is defined as follows: 3SA2scaled=SA2meas⋅CCSmedian,[DMA]median where [SA₂]_scaled refers to the scaled [SA₂]_meas; C(CS_median, [DMA]_median) is the scaling coefficient for [SA₂]_meas and was calculated by: 4CCSmedian,[DMA]median=SA2sim,medianSA2sim where [SA₂]_sim denotes the simulated SA₂ concentration calculated by inputting measured [SA₁], [DMA], CS and temperature into the cluster dynamics-multicomponent sectional model; [SA₂]_sim,median was calculated using measured [SA₁] and temperature, combined with the median [DMA] (2.3 pptv) and the median CS (0.017 s⁻¹) in all NPF events. [SA₂]_sim,median is regarded as the theoretical [SA₂]_meas when measured [DMA] and CS attain their event medians. [DMA] was unavailable at SH. Considering high [DMA] (0.7–54.3 pptv) in other campaigns in urban Shanghai (Yao et al., 2016; Chang et al., 2021), a fixed [DMA] (5 pptv) was set for scaling, almost reaching the nucleation limit under the atmospheric [SA₁] (Almeida et al., 2013). The analogous scaling methodology for particle formation rates is detailed in the Supplement.

SA and DMA can explain the atmospheric nucleation observed at all sites. This finding is supported by the correlation between [SA₁] and particle formation rates, the composition of detected clusters, the alignment of simulated and measured nucleation intensity ([SA₂] and particle formation rates), and the dependences of NPF on temperature and [DMA]. The first two points are addressed in this section, while the remaining evidence will be discussed in Sect. 3.2 and 3.3.

Figure 1 shows the measured particle formation rates at 1.7 nm diameter (J1.7,meas) as a function of [SA₁] and compares them with those in other studies. All measured particle formation rates are much higher than SA-NH₃ at corresponding temperatures of Cosmics Leaving Outdoor Droplets (CLOUD) experiments, which suggests the existence of precursors with higher basicity, like amines (Kirkby et al., 2011; Almeida et al., 2013). Our data (except TL) are in accordance with SA-DMA-NH₃(-OOMs) nucleation at 293 K of CLOUD, even though the median temperature in our campaigns was 287 K. Data from TL follow the simulated line for SA-DMA nucleation at 303 K. Furthermore, our observed results align closely with those at SH and BJ, where SA and DMA have been suggested to be key nucleating precursors (Yao et al., 2018; Cai et al., 2021), indicating a potentially consistent nucleation mechanism across these locations. Compared with CLOUD experimental conditions (Table 2), our campaigns exhibited higher CS and lower [DMA], both of which were unfavorable for NPF. This explains the generally lower particle formation rates observed in our measurements relative to those from CLOUD under varying temperature conditions. Therefore, the observed nucleation is likely driven by SA and enhanced by strong stabilizing precursors such as DMA. Other nucleation mechanisms are unlikely to dominate under these conditions.

The composition of the measured cluster provides further evidence for the involvement of DMA in the formation of SA clusters (Fig. 2). A number of neutral clusters, including SA and SA-DMA clusters, were observed at WD, DL and TL. These clusters are described as SA monomer (SA₁), dimer (SA₂), trimers (SA₃DMA₀₋₂) and tetramers (SA₄DMA₁₋₂), contributing to NPF. The absence of DMA in pure SA clusters can be attributed to in-situ fragmentation within the mass spectrometer (Alfaouri et al., 2022), suggesting more DMA molecules were expected to be existed in clusters. Similar patterns of SA-DMA clusters were also measured by CI-TOF-MS in other urban sites (Yao et al., 2018; Yin et al., 2021). Besides, the normalized signal of SA trimer and tetramer show good correlations (r2=0.44–0.76) with the number concentration of particles below 3 nm (Fig. S3). Such correlations between clusters and newly formed particles were reported in other atmospheric observations (Bianchi et al., 2016; Yan et al., 2021), indicating that these clusters typically signified the molecular clustering processes in NPF events. Other molecules that may participate in nucleation, such as OOMs and NH₃, were not detected in clusters, as they are generally in the form of ion clusters rather than neutral clusters (Bianchi et al., 2016; Yin et al., 2021; Cai et al., 2024).

We analyzed the factors determining the occurrence of NPF events in different campaigns by contrasting NPF and non-NPF events (Fig. 3). [SA₁] during NPF periods was 0.5–2 times higher than that during non-NPF periods at DL and TL, suggesting [SA₁] was key to determining the occurrence of NPF at these sites (Fig. 3a). This pattern resembles that observed in Barcelona (Brean et al., 2020) but differs from that observed in Beijing (Deng et al., 2020; Yan et al., 2021), where low CS was related to the occurrence of NPF without evident variations in [SA₁]. CS during NPF periods was generally lower than that during non-NPF periods in all campaigns, except DLS, further confirming that high preexisting aerosols suppressed the occurrence of NPF (Fig. 3b). However, NPF events were not significantly dependent on the CS in Po Valley, indicating other influencing factors govern the occurrence of NPF in less polluted atmospheres (Cai et al., 2024). Therefore, both the strength of precursor sources and pre-existing sink were important to the occurrence of NPF at our sites.

Besides SA, other potential precursors related to NPF in polluted regions including DMA, NH₃ and OOMs (Fig. S4). These species are known to enhance SA-driven nucleation (Kirkby et al., 2011; Almeida et al., 2013; Riccobono et al., 2014) and promote particle growth (Tröstl et al., 2016). Increasing [DMA] considerably enhances SA₂ formation under fixed temperature ranges (Fig. S5), and this effect diminishes as [DMA] approaches nucleation saturation (Almeida et al., 2013). This phenomenon supports the contribution of DMA to atmospheric nucleation and is consistent with the results from a flow reactor (Jen et al., 2014). Moreover, it is likely that OOMs and NH₃ played a synergistic role in nucleation under our campaign conditions. Multiple studies have detected clusters containing these precursors, such as SA-DMA-NH₃, SA-NH₃-OOMs, SA-NH₃ and SA-OOMs, in the presence of DMA in polluted atmospheres, and some of these clusters showed positive correlations with particles below 3 nm (Yan et al., 2021; Yin et al., 2021; Cai et al., 2024). In CLOUD studies, the contributions of OOMs and NH₃ to cluster formation were not as considerable as that of DMA (Kürten et al., 2018; Xiao et al., 2021). Given that our field measurements exhibited similar [NH₃] and relatively low [OOMs] compared to those in CLOUD experiments (Table 2), it follows that their effects were unlikely to be greater than DMA in our campaigns. Despite the potential participation of other precursors, the observation-simulation agreement suggests DMA is a major base that stabilizes SA clusters (Fig. S5). However, [DMA] and [NH₃] were not markedly elevated during NPF periods (Fig. S4). The likely reason is that the suppression of NPF by high CS masked the enhancing effect of DMA and NH₃, as they were positively correlated with CS (r2=0.31 and 0.39, respectively, Fig. S6).

Although the occurrence of NPF is not strongly dependent on ambient temperature in individual campaigns (Fig. 3c), the intercomparison across campaigns indicates a general negative correlation between NPF frequency and temperature, reflecting seasonal characteristics (Fig. 3d). This trend is consistent with long-term measurements in Chacaltaya (Rose et al., 2015), Beijing (Deng et al., 2020) and Gwangju (Lee et al., 2024), where NPF was most frequent in winter and least frequent in summer. The intercomparison of campaigns further shows that temperature played a key role in determining the intensity of NPF indicated by [SA₂] and J1.7,meas (Fig. 3e–f). Temperature even exerted more dominant influence than [SA₁] and CS. For example, despite the highest [SA₁] at TL, its elevated temperatures (298–306 K) resulted in lower median values of [SA₂] and J1.7,meas than those in all campaigns. Conversely, WD had the lowest temperature (281–268 K) and relatively high [SA₁] (7×106–1.8×107 cm⁻³), the intensity of NPF at WD was the highest, even under strong coagulation scavenging (median CS = ∼ 0.05 s⁻¹). A more detailed discussion regarding the influence of temperature on NPF is provided in Sect. 3.3.

Figure 4 shows that [SA₂]_meas is in accordance with [SA₂]_sim when considering the uncertainties. It means DMA, as a major stabilizer, can sufficiently explain the formation of SA₂. In addition to DMA, other gases could have participated in stabilizing SA₂. Kirby et al. (2011) reported the detection of SA₂ in the SA-NH₃ system of CLOUD experiments. Jen et al. (2014) found that methylamine (MA) and trimethylamine (TMA) contributed to the formation of neutral SA₂. Riccobono et al. (2014) observed that OOMs were able to be bounded to ion SA₂. Furthermore, [SA₂]_meas is slightly lower than [SA₂]_sim overall. Similar discrepancies between measured and simulated cluster concentrations have also been reported in CLOUD experiments (Kürten et al., 2014). This systematic underestimation is likely attributable to measurement errors, because not all SA₂ is fully detected, as some may dissociate within the mass spectrometer (Alfaouri et al., 2022). The observation-simulation comparison of J1.4 is shown in Fig. S7, where simulation results fall within acceptable ranges upon uncertainty analysis. The consistency between measured and simulated parameters ([SA₂] and J1.4) supports the significance of SA-DMA collision in NPF.

The consistency between measured and simulated parameters also validates the applicability of the model for data scaling. After accounting for the influences of CS and [DMA], [SA₂]_scaled exhibits a significant decreasing trend with rising temperature, showing agreement with simulated results (Fig. 5). This trend underscores the effect of temperature in governing the stability and abundance of clusters in nucleation pathways. At the molecular level, it is proposed that SA and DMA form SA₁DMA₁ clusters, which subsequently contributes to SA₂ formation, during nucleation (Olenius et al., 2017; Myllys et al., 2019). Compared with SA₂(DMA)1-2, SA₁DMA₁ is more sensitive to temperature (Cai et al., 2022b). Thus, in addition to the evaporation of SA dimer, SA₁DMA₁ formation also acts as a rate-limiting step in clustering. Kürten et al. (2016) and Brean et al. (2020) observed relatively low ratios of [SA₂] to [SA₁] (∼0.01) at an urban site and a rural site, respectively, and speculated that they were related to higher temperatures (298–308 K).

An intercomparison of the panels in Fig. 2 shows that the abundance and variety of larger SA-DMA clusters (SA trimers and tetramers) decline with increasing temperature, despite variations in precursor concentrations and CS across sites. For instance, although TL exhibited higher [SA₁] (∼2.6×107 cm⁻³) during high-temperature (∼303 K) NPF periods, the abundance and diversity of measured clusters were lower than those at low-temperature sites (WD and DLW). The observed reduction in the abundance of larger clusters at elevated temperatures is constrained by smaller ones (SA monomers and dimers), since the evaporation rates of SA trimers and tetramers show relatively low sensitivity to temperature (Olenius et al., 2017). The proportion of base molecules in clusters also decreased with increasing temperature in the four selected NPF events, which was also reported in CLOUD experiments (Schobesberger et al., 2015). Furthermore, with the increase of cluster size, NH₃ tends to gradually replace DMA in ion clusters (Schobesberger et al., 2015; Yin et al., 2021), enhancing the stability of SA-base clusters (Bzdek et al., 2017), which helps them resist evaporation.

As shown in Fig. 6, the particle formation rate exhibits a negative correlation with temperature. Notably, for a fixed [SA₁], the formation rate varies by approximately 3 orders of magnitude over a 30 K temperature range, and this extent of variation is comparable to that reported in chamber experiments simulating the conditions of polluted environments (Xiao et al., 2021) and atmospheric observations in urban area (Yu et al., 2016). This highlights the critical role of temperature in modulating nucleation, suggesting that temperature fluctuations alone can induce major variability in NPF without the change in the species and concentrations of nucleation precursors. In other words, SA and DMA can still explain the wide range of J1.4,scaled at these sites.

In the analyses presented above, temperature is regarded as a dominant factor determining the intensity of NPF over large regional scales. The direct effect of temperature on NPF is negative, through altering the evaporation rates of clusters (Olenius et al., 2017; Myllys et al., 2019). This has been consistently demonstrated in well-controlled chamber experiments with different nucleation mechanisms (Kirkby et al., 2011; Simon et al., 2020; Xiao et al., 2021; He et al., 2023). When temperature differences are substantial, its inhibitory effect on NPF becomes evident in complex ambient environments. For example, Baalbaki et al. (2021) reported the particle formation rate in warmer months was actually lower than that in cooler months with comparable [SA₁] levels in the Eastern Mediterranean. Inter-site comparisons in India showed a negative correlation between particle formation rate and temperature, although precursor concentrations were not measured (Kanawade et al., 2022). However, under conditions of limited temperature variability, the effect of temperature is less directly observable, and higher temperatures may even appear to favor NPF (Größ et al., 2018; Brean et al., 2020; Yan et al., 2021; Victor et al., 2024). This may stem from other temperature-related factors. For example, in atmospheric observations, temperature is often correlated positively with solar radiation, which directly promotes the formation of nucleation precursors (Kürten et al., 2016; Brean et al., 2020). Additionally, temperature is typically negatively correlated with relative humidity, and high humidity suppresses NPF via hygroscopic growth of pre-existing particles (Määttänen et al., 2018).

The analyze above has shown that SA and DMA can explain atmospheric nucleation. Here, the initial growth of nucleated particles is investigated. Figure 7a compares the simulated growth rate of 1.4–1.7 nm particles (GR_1.4−1.7) with two sets of condensable vapors at BJ and DLS. When only SA and its clusters are included, the simulated GR_1.4−1.7 ranges approximately from 0.3 to 3.4 nm h⁻¹. The simulated GR_1.4−1.7 is enhanced when OOMs are also considered as condensable vapors on the basis of the contribution of SA and its clusters, ranging approximately from 1.2 to 22.6 nm h⁻¹. Assuming GR_1.4−1.7 is roughly approximated to the growth rate of particles below 3 nm, these simulated values are generally in accordance with the measured range (0.5–20.4 nm h⁻¹) in previous reports from the eastern region of China (Xiao et al., 2015; Dai et al., 2017; Yao et al., 2018; Hong et al., 2023). The corresponding simulation results from the other four campaigns are generally consistent with those at BJ and DLS, differing mainly in the extent of growth rate enhancement (Fig. S8a).

The comparison between J1.7,meas and simulated J1.7 (J1.7,sim) provides support for the contribution of OOMs to the growth of nucleated particles (Fig. 7b). When only SA and its clusters are considered, a substantial deviation, sometimes more than 3 orders of magnitude, is observed between J1.7,meas and J1.7,sim. Compared to the simulation of J1.4 (Fig. S7), J1.7,sim shows a noticeable decline at DLS and BJ. The inclusion of OOM-induced growth markedly increases J1.7,sim, leading to better agreements with measurements, which can also be supported by observations in CLOUD experiments (Tröstl et al., 2016). The corresponding improvement are limited at WD, DLW, TL and SH, where the contribution of SA and its clusters seems sufficient to explain GR_1.4−1.7 (Fig. S8b). In fact, some ultralow volatile organic compounds within OOMs may be involved in nucleating (Simon et al., 2020). Nevertheless, even without considering their contribution in this stage, the condensation of OOMs exerts a considerable influence on initial growth, as reflected in J1.7. Moreover, J1.7 exhibits strong temperature dependence, similar to J1.4 (Fig. S9).