The observation period for this study was from 30 May to 15 June 2018. Hourly surface air quality data (PM_2.5, PM₁₀, SO2, NO2, CO, and O3) and meteorological elements (wind speed, wind direction, temperature (T), and relative humidity (RH)) were obtained from the Ministry of Ecology and Environment of China (MEE) (https://www.mee.gov.cn/, last access: 3 June 2026) and the Nanjing University of Information Science and Technology (NUIST) meteorological station, respectively. In addition, vertical observation data (O3, PM_2.5, and black carbon (BC)) and ground-based aerosol particle size distribution (5 min resolution, 0.01–10 µm) were respectively collected by an unmanned aerial vehicle (UAV) observation platform and a WPS-1000 instrument at the Intelligent Manufacturing Industrial Park in the northern suburbs of Nanjing (Zhongshan Park; 32.35° N, 118.72° E). Detailed descriptions of the site environment and instrumental configurations can be found in Shi et al. (2022).

To ensure the reliability of the analysis, all observational data were first subjected to quality control. Subsequently, the ground-level meteorological elements and pollutant concentrations used for SHAP analysis were averaged hourly, while the time resolution of the vertical observation data was set to 3 h to accurately reflect the atmospheric vertical structure during the study period.

Based on previous studies (Dal Maso et al., 2005; Herrmann et al., 2014; Kerminen et al., 2018; Kulmala et al., 2004; Yue et al., 2011), NPF events in this study were identified according to the following three criteria: (1) A clear new particle mode appears in the particle number concentration size distribution, with an initial particle size within the nucleation (Nuc) mode range (10–20 nm); (2) This mode persists for at least 1 h during the observation period; (3) The particle size of this mode continuously evolves towards larger sizes over time, accompanied by a continuous increase in the particle number concentration within the mode. Only when all the above conditions are met is it considered an NPF event, and that day is defined as an NPF day, whereas the remaining days were classified as non-NPF days.

Meanwhile, according to the Ambient Air Quality Standards (GB 3095–2012; MEE, 2012a) and the Technical Regulation on Ambient Air Quality Index (AQI) (HJ 633–2012; MEE, 2012b), the ozone pollution level during the observation period was classified using the maximum daily 8 h average ozone concentration (MDA8-O3). Specifically, days were defined as Non-O3 (MDA8-O3<160 µgm-3), Low-O3 (160<MDA8-O3<215 µgm-3), and High-O3 (MDA8-O3>215 µgm-3).

Finally, by combining the NPF event identification with the ozone pollution classification, the observation period was divided into four scenarios: 1.

NPF (Low-O3): 30 May, 3 June, and 11–13 June (hereafter NPF);

The growth rate (GR, nmh-1) is used to characterize the temporal evolution of the particle diameter of newly formed mode (Dal Maso et al., 2005; Kulmala et al., 2012): GR=dDpdt=ΔDpΔt where Dp is the geometric mean diameter of the aerosol particles.

The formation rate (FR, cm-3s-1) represents the rate of change of the number concentration of Nuc mode particles, calculated following the method proposed by Kulmala et al. (2004), while neglecting the flux of particles growing beyond the 20 nm upper limit (Wang et al., 2013b): FR=dNnucdt+CoagsNuc⋅NNuc where Nnuc is the total number concentration within the Nuc mode, and CoagsNuc denotes the coagulation sink within the Nuc mode. And the coagulation sink (Coags, s-1) describes the loss rate of target particles due to coagulation with background particles and is defined as (Kulmala et al., 2001a): Coags(Dp)=∫K(Dp,Dp′)n(Dp′)dDp′ where K(Dp,Dp′) is the coagulation coefficient proposed by Fuchs et al. (1965), n(Dp′) is the number concentration distribution of background particles.

The condensation sink (CS, s-1) is used to characterize the ability of background aerosols to absorb vapor molecules, and was calculated as (Dal Maso et al., 2005; Kulmala et al., 2001b): CS=2πD∑iβidp,iNi where D is the diffusion coefficient of the vapor molecules, βi is the transition regime correction factor, and dp,i and Ni are the diameter and number concentration of each size bin, respectively.

In addition, based on the empirical linear relationship between GR and sulfuric acid vapor concentration (Kulmala et al., 2001b; Nieminen et al., 2010), the condensable vapor concentration (C, cm-3) was estimated using the following parameterization: C=GR⋅1.37×107

Under the steady-state assumption, the condensable vapor production rate (Q, cm-3s-1) can be further expressed as: Q=CS⋅C.

The SHAP (Shapley Additive exPlanations) method is a game-theory-based method for machine learning model interpretability, used to quantitatively assess the marginal contribution of each input feature to the model prediction (Lundberg and Lee, 2017; Shapley, 2020). Under the SHAP framework, the prediction for an individual sample can be expressed as the sum of a baseline value and the contributions of all features: f(x)=∅0+∑i=1M∅i where f(x) denotes the model prediction for sample x, ∅0 is the model baseline value, M is the total number of features, and ∅i represents the SHAP value of the ith feature. The sign of ∅i indicates whether the feature promotes or suppresses the prediction, while its absolute magnitude reflects the strength of its contribution.

Considering the complex nonlinear characteristics among multiple variables in the atmospheric system, this study utilizes generalized additive models (GAM) and the KernelSHAP algorithm (Aas et al., 2019; Bordt and Luxburg, 2022; Lundberg and Lee, 2017; Murase et al., 2009) to quantitatively assess the relative contributions of meteorological elements, pollutant concentrations, and background particle parameters to the changes in particle number concentrations of Nuc mode. Feature importance plots and SHAP summary plots are used to quantify the relative importance of each factor (Lundberg et al., 2020; Zhao et al., 2025), thereby intuitively identifying the dominant factors under different pollution scenarios. Furthermore, SHAP dependence plots are used to describe the average marginal impact of a single variable on model predictions (Lundberg and Lee, 2017; Wei et al., 2025; Yuan et al., 2025), and nonlinear fitting of the scatter distributions was further performed to elucidate the specific response relationships between the variable and the number concentrations of mode.

As shown in Fig. S1 in the Supplement, the aerosol number concentration and its size distribution exhibited significant phased evolution characteristics during the observation period. For example, from 6 to 8 June, overall pollution levels were relatively high, with the 20–70 nm size range dominating the particle size distribution and persisting for an extended duration. The total particle number concentration in the 10–100 nm range (N10-100) consistently remained at a high level and displayed a clear increasing trend, with peak values exceeding 105 cm-3. Figure 1c–f show that the number concentrations of the four modes of particles also remained high, but there was no obvious enhancement. During this period, the CS level remained persistently high, with an average value of approximately 0.089 s-1 (Fig. 1g), and the concentrations of the six environmental factors were generally high but showed no pronounced fluctuations (Fig. S2). These features collectively indicate that aerosol evolution during this stage was predominantly controlled by background particles.

In contrast, during certain periods, the particle size distribution revealed clear growth processes from smaller to larger particle diameters (Fig. S1), lasting approximately 1–2 h. During these episodes, particle number concentrations in the nucleation (Nuc) and Aitken (Ait) modes decreased sharply (Fig. 1c and d), whereas those in the accumulation (Acc) and coarse (Coa) modes exhibited a decrease followed by a subsequent increase (Fig. 1e and f), reflecting the rapid growth of newly formed particles into larger size modes. Simultaneously, lower CS level (Fig. 1g) and weak wind speeds (Fig. 1a) also provided favorable conditions for the survival and growth of newly formed particles.

Based on the classification criteria in Sect. 2.2, a total of five NPF days were identified. Following the method of Birmili et al. (2003), this study determined the time range of each NPF process by using the moments when the particle number concentration in the Nuc mode (10–20 nm) rose and fell to 1/e of the daily peak value as the onset and termination of the event. Relevant parameters were then calculated based on the formulations described in Sect. 2.3 (Table 1). As shown in Table 1, the intensity and duration of the NPF process are not controlled by a single factor, instead, they are governed by the dynamic balance between precursor strength (source) and background particle removal capacity (sink).

Taking 13 June as an example, although both CS (6.20×10-2 s-1) and Coags (18.74×10-5 s-1) reached the highest levels among the five events, meaning that newly formed particles and precursors would be strongly removed, which is theoretically unfavorable for nucleation. However, C and Q reached high levels of 7.95×107 cm-3 and 3.81×106 cm-3s-1, respectively, favoring precursor formation. As a result, the FR reached its maximum value of 0.71 cm-3s-1, indicating that an extremely strong source can effectively offset the removal effect of a high sink. In contrast, on 3 June, the FR was only 0.03 cm-3s-1, suggesting slower nucleation initiation. However, both CS (3.30×10-2 s-1) and CoagS (6.56×10-5 s-1) were the lowest among the five events, the background removal effect was weak, and the final particle growth rate far exceeded that of other events (GR=5.99 nmh-1). This comparison clearly demonstrates that the sources and sinks are closely related in the NPF process: a strong source can compensate for the removal effect of a high sink, while a weak sink facilitates sustained particle growth even under conditions of limited precursor supply.

However, the analysis above only reveals some of the parametric characteristics of NPF, and the key mechanisms determining whether NPF occurs under different O3 pollution backgrounds still need to be explored. To further elucidate these differences, we compared the evolution of particle size distributions across different scenarios. And we found that the NPF scenario exhibited a typical new particle formation signal, with Nuc mode particles significantly increasing around 10:00 (all clock times reported in this paper are given in local Beijing Time (UTC+8)) and continuously growing to larger sizes (Fig. S3a). In contrast, neither the Non-O3 nor the High-O3 scenarios showed clear nucleation characteristics (Fig. S3b and c), but the reasons differed substantially between the two cases.

Under the Non-O3 scenario, the particle size distribution was relatively disordered, and there was no significant growth process of Nuc mode particles (Fig. S3b). Although the relatively low background particle concentrations (Fig. 2) and CS levels (Fig. S5c) would, in principle, favor new particle formation, the high humidity environment created by the daily average RH of 80.1 % (Fig. S4b) may also trigger hygroscopic growth effects, thereby exacerbating the scavenging of newly formed clusters by background particles (Molnár et al., 2020; Zang et al., 2019). However, this is unlikely to be the dominant factor for the absence of NPF in this scenario. Instead, the consistently low O3 concentration (Fig. S4d) and T (Fig. S4a) throughout the day lead to weak photochemical reaction activity. Meanwhile, SO2 supply was extremely limited: both its mean concentration and temporal increase were the lowest among the four scenarios (Fig. S4h). Under the combined constraints of weak atmospheric oxidation capacity and insufficient precursor accumulation, the source strength was severely limited, as reflected by persistently low values of C (Fig. S5a) and Q (Fig. S5b). Therefore, we infer that the weak source is the fundamental reason for the absence of NPF under the Non-O3 scenario.

Unlike the Non-O3 scenario, the High-O3 scenario exhibited extremely high background particle concentrations, especially from 00:00 to 09:00. However, during the afternoon period with elevated O3 levels, NPF still did not occur; instead, background particle concentrations even showed a slight decline (Fig. S3d). During the critical nucleation period (08:00–12:00), NAcc remained persistently high (Fig. 2c), resulting in drastic fluctuations in CS with an average value as high as 9.27×10-2 s-1, approximately twice that of the NPF scenario (4.69×10-2 s-1) (Fig. S5c). Although elevated O3 levels in the afternoon could enhance precursor formation (Fig. S4d), as evidenced by strong fluctuations in Q (Fig. S5b), the extremely strong background CS led to rapid uptake of newly generated precursor by pre-existing coarse particles. As a result, C also exhibits unstable fluctuations (Fig. S5a) because it failed to accumulate. Thus, under the High-O3 scenario, a strong sink can suppress NPF by efficiently removing precursors, despite favorable photochemical conditions.

According to the classification criteria in Sect. 2.2, both the NPF and Low-O3 scenarios had similarly low O3 pollution levels (160–215 µgm-3). However, NPF occurred only in the former, whereas the latter exhibited a slight increasing trend in Ait mode particle concentrations (Fig. S3c). To further explain the reasons for this contrast, we compared the spatiotemporal evolution of boundary layer structure under the two scenarios.

Under the NPF scenario, the near-surface air temperature decreased with height at 05:00, while an inversion layer existed at approximately 900 m (Fig. S6), implying that convective processes could respond rapidly and be initiated after sunrise (Lapworth, 2006). With increasing solar radiation, rapid surface warming (Fig. S4b) promoted the development of turbulence (Kaimal et al., 1976; Li et al., 2026), especially beginning around 08:00, the rapid lifting of the planetary boundary layer established efficient pathways for vertical exchange (Neu et al., 1994; Stull, 1988). On the one hand, cleaner air aloft was entrained into the mixed layer, rapidly diluting aerosols in the lower layers (Nilsson et al., 2001). This was particularly evident below 300 m, where both PM_2.5 (Fig. 3) and BC (Fig. 4) concentrations decreased sharply with height. Near the surface, this process manifested as a pronounced decline in NAcc starting around 07:00 (Fig. 2c), leading to a simultaneous decrease in CS (Fig. S5c) (Korhonen et al., 2004; Lehtinen et al., 2003). In addition, the low RH conditions (Fig. S4b) likely suppressed particle hygroscopic growth, further weakening the CS level (Birmili and Wiedensohler, 2000; Hamed et al., 2007). On the other hand, the inversion layer near 900 m was broken (Fig. S6), accompanied by a weakening of the vertical gradient in the O3 profile within the lower layers (Fig. S9), indicating downward transport of O3 aloft (Song et al., 2024), which led to increased near-surface O3 concentrations (Fig. S4d) and more favorable conditions for nucleation (Jonsson et al., 2007). Crucially, the process of weakened sinks and enhanced atmospheric oxidation capacity driven by the boundary layer coincided temporally with the increase in SO2 concentrations between 07:00 and 09:00 (Fig. S4h). Therefore, the precursors were able to survive and accumulate, ultimately triggering nucleation and sustaining growth.

In contrast, the Low-O3 scenario was controlled by a stable boundary layer before sunrise. At 05:00, a pronounced inversion layer was present within the 100–150 m layer (Fig. S6), accompanied by high relative humidity (Fig. S7) and weak wind conditions (Fig. S8), collectively establishing a highly stable boundary layer structure. This strongly suppressed the development of turbulent mixing after sunrise, and vertical exchange between the lower and upper layers was persistently limited. As a result, near-surface pollutants were not effectively diluted by cleaner air aloft, and PM_2.5 and BC concentrations remained elevated near the surface (Figs. 3 and 4), while NAcc showed no significant change (Fig. 2c). Correspondingly, the CS level did not weaken; instead, it increased rapidly around 10:00 (Fig. S5c), further intensifying the sink strength. This enhancement was likely associated with persistently high near-surface RH (Fig. S4b), which promoted hygroscopic growth of background particles and thereby increased CS (Ali et al., 2025). Meanwhile, although SO2 concentrations showed an increasing trend under this scenario (Fig. S4h), both the magnitude of the increase and the peak values were substantially lower than those observed under the NPF scenario, indicating limited precursor accumulation. More importantly, when SO2 increased, CS did not show a corresponding decrease but instead remained at a high level throughout the critical period. Therefore, we conclude that the asynchrony between source enhancement and sink weakening effectively suppressed the occurrence of NPF under the Low-O3 scenario.

As shown in Fig. 5, the NPF scenario exhibits the most complex and densely connected correlation network (Fig. 5a). Notably, a significant and strong correlation between the Nuc mode particle concentration and SO2 is observed, which is the only case among the four scenarios where the Nuc mode is directly coupled with a precursor source, indicating that sufficient precursors are required for new particle formation. Meanwhile, both the Acc and Coa modes show significant correlations with multiple atmospheric pollutants, indicating that particle evolution is jointly influenced by background particles. For the Non-O3 scenario (Fig. 5b), the correlations are mainly concentrated in the Acc mode, which shows a significant strong correlation with primary pollutants; while under the Low-O3 scenario (Fig. 5c), the Coa mode is correlated not only with pollutants but also with meteorological elements. However, unlike the NPF scenario, in these two non-NPF scenarios, the Nuc mode is mainly significantly constrained by CS, and its correlations with source-related factors are markedly weakened. Under the High-O3 scenario (Fig. 5d), the overall correlation network is further simplified. Only a strong significant correlation between the Acc mode and CS remains evident, whereas correlations among other particle modes and atmospheric elements are generally weaker.

As the initial stage of the NPF process (Kulmala et al., 2004), the Nuc mode is crucial for understanding the underlying mechanisms governing NPF occurrence. However, due to the complex nonlinear interactions among multiple atmospheric variables, conventional correlation analysis alone is insufficient to disentangle these mechanisms. Therefore, this study introduces the generalized additive model (GAM) in combination with the SHAP method (described in Sect. 2.4) to identify the dominant drivers under different scenarios through feature importance and SHAP summary plots (Fig. 6), and to further reveal the nonlinear response characteristics of these factors to Nuc mode number concentration through SHAP dependence.

Under the NPF scenario, the mean SHAP values of T and SO2 are 42.9 and 25.2, respectively (Fig. 6a), indicating that both variables generally have a positive impact on the predicted Nuc values. Their importance ranks among the highest across all variables, accounting for 5.5 % and 7.3 %, respectively (Fig. 6b). Scatter points corresponding to high values (red) are predominantly distributed on the positive SHAP side, whereas low-value samples (blue) mainly correspond to negative SHAP values (Fig. 6b), suggesting a positive association between these two variables and predicted Nuc values. This relationship is further confirmed by the dependence plots, which show a pronounced increase in SHAP values when T>28 °C (Fig. 7a) and SO2>10 µgm-3 (Fig. 7f), with the largest amplitudes among all four scenarios. These results indicate that high predicted Nuc values under the NPF scenario are always associated with high temperature and sufficient precursor conditions. In contrast, the CS exerts a clear negative effect on predicted Nuc values, especially when CS is high. Its dependence plot shows that the fitted curve initially increases and then decreases with increasing CS values, turning negative beyond approximately 0.085 s-1 (Fig. 7m), consistent with a mean SHAP value of -0.9 (Fig. 6a). Under the Low-O3 scenario, the dominant contributors to predicted Nuc values differ significantly, with the top five variables in terms of importance being NO2 (15.2 %), Coa (13.3 %), Ait (10.8 %), Acc (7.7 %), and CS (7.5 %) (Fig. 6d), all closely related to background particles. This indicates that, under Low-O3 conditions, background particles tend to increase the predicted values.

Under the Non-O3 scenario, the mean SHAP values of T, SO2 and O3 are -94.4, -34.5, and -26.1, respectively, and high-value samples are predominantly distributed in the negative SHAP value region (Fig. 6c). This may be attributed to the fact that higher values of these photochemically related variables typically occur in the afternoon, when intensified boundary layer mixing dilutes near-surface particles. Such co-variation explains their generally negative SHAP contributions to the predicted Nuc values. Notably, RH exhibits a high mean SHAP value of 153.5 (Fig. 6a), and its dependence curve increases monotonically from 80 % and remained positive thereafter (Fig. 7b), indicating that high humidity conditions are more likely to correspond to higher predicted Nuc values. This is likely because high RH promotes hygroscopic growth of background particles and modulates the small-size end of the particle size distribution, which the model statistically associates with elevated NNuc. For the High-O3 scenario, despite elevated O3 concentrations, the importance of O3 is only 3.6 %, suggesting that O3 is not the key factor controlling Nuc predictions. Although SO2 shows a positive mean SHAP value of 81.4 (Fig. 6a), indicating a promoting effect on Nuc predictions, the high-concentration data points of PM_2.5 and Coa are almost all fell into the negative SHAP value region (Fig. 6e). Given that these two variables are the most important contributors in this scenario (Fig. 6e), the results demonstrate that background particles significantly inhibit the increase in Nuc mode. This finding is consistent with the previous inference that particles are generated but rapidly scavenged under High-O3 scenarios.