The seasonal distribution of NPF events at ATOLL is displayed in Fig. 2. SMPS missing data (in Fig. 2) reach up to about 40 % from January to April due to the yearly calibrations at the manufacturer premises and a few laboratory campaigns (October 2018–June 2019). Over the 4 years of measurements (2017–2020), 96 d (11%) were classified as NPF event days (Ev), 355 (40 %) as undefined days (Un) and 432 (49 %) as non-event days (No). One can also note that most of the NPF events identified were observed during spring (March–April–May, with 27 events corresponding to 15 % of days when observations were available during this season over the 4-year period) and summer (June–July–August, with 53 events corresponding to 19 %), with a maximum observed in June consistent with a previous study over central Europe (Dall'Osto et al., 2018). During winter, the number of events is extremely limited (only one event observed in February). In the following sections, only observations from spring and summer seasons will be discussed due to the low representativeness of NPF events in fall (n=15) and winter (n=1). Moreover, the undefined event days are seen all year round (frequency around or larger than 20 %) with a clear peak in August (frequency at 62 %) consistent with observations over the boreal forest where undefined days were also observed to be most frequent in early fall (Buenrostro Mazon et al., 2009).

Using long-term measurements from 36 sites (polar, rural, high altitude, remote, and urban), Nieminen et al. (2018) reported an annual NPF frequency below 15 % for half of the sites (18 sites from all types) and occasionally over 30 % for 10 sites. Moreover, they highlighted a seasonal variation of NPF occurrence with larger (lower) frequency, about 30 % (10 %), during spring (winter). A frequency analysis of NPF occurring only over urban or anthropogenically influenced sites show large site-to-site differences for all seasons. Indeed, Nieminen et al. (2018) reported NPF occurrence frequencies varying from 20 % (Helsinki, Finland; Sao Paulo, Brazil) to 80 % (Beijing, China; Marikana, South Africa) during spring and from 7 % (Helsinki) to 78 % (Marikana) during winter. Yearly averages of NPF occurrence frequencies are between 11 % (Helsinki) and more than 60 % (Beijing and Marikana).

The ATOLL event frequency (seasonal variation and values) is similar to observations performed in Paris while the frequency of undefined and non-event days is quite different (Dos Santos et al., 2015). Indeed, in Paris the non-event frequency is larger than 60 % except in July and August, whereas over ATOLL the non-event frequency shows a clear seasonal pattern with lower frequency (<40 %) from April to August. Moreover, undefined event frequency in Paris shows a minimum (<5 %) in May and June and remains quite steady during the rest of the year (around 20 %). One can note that the frequency of undefined events is much higher over ATOLL all year long with an average of 40 %. The frequency of undefined events observed at ATOLL is clearly larger than the frequencies observed over a more polluted site (Paris) and similar to those observed over pristine sites in Siberian and Finnish boreal forests (Uusitalo et al., 2021). This could mean that ATOLL is under the influence of air masses or particle and precursor sinks that favor the burst of UFP.

Hourly averaged median particle number size distributions (PNSDs) obtained from the SMPS are shown in Fig. 3 separately for NPF event (around 800 PNSD), undefined (around 2300 PNSD), and non-event (around 1700 PNSD) days observed during the warm period (only spring and summer). For all event days, the PNSD were first sorted for each hour of the day. Then, the median PNSD was calculated for each hour of the day. PNSD shown in Fig. 3a is then representative of a “typical” NPF event day (Kulmala et al., 2022). The same data filtering was done for PNSD observed during undefined (Fig. 3b) and non-event days (Fig. 3c). Atmospheric NPF and subsequent particle growth are seen in Fig. 3a as an appearance of new aerosol particles with small diameters followed by the growth of these particles toward larger sizes. If this phenomenon is taking place regionally (few tens of km in radius), a so called “banana plot” is observed in PNSD as a function of time at a fixed location. The time evolution of the PNSD for “typical” NPF event day (Fig. 3a) displays a similar growth pattern for newly formed particles to the one observed for individual NPF event days (see Figs. S1 and S2 in the Supplement for examples). Indeed, one can clearly see a UFP mode appearing from 10:00 to 15:00 (UTC) and growing during the rest of the day. The NPF starting time and the growth rate will be discussed in the following section. By 23:00 UTC, the newly formed particles reach an average diameter of 50 nm, similar to the median modal diameter of the pre-existing particles observed during the morning (00:00–08:00 UTC). The PNSD observed during “typical” undefined days (Fig. 3b) highlights a burst of UFP again from 10:00 to 15:00 UTC that neither grow nor persist over the whole afternoon. The behavior of the median PNSD is again similar to the individual undefined events observed during this period (not shown here). The PNSD observed during “typical” non-event days (Fig. 3c) shows no sign of particle growth, as expected.

Figure 4 shows the monthly variation of the starting time and particle GR15.7–30nm of each event observed at ATOLL. Most NPF events start between 09:00 and 14:00 UTC (74 %), with fewer events starting in the early morning (07:30–09:00 UTC, 6 %) and late afternoon (15:00 and 19:30 UTC, 20 %). NPF starting time as well as GR15.7–30nm strongly depend on the month during which the event is observed. Indeed, the NPF starting time occurs later during spring days on average (also true for fall and winter), while the earliest time was reached in May and June (around 08:20 UTC). Nocturnal events are rarely observed, with only one occurrence in August 2018. No diurnal NPF event was observed after 16:00 UTC in summer. During spring and fall, the average NPF starting time varies between 10:00 and 19:00 UTC. The start time monthly variability seems linked to sunrise and sunset times. In the following section, the relationship between the total solar irradiation and NPF occurrence will be examined.

The event ending time was determined as the time when the growth of the freshly formed particles was over, i.e., when the diameter reached the diameter of the pre-existing particles. The duration of the nucleation events at ATOLL was then estimated and varies from 1 h up to 28 h. On average, NPF duration is shorter from May to August (around 8 h) and increases up to around 13 h on average in March. This seasonal behavior could be due to the presence or availability of condensable vapors, air mass origins, and environmental conditions favorable to NPF events (see Sect. 3.2).

The GR15.7–30nm values observed at ATOLL lie within 0.8 to 15.7 nm h-1 and show a strong monthly variability with the lowest values observed in spring (and fall, not shown here). The largest median values are observed in May and August, while the 75th percentile highlights larger values of GR15.7–30nm during summer (Fig. 4b). GR15.7–30nm values were in addition plotted as a function of temperature for all years and seasons in Fig. 5, which highlights that below 20 ∘C, GR15.7–30nm values are lower than 6 nm h-1, while, under warmer conditions (T>20 ∘C), GR15.7–30nm reach values up to 16 nm h-1. These results show a temperature dependence (R≈0.4) of the particle growth consistent with previous observations over the boreal forest (Liao et al., 2014). Higher temperatures have been shown to favor the emission of biogenic precursors, including monoterpenes known to favor the occurrence of NPF events (Kulmala et al., 2004). Previous studies (Paasonen et al., 2018; Yli-Juuti et al., 2011) have shown that GRs usually exhibit larger values during warm periods especially during summer, and that there is a link between GR seasonal patterns and the high abundance of biogenic volatile organic compounds (VOCs) during warmer periods (spring and summer) over the boreal forest. Therefore, the observed seasonal variation of GR15.7–30nm may be related to temperature-dependent emissions of organic compounds in the vicinity of ATOLL (Fig. 5). This hypothesis is supported by the larger contribution of organics during NPF event days observed in Fig. 9. However, over urban areas such as Beijing or Shanghai, GR15-25nm showed no clear seasonal variation (Yao et al., 2018). As previously observed in Fig. 3a, the median diameter reached at the end of all NPF events is around 50 nm. Moreover, the seasonal variation of the NPF event durations could be related to the GR15.7–30nm seasonal variation. The lower GR15.7–30nm values are associated with the longer NPF duration. The seasonal variation of NPF duration highlighted earlier could then only be a consequence of the GR15.7–30nm seasonal variation.

The cloud fraction was calculated from the sky imager dataset following the method by Shukla et al. (2016) and sorted as a function of event, undefined, and non-event days. The effect of cloudiness on NPF event occurrence is shown in Fig. 6a, with a specific focus on measurements collected between 09:00 and 14:00 UTC, i.e., the period of time where most NPF events tended to start. There is a clear inverse correlation between cloud fraction and NPF occurrences. The average cloud fraction is around 0.47 during event days, 0.68 during undefined days, and 0.74 during non-event days. Moreover, the 25th percentiles of the cloud fractions for NPF event (0.06), undefined (0.47), and non-event days (0.63) clearly show that the absence of clouds (lower cloud fraction) is mostly associated with NPF event days. This result is consistent with previous studies performed over the boreal forest (Dada et al., 2017) and is linked to the fact that radiation seems essential for NPF during the warmer period (spring and summer), as the events occur almost solely during daylight hours (Kulmala et al., 2004). Figure 6b shows the average diel total solar radiation observed during NPF event, non-event, and undefined days for spring and summer. As expected, the total solar radiation is on average always larger during event days in comparison to non-event days, with a more pronounced difference observed during spring.

Other environmental parameters known to influence the occurrence of NPF events, such as temperature and RH, were also investigated to highlight diel and seasonal variations (Fig. 7). Our results confirm that NPF is favored by low values of ambient RH (Fig. 7a), especially during spring, consistent with previous studies (Duplissy et al., 2016; Hamed et al., 2011; Merikanto et al., 2016). A few reasons can explain this tendency: (1) high RH values (RH >90 %) observed at the surface are usually associated with the presence of low-altitude clouds reducing the incoming total radiation and then preventing NPF occurrence; (2) at moderately high RH (RH >40 %), hydrophilic aerosols could grow through condensation which will enlarge the sink for possible precursors; and (3) high RH values may limit the formation of some semi-volatile VOCs through ozonolysis reactions, inhibiting the formation of condensable vapors necessary for nucleation (Fick et al., 2003; Tillmann et al., 2010).

Figure 7b shows the diel median temperature conditions (T) during NPF event, non-event, and undefined days. NPF events occurred for temperatures ranging between 3 and 33.5 ∘C. In both seasons, averaged temperatures during event days are always larger than during non-event days, again with larger differences during spring. One should note that days with high temperatures in spring and summer are usually also days with high solar radiation, consistent with conclusions from Fig. 6. The temperature difference between undefined days and event days is clearly marked during spring and fades away during summer. As previously discussed, higher temperatures favor the emission of biogenic precursors, including monoterpenes, known to favor the occurrence of NPF events (Kulmala et al., 2004). Isoprene emission is also larger at higher temperatures, but according to Heinritzi et al. (2020) it is one example where a biogenic compound inhibits NPF events. Moreover, a high temperature can also lead to the evaporation of molecular clusters which may inhibit NPF events (Dada et al., 2017; Deng et al., 2020).

The CS characterizes the loss rate of atmospheric vapors to aerosol particles. The diel variations of CS calculated for spring and summer for NPF event, undefined, and non-event days are shown in Fig. 8a. Hourly averaged CS values are high (larger than 2×10-2 s-1) during NPF event days occurring during spring and summer (Fig. 8a). CS values ranging from 0.6 up to 10.7×10-2 s-1 were reported during NPF event days and over different urban sites (Beijing, Nanjing or Hong Kong) (Xiao et al., 2015). Over pristine sites, such as Hyytiälä (Finland), the CS values are between 0.05 and 0.35×10-2 s-1. Low values of CS, often considered as the major limiting factor in the NPF occurrence, do not inhibit the occurrence of NPF events at ATOLL, consistent with previous observations in similar environments, such as the Melpitz (Germany) observatory (Größ et al., 2018) or over Chinese megacities (Xiao et al., 2015). One can assume that the presence of large concentrations of precursors could explain the formation of particles over polluted sites such as ATOLL. Unfortunately, precursors were not measured over the 4-year period; therefore, this assumption would require further investigation beyond the scope of this study. Nevertheless, recent studies, performed in the CLOUD chamber, demonstrate that the presence of nitric acid (HNO3) and ammonia (NH3), typical within urban environments and particularly in the north of France (Roig Rodelas et al., 2019), contribute to fresh particle survival by dramatically increasing their growth rate (Marten et al., 2022; Wang et al., 2020).

In the afternoon of NPF event days, the CS increases due to the growth of freshly emitted particles, especially during summer. The contribution of newly formed particles (Dp<50 nm) to the CS is about 36 % and 27 % during summer and spring, respectively, while the contribution of pre-existing particles (Dp>150 nm) to the CS is below 20 % for both seasons. Moreover, during non-event days the size-resolved median CS is shifted toward larger particle diameters with a maximum observed around 100 nm for all seasons.

To evaluate the impact of the background CS on NPF occurrences, all CS values observed from 07:00–09:00 UTC (CS07:00–09:00), the period before the NPF starting time (green area on Fig. 4a), were averaged during NPF event, non-event, and undefined days. It was found that the total CS07:00–09:00 was larger (around 16 %) during non-event days in comparison to undefined and event days. Moreover, this difference is mostly due to particles larger than 70 nm according to the size-resolved CS07:00–09:00 (Fig. 8b). The difference between non-event and event days is lower than what is usually observed over pristine sites (Lyubovtseva et al., 2005) but significant enough to trigger the NPF event occurrence.

Du et al. (2022) studied the chemical composition of particles contributing to the CS when NPF occurrence is at its highest (10:00–15:00 local time) over Beijing. They observed a large increase of nitrate and a decrease of organics in PM2.5 with increasing CS values for NPF event and non-event days. As the CS observed over ATOLL is largely influenced by the freshly formed particles, the chemical composition of particles as a function of CS can be presented during two specific periods: before (07:00–09:00 UTC) and during (09:00–14:00 UTC) the period when the NPF occurrence is at its highest for NPF event and non-event days (Fig. 9). During non-event days, both periods (Fig. 9b and d) exhibit a similar mass fraction for all compounds with on average 41 % of organics, 16 % of nitrate, 21 % of sulfate, 11 % of ammonium, less than 1 % of chloride, and around 10 % of black carbon (BC). As the aerosol sources during non-event days are supposed to be the same throughout the day, this result was actually expected.

Larger contribution of organics to the CS is observed for NPF event days during the NPF period (CS09:00–14:00∼54 % on average, Fig. 9c) in comparison with the period right before the start of the NPF events (CS07:00–09:00∼46 % on average, Fig. 9a). Indeed, for large values of CS09:00–14:00 (>0.045 s-1) the contribution of organics is larger than 50 %, reaching a maximum of 69 % for CS09:00–14:00 of 0.085 s-1. This result suggests that organic vapors may be involved in the particle growth.

Additionally, the correlation coefficients (R) between meteorological parameters and gaseous or particulate pollutants are reported in Table 1 for the entire period of measurements (all seasons). Hourly averages over a time window between 09:00 and 14:00 UTC (NPF event starting time period) of a few variables (total CS, T, RH, and BC from wood burning (BCwb)) were used to calculate those correlation coefficients (corresponding to 7025 and 35 433 data points for NPF event and non-event days, respectively).

The correlation of BCwb with the CS during non-event days is high (R=0.67) and is clearly absent during NPF event days (R=0.19). One can also note that NOx concentrations have a positive correlation (0.30) with CS during NPF non-event days, while the same correlation is negative (-0.17) during NPF event days. NOx sources over urban areas are mostly anthropogenic ones (residential heating, traffic, and industries), which is consistent with its relatively high correlation coefficients with BCwb (0.47 and 0.65). As highlighted in Barreira et al. (2021), BCwb and NOx are evolving through the year showing a minimum in summer and a maximum in winter when sources are stronger due to colder temperatures and residential heating emissions. As non-event days are mostly (62 %) observed during cold months (fall and winter, not shown here) and NPF events are largely (82 %) observed during warmer months (spring and summer), the correlation between BCwb, NOx, and CS during non-event days is expected. However, during spring, air masses observed during NPF events are clearly “cleaner” (in terms of NOx and BCwb) than non-event cases. Indeed, NOx and BCwb concentrations are lowered by 18 % and 36 %, respectively, during NPF event days occurring in spring in comparison to non-event days. During summer, NOx and BCwb concentrations reach an annual minimum, and therefore both pollutant concentrations are similarly correlated between NPF event and non-event days (lowered by -0.04 % and 0.01 % during NPF event days).

Moreover, during NPF event days the temperature is positively correlated (0.55) with the CS, while during non-event days this correlation is clearly not observed (0.06). As discussed previously, this coupling was expected as it could be related to larger VOC emissions leading to enhanced particle growth and to higher concentrations of larger particles (Sect. 3.4).

Environmental parameters such as CS, T, and RH (Figs. 6, 7 and 8) observed during undefined events exhibit values mostly between those observed during event and non-event days. A deeper analysis of undefined days is therefore needed to evaluate if the UFP observed during those days are coming from failed events or from pollution-related peaks (Buenrostro Mazon et al., 2016). A first analysis on undefined days reveals that on these days, particle growth stopped suddenly due to (i) a decrease of the total irradiance due to a cloud passing over the site (20 % of cases), (ii) a shift of the wind direction (17% of cases), or (iii) both parameters changing simultaneously (35 % of cases).

The shift of the wind orientation leading to a stop of the particle growth indicates that NPF events are associated with certain wind directions or air mass origins. To investigate this, HYSPLIT back trajectories were first sorted as a function of NPF event, non-event, and undefined days. Only back trajectories arriving between 09:00 and 14:00 UTC (period of NPF high occurrences) were selected for further analysis. During the NPF events, the predominant air masses were tracked back along the eastern North Sea region (Fig. 10a). Comparing these results to back trajectories for non-event days highlights a more continental influence. Indeed, most of the back trajectories during non-event days pass over large cities (Dunkirk, Paris, London, Rotterdam) before reaching Lille metropolis (Fig. 10b). Those air masses might then have been slightly enriched in primary precursor vapors. This result is consistent with previous results showing that “cleaner” air masses are associated with higher probability of NPF events (Bousiotis et al., 2019).

The nucleation strength factor (NSF15.7–100) is calculated as the ratio of fine (15.7<Dp<100 nm) to accumulation (100<Dp<800 nm) particle concentrations observed during NPF event days over the same ratio observed during non-event days (Salma et al., 2017). Fine and accumulation mode particle number concentrations (N15.7–100 and N100-800) were retrieved from the SMPS data (Fig. 11a). The limited atmospheric residence time of fine particles (typically lower than 10 h, Seinfeld and Pandis, 2016) means that a large portion of the N15.7–100 concentrations can be related to local emissions and/or formation processes, including NPF events. On the contrary, due to a longer residence time within the atmosphere (up to 10 d, Seinfeld and Pandis, 2016), N100-800 is more related to large spatial and temporal scales. Therefore, the numerator represents the increase of N15.7–100 relative to N100-800 caused by all sources, while the denominator represents the same property due to all sources except NPF. The NSF method is based on the hypothesis that aerosol sources are similar from day to day and from season to season, excepting the sporadic occurrence of NPF. Considering the large number of NPF event (96) and non-event (432) days used to calculate NSF15.7–100, one can assume that the sporadic/occasional (i.e., not observed on daily basis) sources of UFP other than NPF events (e.g., volcanic plumes) have little impact on the NSF15.7–100 in comparison to the sources that are always active (such as traffic, industries, etc).

NSF is generally used to better assess the contribution of NPF to fine particle number concentrations relative to the regional background particle number concentrations. If the NSF ≈1, then the relative contribution of NPF to particle number concentration with respect to other sources is negligible, as observed at the Granada (Spain) urban site (Casquero-Vera et al., 2021). Moreover, Salma et al. (2017) also defined two thresholds for NSF6–100 to describe NPF contribution as a single source: a considerable contribution (1< NSF6–100<2) or larger than all other sources together (NSF6–100>2). One should keep in mind that these thresholds were defined accordingly to the lower cut-off diameter originally set at 6 nm. As the lower cut-off diameter used in this study is a bit larger (15.7 instead of 6 nm) than the one used by Salma et al. (2017), the calculated NSF15.7–100 would necessarily be underestimated in comparison to NSF6–100 from Salma et al. (2017). The hourly median value of fine-to-accumulation particle concentration ratio was computed for NPF event and non-event days. Figure 10 shows the NSF15.7–100 diel variation observed at ATOLL over 4 years of measurements.

During spring, the NSF15.7–100 factor remains quite constant (about 1.5) during night and morning and peaks at 16:00 UTC to reach a maximum of 2.5 (Fig. 11b). This indicates that NPF has a significant effect on particle number concentration only a few (2–3) hours after the averaged NPF starting time. During summer, the tendency of the NSF15.7–100 is quite similar with a unique peak at 13:00 UTC (again 2–3 h after the averaged NPF starting time). At that time the median NSF15.7–100 values reach 4, while from 21:00 to 06:00 UTC the NSF15.7–100 remains low (averaged at 1.08). Therefore, during summer, the NPF contribution to particle number concentration is extremely high from 10:00 to 18:00 UTC and then negligible for the rest of the day in comparison to other sources.

Such NSF10–100 diel variations were observed in other European cities (Budapest, Vienna, and Prague) with maximum values reaching 2.7, 2.3, and 3.4, respectively, for a lower cut-off diameter set at 10 nm (Németh et al., 2018). Moreover, Salma et al. (2017) reported NSF6–100 peaks at midday varying from 2.2 and 2.7 for Budapest city center and from 2 to 7.2 for near city background for each season with NSF6–100 maximum reached during winter. The nucleation frequency during winter in Budapest is low (<10 %), similarly to our observations; however, the impact of these limited number of NPF events on particle number concentrations is high. It may be mentioned that the NSF15.7–100 factor over ATOLL peaked at 3.5 and 2.3 during winter and fall, respectively.

As previously shown by Sebastian et al. (2021), NPF events can also play a major role on the Earth's radiative budget when the newly formed particles grow to climate-relevant sizes (50–100 nm). In order to understand the NPF influence on these particles, the NSF50–100 was also calculated (see Fig. S3). The results show a large increase of up to 1.6 of the NSF50–100 in the early afternoon for both seasons. This suggests a potential impact on CCN concentrations that needs to be further studied with proper instrumentation.