The composition of atmospheric anions was measured using the atmospheric-pressure interface time-of-flight mass spectrometer (APi-TOF) (Junninen et al., 2010). The instrument was situated inside a container in the forest, directly sampling the air outside. To minimize the sampling losses, we firstly drew the air at a greater flow rate within a wide tube (40 mm inner diameter), and another 30 cm long coaxial tube (10 mm outer diameter and 8 mm inner diameter) inside the wider one was used to draw 5 L min-1 towards the APi-TOF, 0.8 L min-1 of which entered through the pinhole. After entering the pinhole, the ions were focused and guided through two quadrupoles and one ion lens and finally detected by the time-of-flight mass spectrometer.

Unlike the commonly used chemical-ionization mass spectrometer (CIMS), the APi-TOF does not do any ionization, so it only measures the naturally charged ions in the sample. In the atmosphere, the ion composition is affected by the proton affinity of the species: molecules with the lowest proton affinity are more likely to lose the proton and thus become negatively charged after colliding many times with other species; similarly, molecules with the highest proton affinity would probably become positively charged ions. In addition to the proton affinity, the neutral concentration also plays a role in determining the ion composition by affecting the collision frequency. Due to the limited ionization rate in the atmosphere, there is always a competition between different species in taking the charges. For example, H2SO4 often dominates the spectrum in the daytime when it is abundant, while at nighttime nitrate ions and their cluster with HOMs are always prominent due to the low chances of colliding with the H2SO4. Since the signal strength of an ion in the APi-TOF depends not only on the abundance of the respective neutral molecules but also on the availability of other charge-competing species, it is very important to note that the APi-TOF cannot quantify the neutral species.

One important virtue of APi-TOF is that it does not introduce extra energy during sampling, which ensures the sample is least affected when compared to other measurement techniques such as CIMS although fragmentation cannot be fully avoided inside the instrument (Schobesberger et al., 2013). Because of this, it is a well-suited instrument to directly measure the composition of weakly bonded clusters in the atmosphere.

The APi-TOF data were processed with the tofTools package (version 6.08) (Junninen et al., 2010). Since the ion signal in APi-TOF is usually weak, a 5 h integration time was used, after which the signals of H2SO4-NH3 clusters and HOMs were fitted (see Fig. 1). For HOM signals, we used the same peaks reported in Bianchi et al. (2017), and the total signal of HOM ions is the sum of all identified HOMs.

It should also be mentioned that the voltage tuning of the instrument was not the same in the years we analyzed, which led to differences in the ion transmission efficiency function. For example, we noticed that in 2011, the largest H2SO4-NH3 clusters contained 6 H2SO4 molecules, whereas more than 10 H2SO4 were observed in the clusters in other years. This was very likely due to the very low ion transmission in the mass range larger than about 700 Th for the measurements in 2011. However, this should not affect our results and conclusions because clusters consisting of six H2SO4 molecules had little difference from larger clusters in affecting the IIN in terms of occurrence probability (see more details in Sect. 3.3.1).

The concentrations of H2SO4 and HOMs were measured by the chemical-ionization atmospheric-pressure interface time-of-flight mass spectrometer (CI-APi-TOF). The details of the quantification method for H2SO4 can be found in Jokinen et al. (2012) and those for HOMs in Kirkby et al., 2016. For all data, we applied the same calibration coefficient (1.89×1010 cm-3) reported by Jokinen et al. (2012).

Although the tuning of the CI-APi-TOF was not exactly the same during the measurement period included in this study, no systematic difference was found in the concentrations of H2SO4 and HOMs from different years.

The mobility distribution of charged particles and air ions in the range 3.2–0.0013 cm2 V-1 s-1 (corresponding to mobility diameter 0.8–42 nm) were measured together with the size distribution of total particles in the range ∼ 2.5–42 nm using a NAIS (Airel Ltd.; Mirme and Mirme, 2013). The instrument has two identical differential mobility analyzers (DMAs) which allow for the simultaneous monitoring of positive and negative ions. In order to minimize the diffusion losses in the sampling lines, each analyzer has a sample flow rate of 30 L min-1 and a sheath flow rate of 60 L min-1. In “particle mode”, when measuring total particle concentration, neutral particles are charged by ions produced from a corona discharge in a “pre-charging” unit before they are detected in the DMAs. The charging ions used in this process were previously reported to influence the total particle concentrations below ∼ 2 nm (Asmi et al., 2008; Manninen et al., 2010); for that reason, only the particle concentrations above 2.5 nm were used in the present work. Also, each measurement cycle, i.e., 2 min in ion mode and 2 min in particle mode, is followed by an offset measurement, during which the background signal of the instrument is determined and then subtracted from measured ion and particle concentrations. In addition, particle size distributions between 3 and 990 nm were measured with a differential mobility particle sizer (DMPS) described in detail in Aalto et al. (2001). Based on earlier work by Kulmala et al. (2001), these data were used to calculate the condensation sink (CS), which represents the rate of loss of condensing vapors on preexisting particles.

The meteorological variables used as supporting data in the present work were measured on a mast, all with a time resolution of 1 min. Temperature and relative humidity were measured at 16.8 m using a PT-100 sensor and relative humidity sensors (Rotronic Hygromet MP102H with Hygroclip HC2-S3, Rotronic AG, Bassersdorf, Switzerland), respectively. Global radiation was measured at 18 m with a pyranometer (Middleton Solar SK08, Middleton Solar, Yarraville, Australia) and further used to calculate the cloudiness parameter, as done previously by Dada et al. (2017, and references therein). This parameter is defined as the ratio of measured global radiation to theoretical global irradiance so that parameter values <0.3 correspond to a complete cloud coverage, while values >0.7 are representative of clear-sky conditions.

The formation rate of 2.5 nm particles includes both neutral and charged particles, and it was calculated from the following equation: J2.5=dN2.5-3.5dt+CoagS2.5×N2.5-3.5+11nmGR1.5-3×N2.5-3.5, where N2.5-3.5 is the particle concentration between 2.5 and 3.5 nm measured with the NAIS in particle mode, CoagS2.5is the coagulation sink of 2.5 nm particles, as derived from DMPS measurements, and GR1.5-3 is the particle growth rate calculated from NAIS measurements in ion mode. Calculating the formation rate of 2.5 nm ions or charged particles includes two additional terms to account for the loss of 2.5–3.5 nm ions due to their recombination with sub -3.5 nm ions of the opposite polarity (fourth term of Eq. 2) and the gain of ions caused by the attachment of sub -2.5 nm ions on 2.5–3.5 nm neutral clusters (fifth term of Eq. 2): J2.5±=dN2.5-3.5±dt+CoagS2.5×N2.5-3.5±+11nmGR1.5-3×N2.5-3.5±+α×N2.5-3.5±N<3.5∓-β×N2.5-3.5N<2.5±, where N2.5-3.5± is the concentration of positive or negative ions between 2.5 and 3.5 nm, N<2.5± is the concentration of sub -2.5 nm ions of the same polarity, and N<3.5∓ is the concentration of sub -3.5 nm ions of the opposite polarity, all measured with the NAIS in ion mode; α and β are the ion–ion recombination and the ion-neutral attachment coefficients, respectively, and were assumed to be equal to 1.6×10-6 cm3 s-1 and 0.01×10-6 cm3 s-1, respectively. We consider these values to be reasonable approximations, keeping in mind that the exact values of both α and β depend on a number of variables, including the ambient temperature, pressure, and relative humidity as well as the sizes of the colliding objects (ion–ion or ion–aerosol particle) (e.g., Hoppel, 1985; Tammet and Kulmala, 2005; Franchin et al., 2015).

GR1.5-3 were calculated from NAIS data in ion mode using the “maximum” method introduced by (Hirsikko et al., 2005). Briefly, the peaking time of the ion concentration in each size bin of the selected diameter range was first determined by fitting a Gaussian to the concentration. The growth rate was then determined by a linear least square fit through the times. The uncertainty in the peak time determination was reported as the Gaussian's mean 67 % confidence interval and was further taken into account in the growth rate determination.

A similar approach was used to estimate the early growth rate of the H2SO4-NH3 clusters detected with the APi-TOF. Prior to growth rate calculation, we first converted cluster masses into diameters in order to get growth rate values in nm h-1 instead of amu h-1. For that purpose, we applied the conversion from Ehn et al. (2011), using a cluster density of 1840 kg m-3. The time series of the cluster signals were then analyzed in the same way as ion or particle concentrations using the maximum method from Hirsikko et al. (2005), and the growth rate was calculated using the procedure outlined above. Our ability to determine the early cluster growth rate from APi-TOF measurements was strongly dependent on the strength of the signal of the different H2SO4-NH3 clusters. As a consequence, the reported growth rates characterize a size range which might vary slightly between the events, falling in a range between 1 and 1.7 nm.

We examined the daytime ion composition of 134 days from three consecutive springs (2011–2013) in Hyytiälä. Consistent with the findings by previous studies showing that H2SO4 clusters are the most abundant ions in the daytime (Ehn et al., 2010; Bianchi et al., 2017), we found that NH3-free H2SO4 clusters can contain up to three H2SO4 molecules when counting the HSO4- also as one H2SO4 molecule ((H2SO4)2HSO4-) and that NH3 is always present in clusters containing four or more H2SO4 molecules. The latter feature suggests the important role of NH3 as a stabilizer in growing H2SO4 clusters (Kirkby et al., 2011). NH3-free clusters (at least dimers H2SO4HSO4-) were observed on 116 measurement days, but the signal intensity varied from day to day. Bigger clusters that contained NH3 were observed on 39 days, containing a maximum of 4 to 13 H2SO4 per cluster. Figure 1 provides four examples of daytime ion spectra, including an NH3-free case (Fig. 1a) and three cases with a different maximum size of H2SO4-NH3 clusters (Fig. 1b–d), illustrating the significant variations in signal and maximum size of H2SO4-NH3 clusters. In the NH3-free case, a larger number of HOM clusters (green circles) was observed, indicating a competition between H2SO4 and HOMs in taking the charges. The largest detected cluster during the measurement was (H2SO4)12 (NH3)13HSO4-, which corresponds to a mobility-equivalent diameter of about 1.7 nm according to the conversion method (Ehn et al., 2011) and is big enough to be detected by particle counters. Since the observed formation of such large H2SO4-NH3 clusters is essentially the initial step of IIN, we anticipate that the variation in H2SO4-NH3 clusters will influence the occurrence of IIN.

To find out the dominating parameters that affect the formation of H2SO4-NH3 clusters, we performed a correlation analysis that included the ambient temperature, relative humidity (RH), wind speed, wind direction, CS, and the gas-phase concentrations of NH3, H2SO4, and HOMs. Among all the examined parameters, we found that the ratio between concentrations of HOMs and H2SO4 had the most pronounced influence on the appearance of H2SO4-NH3 clusters. As shown in Fig. 2, all H2SO4-NH3 clusters were detected when [HOMs] / [H2SO4] was smaller than 30. No such dependence was observed for only [HOMs] or [H2SO4]. This implies that the appearance of H2SO4-NH3 clusters is primarily controlled by the competition between H2SO4 and HOMs in getting the charges. More specifically, HSO4-, the main charge carrier in the daytime, may either collide with neutral H2SO4 to form large clusters to accommodate NH3 or collide with HOMs, which prevents the former process. In addition, a reasonable correlation was found between [HOMs] / [H2SO4] and temperature, likely explained by the emission of volatile organic compounds (VOCs) increasing with temperature, leading to higher HOMs concentrations, whereas the formation of H2SO4 is not strongly temperature-dependent. This observation indicates that the formation of H2SO4-NH3 clusters may vary seasonally: we expect to see them more often in cold seasons when HOM concentrations are low and less often in warm seasons.

Parameters other than [HOMs] / [H2SO4] and temperature seemed to have little influence on the formation of H2SO4-NH3 clusters. Interestingly, we found that NH3 was even lower when H2SO4-NH3 clusters were observed, indicating that the NH3 concentration is not the limiting factor for forming H2SO4-NH3 clusters (also see Sect. 3.4). In addition, H2SO4-NH3 clusters were observed in a wide range of RH spanning from 20 % to 90 %, suggesting that RH does not affect the cluster formation. Besides, no clear influence from CS, wind speed, or wind direction was observed.

For the 134 days of measurements, we were able to identify 67 IIN events using the NAIS data, out of which H2SO4-NH3 clusters were observed on 32 days, implying that at least 35 IIN events were likely driven by mechanism(s) other than H2SO4-NH3. In Fig. 5, we classified the days according to the types of IIN observation: 32 IIN events involving H2SO4-NH3 (S–E), 3 nonevents with the presence of H2SO4-NH3 clusters (S–NE), 35 IIN events involving other mechanisms (O–E), 41 other nonevent days (O–NE), and 23 days with unclear types. We further present the respective statistics of additional measurements for the first four types of days, including the concentrations of plausible precursor vapors, condensation sinks, and meteorological parameters. It should be noted that the S–NE has only three days; thus, the statistics on this type of day might not be fully representative.

Consistent with the previous discussion (Fig. 2), low temperatures are conducive to IIN events via the H2SO4-NH3 mechanism whilst being the highest other type of events (O–E) (Fig. 5a). The clear-sky parameter (100 % – clear sky; 0 % – cloudiness) shows a noticeably higher value during both event types compared to the nonevent cases (Fig. 5b), indicating that photochemistry-related processes are important for all events. Moreover, the CS is obviously lower for both types of events than on nonevent days (Fig. 5c). Although a strong effect of CS on the appearance of H2SO4-NH3 clusters has not been noticed, it is a most important parameter in regulating the occurrence of IIN. Similar effects of cloudiness and CS on governing the occurrence of NPF have been reported by Dada et al. (2017) based on long-term data sets.

Remarkably, NH3 has very low concentrations during H2SO4-NH3 events in comparison to the other type of events (Fig. 5d). This is likely due to high NH3 concentrations coinciding with higher temperature and thus elevated HOMs concentration or the lower stability of H2SO4-NH3 clusters at high temperatures that can evaporate NH3 back to the atmosphere. This observation rules out the addition of NH3 as a limiting step in the H2SO4-NH3 nucleation mechanism, but the participation of NH3 in the other type of events cannot be excluded.

H2SO4 has the highest concentrations during the H2SO4-NH3-involved events (Fig. 5e), but the concentration of H2SO4 in S–NE days is not much lower, suggesting that the occurrence of H2SO4-NH3-involved events is not solely controlled by the H2SO4 concentration. The incorporating the effect of CS ([H2SO4] / CS) significantly improves the separation (Fig. 5f). McMurry and colleagues (Mcmurry et al., 2005) introduced a parameter L (Eq. 3) to quantitatively evaluate the likelihood of NPF, and they found that NPF mostly occurred when L is smaller than 1. A similar result has been reported by Kuang et al. (2010), and a slightly different threshold L value of 0.7 was determined. L=CS[H2SO4]×1β11 Here, L is a dimensionless parameter representing the probability that NPF will not occur, and β11 is the collision rate between H2SO4 vapor molecules, which is characterized as 4.4×10-10 cm3 s-1. Our results suggest a consistent L that most (75 percentile) S–E cases happen when L is lower than 0.73 and most (75 percentile) S–NE cases are observed when L is larger than 1.54.

HOM concentrations are highest in the case of other events, revealing that HOMs play a key role in this mechanism (Fig. 5f), although the contribution of H2SO4 in this HOM-involving IIN mechanism cannot be excluded. Similar to the H2SO4-NH3-driven cases, incorporating the CS better distinguishes the event and nonevent cases.

Overall, our results suggest that the concentrations of H2SO4 and HOMs, together with the CS, govern the occurrence of IIN, whereas their ratio determines the exact underlying mechanism (Fig. 2). Although H2SO4-NH3 and HOMs clearly drives the S–E and O–E events, respectively, we cannot exclude the later participation of HOMs in S–E cases or H2SO4 in O–E cases. Different NPF mechanisms have also been identified at the Jungfraujoch station (Bianchi et al., 2016; Frege et al., 2018) when influenced by different air masses. At the SMEAR II station, on the other hand, our results suggest that the natural variation in temperature is already sufficient to modify the NPF mechanism by modulating the biogenic VOC emissions.

In order to obtain further insight into the importance of IIN during our measurements, we compared the formation rate of 2.5 nm ions, JION=J2.5± (see Eq. 2), to the total formation rate of 2.5 nm particles, JTOT=J2.5 (see Eq. 1). The ratio JION/JTOT is equal to the charged fraction of the 2.5 nm particle formation rate. In analyzing field measurements, a similar ratio at a certain particle size (typically 2 nm) has commonly been used to estimate the contribution of ion-induced nucleation to the total nucleation rate (see Hirsikko et al., 2011, and references therein). It should be noted that JION/JTOT represents only a lower limit for the contribution of ion-induced nucleation, as this ratio does not take into account the potential neutralization of growing charged sub -2.5 nm particles by ion–ion recombination (e.g., Kontkanen et al., 2013; Wagner et al., 2017). At present, measuring the true contribution of ion-induced nucleation to the total nucleation rate is possible only in the CLOUD chamber (Wagner et al., 2017).

We were able to calculate JION and JTOT for 57 (out of 67) cases, and the ratio JION/JTOT varied from 4 to 45 %, showing a clear correlation with the HOM signal (Fig. 6a). This indicates the participation of HOMs even in H2SO4-NH3-driven cases. In addition, most of the high JION/JTOT ratios were observed at moderate or low H2SO4 concentrations; e.g., JION/JTOT > 15 % was only observed when [H2SO4] < 6×106 cm-3. These observations indicate that HOMs are important in high JION/JTOT cases, while during events driven by H2SO4-NH3 clusters, low JION/JTOT is more often observed. Accordingly, the median value of JION/JTOT for the H2SO4-NH3 cases is about 12 % and is clearly higher (18 %) in HOM-driven events (Fig. 6d). Figures 6b and c reveal that both JION and JTOT values are in fact higher in H2SO4-NH3 cases, but the neutral nucleation pathway is relatively more enhanced, leading to the lower ratio. These results suggest that ion-induced nucleation plays a more important role in the events driven by HOMs than in the events driven by H2SO4-NH3. A plausible explanation is that NH3 performs well in stabilizing H2SO4 molecules during the clustering process, whereas ions are a relatively more important stabilizing agent for HOM clustering.