Particle number size distributions, from 5 to 850 nm, were measured using a custom-made twin-DMPS system with a closed-loop sheath circulation and composed of two Hauke-type differential mobility analysers (DMAs). DMPS-1, with a short (5.3 cm) DMA, measured aerosol size distribution from 5 to 57 nm using a sample-to-sheath air ratio close to 1:10. DMPS-2, with a medium-length DMA (28 cm), measured size distribution from 20 to 850 nm using a sample-to-sheath air ratio close to 1:5. The aerosol particles were counted using condensational particle counters (CPCs) at a frequency of 1 Hz with the two CPCs. Particles > 3 nm were measured using the Ultrafine CPC (UCPC) TSI model 3776 (cut-off of 2.5 nm) coupled to the DMPS-1. Particles > 10 nm were measured with the CPC TSI model 3010 (cut-off of 10 nm) coupled to the DMPS-2. The two DMAs were run in a stepwise mode, providing two particle number size distribution cycles approximately every 27 min. The overlap between the size ranges measured by both DMPSs was used to check consistency and to merge both size distributions into one. Additional information can be found in Karlsson et al. (2021). The DMPS measurements were corrected for diffusional losses using the Particle Loss Calculator (PLC) according to von der Weiden et al. (2009) (see Fig. S1 in the Supplement for details).

NAIS was utilised to measure concentrations of ions (charged particles and cluster ions) of both polarities between 0.8 and 40 nm and particles between 2.5 and 40 nm. The NAIS is an aerosol mobility spectrometer; when the sample is left unmodified it detects naturally charged ions and particles, and when the corona charger is used to charge the particle population it measures all particles, including the uncharged (Manninen et al., 2011; Mirme et al., 2007; Mirme and Mirme, 2013). It consists of 2 mobility analyser columns, with a total of 25 electrometers per column. Its lower size thresholds and high temporal resolution make it highly suitable for observing the early stages of NPF. The NAIS provides very accurate size information, regardless of the choice of the inversion algorithm used (in this case, the 25-channel V14.1 inverter algorithm) (Wagner et al., 2016). The lowest detection limit for the NAIS in particle mode is set based on the diameter of the corona charger ions and the inability of the electrical filter to remove all naturally charged particles (Manninen et al., 2011); however, there is a broad consensus that measurements of concentrations of particles below 2.5 nm are inaccurate.

The NAIS at ZEP was installed with a very short metallic inlet, less than 1m long, to minimise diffusional losses. The inlet pointed slightly downward, and a metallic rain shield was attached at the end to ensure that rain did not enter into the instrument. The NAIS inlet was heated to prevent ice blocking the inlet and also to limit water condensing inside the tubing. The NAIS was serviced and cleaned once a year. Additional aspects of the NAIS observations, including the apparent overestimation of particle number concentrations when compared to DMPS measurements (see also Kangasluoma et al., 2020) and the loss of negative cluster ions, can be found in Sect. S2.6 of the Supplement.

A nanoparticle scanning mobility particle sizer (Nano SMPS, TSI), comprising a nano-differential mobility analyser (nano-DMA, TSI 3085, USA) and an ultrafine CPC (TSI 3776, USA), provided size distributions of nanoparticles (3–60 nm). See Lee et al. (2020) for further details. Atmospheric dimethyl sulfide (DMS) was measured using an analytical system in which DMS is trapped and eluted before being quantified using gas chromatography equipped with a pulsed-flame photometric detector. The detection limit is approximately 1.5 pptv given air samples of around 6 L. For more details, see Jang et al. (2016) and Park et al. (2018). Meteorological parameters including visibility, relative humidity, wind speed and direction, ambient temperature, and pressure were also further utilised throughout the study.

New particle formation events were classified using schemes described by Dal Maso et al. (2005) and Aliaga et al. (2023). The classification schemes are used complementary. The classification by Dal Maso et al. (2005) focuses more on formation and growth and is perhaps more intuitive to understand; however, it struggles with a large number of undefined cases. On the other hand, the nano-ranking analysis developed by Aliaga et al. (2023) can be used to explore the NPF intensity and focuses on the formation of nucleation mode particles as opposed to the subsequent growth. The Aliaga method classifies NPF events into three groups based on the overall ranking of NPF intensity, avoiding the problem with unidentified event days (see Fig. S16 for the groups). The two classification methods can be compared with one another (see Fig. S14). We used the method for the intensity parameter and the diameter range that showed the best comparison with Dal Maso et al. (2005), i.e. the daily maximum for the total number concentration of 2.8 nm and 5 nm particles (ΔNmax⁡,2.8-5).

In the Dal Maso et al. (2005) scheme an NPF event is defined if there exists a nucleation mode (3–25 nm) which prevails for several hours and shows signs of growth; these events are further subdivided into three separate classes, namely, Class Ia and Ib and Class II. Class I and Class II events are separated on the basis of whether the growth and formation rates of the well-behaved size distribution can be determined with good confidence. Class I is further divided into Class Ia and Class Ib depending on whether there are pre-existing particles obscuring the newly formed mode (Dal Maso et al., 2005). Undefined events are days where there are sporadic occurrences of nucleation mode particles, and this classification is used to separate clear events from clear non-events. For examples of the different classifications and their respective averages see Figs. S12 and S13, respectively.

In this study, undefined days include days where the occurrence of nucleation mode particles (3–25 nm) is linked to windblown snow and situations when ZEP is enveloped by clouds. For more details regarding these sampling conditions see Sect. S2.1 and S2.2 for in-cloud sampling and windblown snow events, respectively. As a result, days classified as undefined are ones which experience bursts of nucleation mode particles, either from windblown snow (see Fig. S4), in-cloud conditions (see Fig. S2), non-growing NPF, or a combination of all three. There is a definite increase in the concentration of particles with diameters around 5 nm when the NAIS measures in conditions of low visibility, and this is not observed in other instruments (see Fig. S3). For windblown snow events, particles with diameters less than 20 nm observed considerable increases in concentrations when the wind speed passed roughly 10 m s⁻¹ (see Fig. S5). Non-events are days that display no nucleation mode (3–25 nm). It is important to note that this scheme assumes that particle formation occurs over a geographically wide area more or less simultaneously. Identification and classification were performed using daily surface plots of particle number size distribution based solely on NAIS data, that is, 2.5–40 nm.

It should be noted that there is a degree of subjectivity to this classification approach as to what is considered a certain class. The addition of the NAIS, in combination with the DMPS system, made it easier to detect events using surface plots, especially when the growing mode struggled to surpass ∼ 6 nm. However, we were not able to identify any NPF events with the NAIS that we could not identify with the DMPS system, as close inspection of the number concentration of the lowest size bins of the DMPS system was sufficient to recognise NPF events.

The nanoparticle ranking analysis method developed by Aliaga et al. (2023) provides a more continuous method to characterise atmospheric NPF, allowing users to gauge the strength of NPF. The nanoparticle ranking analysis was utilised using the daily maximum concentration of 2.8–5 nm particles (ΔNmax⁡,2.8-5), from the negative channel of the NAIS, as the intensity parameter (note that no background value was used, unlike in Aliaga et al., 2023, due to the low concentrations measured at ZEP). In this study, periods which experienced windblown snow or in-cloud events were removed before applying the nanoparticle ranking method (see Figs. S7 and S8), as opposed to the Dal Maso et al. (2005), approach which classified them as undefined days. Special care was taken to clean the data before utilising the nanoparticle ranking analysis method; however, it may still be the case that not all in-cloud and windblown snow events were removed successfully (see Sect. S2.1 and S2.2). Windblown and in-cloud events can influence the daily maximum without necessarily reflecting NPF activity. The strength of NPF activity was split into three groups depending on the intensity (i.e. g1, g2, g3), where g3 is the most intense event, followed by g2 and then g1; see Aliaga et al. (2023) for more details (see Figs. S15 and S16).

The growth rate (GR) describes the rate of change of the modal diameter during an NPF event. For the GR estimation, NAIS and DMPS size distributions were merged at the maximum diameter of the NAIS size range (i.e. 40 nm). The NAIS and DMPS data were both interpolated to 15 min arithmetic means using linear interpolation. The start and end of each NPF event including their sequential growth (i.e. formation and subsequent growth) were estimated by visual inspection. The growing nucleation mode was isolated, and the GR was estimated for the full duration of the NPF event (see Fig. S17). For each size bin, we applied a Gaussian filter (sigma = 1) and found the time in which the concentration of a particular size bin experienced the highest maximum rate of change. Essentially, the evolution of the nucleation mode was tracked using the timings for each identified peak in the rate of change of the growing nucleation mode diameter. The GR was calculated using a simple linear ordinary least squares (OLS) method.

It should be noted that the aforementioned issues concerning the overestimation of particle number concentrations for the NAIS measurements do not impact the calculation of GR as it only examines the changes to the diameter of the nucleation mode. Very few events grew beyond the limit of the NAIS (i.e. 40 nm); hence the impact of a diameter jump from NAIS to DMPS was not considered. We tried to measure the GR of all NPF events (e.g. Class 1a, 1b, and II), even though by definition Class II events lack the strength and consistency, making it difficult to calculate GRs (Dal Maso et al., 2005). The GRs for some Class II events were not estimated due to uncertain tracking of the nucleation growth.

The formation rates, namely J3-7, J7-25, and J3-25 (cm⁻³ s⁻¹), were estimated using the following equation: 1Ji-j=dNi-jdt+Coag×Ni-j+GRΔdp×Ni-j, where Ji-j is the formation rate of particles between diameters i–j nm, CoagS is the coagulation sink of the pre-existing particle population, GR is the growth rate between i and j nm, Δdp is the difference in diameter between i and j in nanometres, and Ni-j is the total concentration of particles between i and j nm (Fig. S18 represents an example for calculating formation rates for particles between 3 and 7 nm).

The Python GUI, npf-event-analyser, was used to provide additional complementary estimations of the GRs and formation rates for the NPF events (i.e. in addition to the OLS fitting method). When using the npf-event-analyser the max concentration method was used for the estimations of GR and J.

The condensation sink (CS) is defined as the rate at which non-volatile vapours condense onto pre-existing particles (Kulmala et al., 2012). The twin DMPS system (5–850 nm) was used to calculate CS for SA vapour. The method for the determination of CS is described by Dal Maso et al. (2002) and uses the following equation: 2CS=2πD∫idp,imax⁡dp,iβdp,iNdp,iddp,i, where dp,i is the diameter of a particle in size class i, Ni is the particle number concentration in the respective size class, and D is the diffusion coefficient of the condensing vapour (in this case condensing vapours were assumed to have H₂SO₄ diffusion properties). We used the transition regime correction factor β from Fuchs and Sutugin (1970).

The concentration of vapours (Cv) required to sustain the calculated GRs and their respective source rates (Q) were estimated using the following equation and assuming the condensation of H₂SO₄: 3Cv=A×dDp/dt, where A is the constant 1.37 × 10⁻⁷ h cm⁻³ nm⁻¹ representative of the molecular properties of SA, and dDp/dt is the rate of change of the nucleation mode, i.e. GR from the start of the NPF until it stops growing (see Sect. 3.1.5 below and Dal Maso et al., 2005, for further details). The constant A incorporates the probability that sulfuric acid molecules will “stick” to particles upon collision, the change in volume which occurs after collision and condensation, and also the frequency of collisions (Fiedler et al., 2005).

Air mass back trajectory analysis was performed using the Hybrid Single-Particle Lagrangian Integrated Trajectory model (HYSPLIT V5.2.1) (Draxler and Hess, 1998; Stein et al., 2015). Ensemble back trajectories were initialised every hour starting at the latitude and longitude of ZEP and at a height of 250 m above ground level (a.g.l.). The ensemble was generated by offsetting the meteorological grid point by one in the horizontal (i.e. dxf = 1.0, dyf = 1.0) and by the default offset of 0.01 sigma units in the vertical (∼ 250 m), thus generating 27 back trajectories for all possible offsets in X, Y, and Z. The starting height of 250 m ensured that the starting location of all the ensemble members was at the surface or above. The back trajectories were calculated for 5 d back in time. Global Data Assimilation System (GDAS) 1° × 1° archive data (http://ready.arl.noaa.gov/archives.php, last access: 8 August 2024) were used as the meteorological fields. No averaging of the back trajectories was performed, reducing them to single back trajectories. HYSPLIT was run from the desktop using the Python package pysplit (https://github.com/mscross/pysplit, last access: 13 April 2021).

The accumulated solar flux in the most recent 6 h prior to arrival was used for the solar insolation term used throughout this study. The solar flux was taken from the original GDAS-derived HYSPLIT output. Furthermore, only endpoints within the mixed layer were used as this is when air masses are influenced by the surface. The last 6 h were used, as opposed to a longer duration, to place more significance on solar radiation closer to the receptor; an accumulated solar flux consisting for a longer duration could lead to misleading results.

Daily mapped chlorophyll a data derived from satellite observations (Aqua MODIS) (downloaded from https://oceancolor.gsfc.nasa.gov/l3/, last access: 4 October 2024) were utilised along with the HYSPLIT output to estimate the chlorophyll a exposure. Exposure of the air masses to chlorophyll a was calculated based on the equation developed by Park et al. (2018), which linked chlorophyll a with DMS measurements on site at ZEP. Chlorophyll a exposure was essentially used as a proxy for DMS emissions. DMS in turn can form H₂SO₄ via SO₂, although this was not explicitly addressed by Park et al. (2018). It should be noted that DMS is not only a precursor to H₂SO₄, but also MSA. Park et al. (2018) utilised the relationship between DMS and air mass exposure to chlorophyll a to account for the differences in the species-specific phytoplankton population between the Greenland Sea and the Barents Sea. For more details on the calculation of the chlorophyll exposure see Sect. 12.

The method utilised here is similar to the NanoMap analysis developed by Kristensson et al. (2014) in which the geographic position of where new particle formation took place was estimated based on the particle number size distribution measurements during NPF events and HYSPLIT back trajectories. In this study, the duration of the nucleation mode was calculated. For every hour of the NPF event, back trajectories were initialised. The length at which the back trajectories were initialised depended on how long the event had lasted. In short, i hours after the event began, the back trajectory will have been initialised to run i hours backwards. So, for every hour except the start time the back trajectories were initialised for the following length of time: back trajectory length = duration - (end time - t), where t ∈ (end to start times). Hence, for an NPF event that lasts 7 h, six back trajectory ensembles were calculated for varying lengths from 7 to 1 h long.

The endpoints for every 5 d back trajectory ensemble were assigned to a marine region, e.g. the Arctic Ocean, Greenland Sea, Barents Sea, Norwegian Sea, or North Atlantic Ocean (see Fig. S21 for defined regions). Days were assigned to a specific marine region based on the cumulative residence time in the specific sector. A threshold of 0.5 (50 %) was used as a qualifier. Days without clear source preference, i.e. the air masses that did not reach the 50 % threshold for either of the pre-defined source regions, were classified as mixed.

The 848 d of valid NAIS measurements (17 April 2022 to 4 October 2024) are classified according to the Dal Maso et al. (2005) classification system. A total of 157 d are classified as NPF events, either Class Ia events (28), Class Ib (19), or Class II (110). A total of 438 d are classified as undefined, and the remaining 271 d are considered to be either non-event days (253) or consisting of too few data (i.e. defined as < 12 h of data per day) (18) (see Fig. 1). Overall, this meant that 19 % of days with valid NAIS measurements experienced an NPF event (i.e. Class Ia, Ib, or II). The majority of days (52 %) are classified as undefined due to the appearance of a non-growing nucleation mode that persisted for some hours. The undefined days are further sub-divided into those containing windblown snow events (19 % of all data) and in-cloud events (8 % of all data) (see Fig. S6). Of the 438 undefined days, 72 are a result of non-growing bursts (i.e. 17 % of the undefined days).

The monthly frequency of NPF events (i.e. Class Ia, Ib, or II) shows events first appearing in April (see Fig. 1), reaching a peak, in terms of the occurrences per month, in May to July with approximately 30 %–40 % of days experiencing NPF. The daily occurrence decreases during the month of June compared with the preceding and succeeding months, a consistent finding throughout the 3 years of data. After July, the frequency of events declines towards the end of summer and into autumn, where NPF events cease to be present beyond November. NPF events were observed as late in the year as November, which is interesting given that this is during the polar night, when the sun stays below the horizon (as witnessed by ZEP), and thus ZEP experiences negligible solar radiation. Multiple NPF events were observed during the polar-night period (see Sect. 3.1.3 for more details). April 2022 appeared anomalous perhaps given that the measurements for that month were not an entire month as the measurements started on 17 April 2022.

Prior studies at ZEP, which used slightly different event classification schemes, reported the occurrence of NPF events to be within the range of 18 %–23 % (Dallósto et al., 2017; Heintzenberg and Leck, 2012; Lee et al., 2020). Nieminen et al. (2018) reported NPF day frequencies of 14 % (March–May), 34 % (June–August), 6.6 % (September–November), and 0 % (December–February). Lee et al. (2020) observed the highest frequency in terms of the formation and growth of N3-25 particles in June (> 40 %), with the NPF frequency in May and July being ∼ 40 % and < 40 %. Dome C in Antarctica and Alert in Greenland are two other polar sites with annual NPF frequencies between 10 % and 20 % (Nieminen et al., 2018), comparable to ZEP.

The interannual variability in the following main parameters, namely NPF intensity, solar insolation, DMS concentration and the CS, is explored in Fig. 2a–b. A proxy for the intensity of events, as opposed to the frequency, was determined by utilising elements of the nanoparticle ranking analysis developed by Aliaga et al. (2023). The maximum daily concentration in 2.8–5 nm particles (ΔNmax⁡,2.8-5) was used to represent the strength of NPF activity (shown to correlate well with calculated J), i.e. the NPF intensity. See Sect. 2.4.1 in the Methods for more details concerning the nanoranking method and about the definition of solar insolation.

ΔNmax⁡,2.8-5 shows various peaks throughout the annual cycle; however, the one striking feature is that every year ΔNmax⁡,2.8-5 has its first and highest peak occurring in late spring and the beginning of summer (i.e. end of April in 2022, beginning of June in 2023, and towards the end of May in 2024) (see the red curve in Fig. 2a). In terms of the annual cycle in NPF event frequency (see Fig. 1), the first peak in NPF event occurrences matches the April–June peak in increased ΔNmax⁡,2.8-5 (Fig. 2a). However, the succeeding peak in NPF event frequency (i.e. in July in Fig. 1) coincides with reduced intensity (ΔNmax⁡,2.8-5). The seasonality of the ΔNmax⁡,2.8-5 value follows that of the solar insolation, and for the years 2023 and 2024, the maximum NPF strength/intensity (i.e. ΔNmax⁡,2.8-5) coincides with the greatest mean solar insolation; a much better relationship is observed when selecting for air masses within the mixed layer as this is when arriving air masses are influenced by the surface (i.e. the orange bars in Fig. 2a). Averaging the intensity parameter and correlating it to the solar insolation calculated based on the entire air mass and the parts within the mixed layer (ML) shows that selection of air masses within the ML leads to a better correlation (see Fig. S27). The annual cycle for the calculated CS exhibits a sustained maximum in late winter and early spring due to the Arctic haze (i.e. February–May), and the CS stays high into the summer before reaching a minimum in autumn, typically the cleanest part of the year (Tunved et al., 2013) (see Fig. 2b). During the Arctic haze period, long-range-transported air masses from Eurasia bring aged aerosol, leading to the higher CS. At the same time, this period is characterised by higher sulfate and SO₂ concentrations, mainly of anthropogenic origin (Platt et al., 2022), and hence there are NPF events occurring and high increased NPF intensity. One additional aspect is that it is clear that increases in ΔNmax⁡,2.8-5 occur during periods where there was a slight decrease in CS, below that of the seasonal CS average. For example, the peak in ΔNmax⁡,2.8-5 in April in 2022 (see Fig. 2b), which occurs slightly prior to the maximum solar insolation, can potentially be explained by the reduction in the CS during that period.

The solar intensity is a controlling factor in the production of SA (i.e. H₂SO₄) via the oxidation of SO₂. In the Arctic, DMS acts as a significant source of sulfate; however, other sulfur compounds can be oxidised, e.g. carbon disulfide and hydrogen sulfide (Pei et al., 2021). The coagulation sink (CoagS) acts as a sink for the newly formed particles, and the CS acts as a sink for nucleating vapours; thus high CoagS and CS can inhibit NPF. NPF days with greater intensity (i.e. ΔNmax⁡,2.8-5) are skewed towards the end of spring and beginning of summer. Similarly, solar insolation is also shifted towards the start of summer, even though the theoretical solar maximum has a symmetrical distribution centred around the middle of summer (see red shaded region in Fig. 2a). The skewed pattern in both the solar insolation and NPF intensity (ΔNmax⁡,2.8-5) can perhaps be explained by annual changes in cloud cover (see Maturilli and Ebell, 2018, for the frequency occurrence of cloudy sky, increasing to ∼ 80 % during the summer from an April minimum of ∼ 40 %–60 %). Late autumn experiences numerous, but relatively weaker, NPF events, with peaks in ΔNmax⁡,2.8-5 (∼ 100–500 cm⁻³) every year at the end of the summer despite the relatively small solar insolation. The transition period between summer and haze (i.e. October–January) is typically the cleanest part of the year and thus exhibits the lowest CS (Tunved et al., 2013). During this part of the year the small amount of solar insolation and vapours present are enough to trigger NPF, possibly as a result of the low CS.

Finally, DMS is the main source of sulfur for clean marine aerosol particles and constitutes an important compound in regards to NPF via its oxidation products. Numerous peaks in DMS are observed during the summertime, with a maximum observed in July (see Fig. 2b). Elevated concentrations of DMS at ZEP coincide with air masses which traverse over marine regions containing chlorophyll a (see Figs. S30–S37, but also noted by Park et al., 2018).

Contrary to expectations, during the polar night (i.e. when the sun does not cross the horizon at Ny-Ålesund) a number of NPF events are observed. As shown earlier, solar insolation is clearly one of the driving parameters for NPF occurrence and intensity, and Ny-Ålesund in November does not receive any direct solar radiation (see Fig. S19 for examples of the polar-night events). For the November polar-night events, air mass back trajectories indicate that air masses have to travel at least half a day backwards before reaching Ny-Ålesund to experience direct solar radiation. In total, five of these events are observed and are detailed in Table 1.

The polar-night NPF event starting on 25 October 2023 appears to be a transported event (TE; see Dada et al., 2018, for details on the definition of a transported event) as we do not observe the entire growth of freshly nucleated particles; instead the growing nucleation mode begins at 4 nm. The extremely low accumulated solar radiation experienced by the arriving air masses during these events means that there should be little available nucleating vapours (less oxidation before reaching ZEP). Two other Arctic sites, namely Utqiaġvik, Alaska, and Tiksi, Russia, also observe NPF events without the sites experiencing any solar radiation (Asmi et al., 2016; Kolesar et al., 2017). However, at these two sites the suggestion is that anthropogenic emissions of semi-volatile gases from nearby oil fields or the build-up of anthropogenic emissions during the haze period can explain these events, an interpretation which is not applicable for ZEP.

The vertical component of the arriving back trajectories associated with these polar-night events shows that air masses originated from higher altitudes (Fig. S17) and that these air masses descend before arriving at ZEP. One possible explanation for these types of events could be that precursor gases, originally emitted from the surface, are transported to high altitudes where the CS is sufficiently low enough to allow them to survive long enough to be nucleated on descent to ZEP. The air masses travel further south and higher in altitude, where the small amount of solar radiation potentially allows for photochemical production of nucleating vapours to build up.

The median duration of NPF events, including their subsequent growth, is approximately ∼ 10 h and seems to be fairly consistent across the annual cycle, with a decrease towards the autumn (see Fig. 3a). Of all events, 75 % > 7 h, and 90 % > 4 h. During the sunlit period, the starting time of events is typically around 09:00 (UTC) for the period April to August. From September onwards, the onset of the observed NPF shifts to later in the day (Fig. 3b). For the period August to October, onset of NPF is approximately 8 h after sunrise at Ny-Ålesund (note that the gradient of the two slopes in Fig. 3b remains constant, but the start time is shifted by 8 h). This could reflect that during the NPF season there is a delay of approximately 8 h from the minimum solar intensity to the onset of NPF, and this could be related to the time it takes for precursor gases to accumulate.

Lee et al. (2020) suggested that the duration of NPF at ZEP was approximately 6–7 h, with the longest duration in summer. In addition, NPF start times were 13:00–14:00 (local time, which is 11:00–12:00 UTC in the summer time). The start times observed at ZEP, here in this study, were typically 2 h earlier, perhaps as a result of the slightly lower minimum particle diameter detection and not the same definition of the onset of nucleation.

The mean (median) GRs for all the events are 2.2 (1.5) nm h⁻¹. For Class Ia, Ib, and II events the average GRs are 1.4 (1.0), 1.7 (1.2), and 2.6 (1.2) nm h⁻¹, respectively. The largest GRs occur during July: 4.0 (2.1) nm h⁻¹. The polar-night events exhibit a significantly reduced GR of 0.43 (0.35) nm h⁻¹ (see Fig. 4a). Using the npf-event-analyser for the Class Ia events the GRs are 0.9 (1.1), 2.1 (2.6), and 4.1 (4.4) nm h⁻¹ for 3–7, 3–25, and 7–25 nm diameter ranges.

The GRs presented here agree well with earlier estimates of GRs by Nieminen et al. (2018) reporting a GR_10−25 nm at ZEP within the range of 1.2–1.6 nm h⁻¹. Kerminen et al. (2018) report a median GR for the Arctic of 2.3 (0.23–4.1, 5th and 95th percentiles) nm h⁻¹, the site type (i.e. compared with other geographical regions) with the smallest GRs.

Formation rates for J3-7nm are 0.14 ± 0.23 cm⁻³ s⁻¹ (mean ± SD) for all events in which calculations of J and GR could be ascertained (see Fig. 4b for the seasonality). Formation rates are generally greater in May, with 2023 not exhibiting this maximum in May. The formation rates for J3-7nm, J3-25nm, and J7-25nm are estimated to be 0.28 ± 0.33, 0.40 ± 0.35, and 0.31 ± 0.28 cm⁻³ s⁻¹ (mean ± SD) for Class Ia events (using the max concentration method and npf-event-analyser; see Sect. 2.3.3 in the Methods).

Previous studies also estimate J for various diameters at Ny-Ålesund and ZEP. Beck et al. (2021) reports a J1.5 equal to 0.27 cm⁻³ s⁻¹ (Beck et al., 2021). Nieminen et al. (2018) presents the seasonal medians for Jnuc of nucleation mode particles (10–25 nm) varying from 0.08 cm⁻³s ⁻¹ in spring to 0.032 cm⁻³ s⁻¹ in summer and to 0.0066 cm⁻³ s⁻¹in autumn. Lee et al. (2020) give J3-7, J7-25, and J3-25 values ranging between 0.001–0.54, 0.003–0.5, and 0.007–0.61 cm⁻³ s⁻¹, respectively, and the averages for J3-7, J7-25, and J3-25 are 0.04, 0.09, and 0.12 cm⁻³ s⁻¹. Kerminen et al. (2018) report a median Arctic J (i.e. varying size ranges) of 0.51 cm⁻³ s⁻¹.

In comparison to GRs and Js at other sites (e.g. Kerminen et al., 2018; Nieminen et al., 2018), we see that processes within the Arctic, as observed at ZEP, are significantly slower. In urban environments, compared with more remote ones, estimations for J are significantly larger due to the larger coagulation sink that needs to be overcome (Cai and Jiang, 2017); here, the coagulation sink is much lower than in urban environments.

The concentration of condensable vapours (Cv) required to sustain the GRs is estimated using Eq. (3) and the calculated growth rates for the various classes of events (i.e. Class Ia, Ib, and II). We show that Cv increases until July before decreasing during the autumn and into the winter months. It is striking to note that the seasonal variation is similar to that of the sum of the measured concentrations of potential aerosol precursor gases measured in Ny-Ålesund during a 2017 campaign (see Fig. 5). The estimated Cv is also of a similar magnitude to the combined sum of measured HOMs, sulfuric acid (H₂SO₄), methanesulfonic acid (MSA), and iodic acid (HIO₃). For Ny-Ålesund, Beck et al. (2021) report increasing IA, SA, and MSA concentrations from the start of the sunlight period and high concentrations prevailing before decreasing around mid-June. HOM concentrations averaged around ∼ 1.8 × 10⁶ cm⁻³ during the spring before increasing to 2.3 × 10⁶ cm⁻³ in June. As a ratio of the total available precursor vapours HOMs account for approximately 0.78 of the entire concentration of precursor vapours after June, and prior to June this fraction was approximately 0.24 (see Fig. S24). It can therefore be argued that the composition of condensable vapours undergoes a dramatic transformation around the start of June, and the composition of newly formed particles during the initial spring peak is different to that of the subsequent peaks after June (see Figs. 1 and 2). Boyer et al. (2024) measured the concentrations of condensable vapours in the Arctic, however at higher latitudes (> 80° N). The estimated Cv at ZEP was on average 5.9 times greater than the combined concentrations of the measured precursor gases given in Boyer et al. (2024) (see Fig. S23). At higher latitudes (> 80° N), there is potentially less photochemistry and biological activity; moreover, the potential sources of precursor gases are more limited (Brean et al., 2023) and may be more influenced by the sea ice cover, further reducing the availability of precursor gases and giving rise to the difference between the estimated Cv at ZEP and total concentrations during MOSiAC.

In Sect, 4.1 we define a region of interest, whereby measurements within this ROI provide an indication of the conditions likely to lead to an NPF day. Observing when these conditions occur offers one approach; however, the ability to predict the occurrence of NPF days can be improved by simply using the proxies for a source and a sink and taking their respective ratio (i.e. solar insolation/CS) (see Fig. 11). For a rolling average window of 30 d the R2, comparing solar insolation/CS and the nano-ranking frequency, is 0.78 (see Fig. S26).

Figure 11 demonstrates that by using a simplified parameter, i.e. solar insolation/CS, albeit with a large rolling averaging window, we achieve a good agreement with both event frequencies (i.e. classified using the Dal Maso et al., 2005, or Aliaga et al., 2023, approach). There are some slight discrepancies between the solar insolation/CS parameter and the event frequencies, particularly at the start and end of the measurement period; the discrepancies could be due to the NPF seasons having started already or not having ended. The relationship between solar insolation/CS and event frequency varies depending on the averaging window utilised, whether the ML is selected, and also the type of classification used (see Fig. 12). The coefficient of determination (R2) comparing solar insolation/CS and the daily event frequency (i.e. rolling average applied) increases and begins to plateau after a window of 2 weeks is applied (14 d, R2 = 0.65) (see Fig. 12). Considering that a degree of averaging needs to be performed as the daily event frequencies are given as 1 s (event) and 0 s (non-event), it seems justified that the solar insolation/CS parameter offers a robust predictive capability once a modest amount of smoothing is performed.