Milan is located in the Po Valley (Fig. 1a) at the coordinates 45.47° N, 9.19° E, at an altitude of 120 m a.s.l. It is the most populated city of the Po Valley with a population of ∼1.4 million, reaching ∼3.2 million when considering the entire metropolitan area (ISTAT, 2024). Our measurements were taken in an urban background area, referred to as the Pascal area (Fig. 1b) due to the presence of the Pascal air quality monitoring station of the regional environmental agency (ARPA Lombardia). The area is located in the eastern part of the city of Milan, and the instruments were installed at the Physics (45.4764° N, 9.2317° E) and Chemistry (45.4754° N, 9.2329° E) Departments of the University of Milan (UNIMI). This is an urban background area, which is affected by several sources of pollution, such as traffic, domestic heating, and transported industrial and agricultural emissions (Colombi et al., 2023).

Our size distribution measurements were performed with a set of three instruments: a TSI Scanning Mobility Particle Sizer (SMPS), an Airel Neutral cluster and Air Ion Spectrometer (NAIS), and an Airmodus A11 nano-Condensation Nucleus Counter (nCNC) system, combining an Airmodus A10 Particle Size Magnifier (PSM) and an Airmodus A20 Condensation Particle Counter (CPC). The nCNC and the SMPS were located on the second floor of the Chemistry Department of UNIMI and measured particle number size distributions between 1.2 and 3 nm (Lehtipalo et al., 2022) and between 11 and 480 nm, respectively. The NAIS measured number size distributions of particles with a diameter between 2.5 and 40 nm and of positive and negative ions with a diameter between 0.8 and 40 nm (Manninen et al., 2016; Mirme and Mirme, 2013). The instrument was located on the first floor of the Physics Department of UNIMI, at a distance of about 160 m from the nCNC and SMPS measurements. While the difference in location between the NAIS and the other instruments may have introduced some uncertainty, all inlets faced the interior of the University's yard, which is not constantly affected by one specific source (for example, traffic), and can, therefore, be considered representative of Milan urban background. For this reason, the combination of the data by these instruments was considered reasonable regardless of their different location. The NAIS measurements began in March 2023 and ended in February 2025, while those of the nCNC and the SMPS started in May 2023 and ended in March 2024. The particle number size distribution data between 27 March 2023, and 26 March 2024 were used for this study.

Considering the high number concentration of sub-3nm particles in the city, the nCNC was equipped with an Airmodus Nanoparticle Diluter (AND; Lampimäki et al., 2023) running with a dilution factor of 5 and measuring instrumental background automatically three times a day for 8 min. The system was run with a core sampling inlet, as integrated into the AND design. Using a dry flow for the dilution, the AND also acted as a dryer. The AND inlet consisted of a 40 cm stainless steel tube sampling ambient air at a flow rate of about 6 L min⁻¹, while the PSM, connected to the AND through a conductive tube, worked with a flow rate of 2.5 L min⁻¹. The nCNC measured in scanning mode with saturator flow scanning between 0.1 and 1.3 L min⁻¹. Each scan lasted 4 min. To guarantee the correct functioning of the instrument, several checks and cleaning procedures were applied. Every week, both the PSM and the CPC were drained, and their connection was cleaned with isopropanol and compressed air. The involved flows and the background were also manually checked. Flushing of the PSM was performed once every two weeks, while the inlet line was cleaned once a month. The overall status of the instrument was checked almost every day. The data from the nCNC were inverted using the kernel inversion method and applying the corrections for the background, the detection efficiency, the dilution factor, and the inlet losses, estimated to be between 20 % and 9.3 %, depending on the particle size (Lehtipalo et al., 2022).

The SMPS (Wang and Flagan, 1990), consisting of a 3080 TSI classifier, a 3081 TSI DMA, and a 3772 TSI CPC, was equipped with a stainless steel inlet drawing 1 L min⁻¹ of ambient air, a 4.9 kV X-ray tube to provide particles with a known charge distribution, and with a silica gel dryer to reduce the relative humidity of the air sample. The DMA scanned between ∼10 and ∼9700 V during a cycle of 3 min, producing size distributions between 11 and 480 nm. Weekly checks of the performance of the instrument included CPC draining and flow checks. The inlet line was cleaned once a month with isopropanol and the silica gel was regenerated when needed. The data were inverted using the TSI Aerosol Instrument Manager program. The data were corrected for counting errors due to multiple charging. For both the nCNC and the SMPS, no clear step changes associated with cleaning were identified and any observed variations did not indicate clear effects of the cleaning procedures.

The NAIS was equipped with a 50 cm copper inlet followed by a downward bend to prevent rain from entering the instrument, resulting in a total inlet length of approximately 60 cm. Ambient air was sampled at a flow rate of 54 L min⁻¹. The instrument measured in particle, ion, and offset mode, changing mode every 90 s. Considering the high inlet flow rate of the NAIS, drying the sample flow was not possible. Instrument cleaning was performed when needed. Concentration increases in specific size bins were used as indicators of electrometer noise and to identify the need for cleaning. These artificially high concentrations were manually excluded from the analysis, and no clear systematic step changes associated with cleaning were observed. The measured data were inverted automatically by the Spectop software following the procedure described by Mirme and Mirme (2013). The data were then corrected for inlet losses (between 15 % and 0.1 %, depending on the particle size; Gormley and Kennedy, 1948) and ion calibration (Wagner et al., 2016). The final particle number size distributions were obtained by averaging those from the positive and negative columns.

Figure 2 illustrates the data availability throughout the campaign. Of all the instruments, the NAIS provided the most comprehensive data coverage, recording data on approximately 95 % of the time. On the other hand, the nCNC and SMPS recorded data for about 40 % and 42 % of the time, respectively. Measurement gaps mostly resulted from technical challenges, including high summer temperatures, power outages, CPC flooding, and delays in equipment shipments.

The total size distributions were obtained by combining the nCNC, NAIS, and SMPS data. First of all, all the data were resampled to a 15-minute time resolution and rebinned to a diameter resolution of 0.05 in log10 scale. Then, the median size distributions of the three instruments were compared for the periods when all three instruments were operating simultaneously (Fig. 3). A scaling factor of 3.8 was applied to the NAIS data, following the approach proposed by Dada et al. (2023). The scaling factor was obtained by comparing the NAIS and SMPS data in the overlapping size region. Then, the number size distributions from the three instruments were combined using the concentrations measured by the nCNC for the particles smaller than 2.2 nm, by the NAIS for the particles in the 2.2–25 nm size range, and by the SMPS for the particles larger than 25 nm. Using the SMPS as a reference instrument, an artifact at the connection between the nCNC and the NAIS data was created.

The relevance of UFP has led the European Union to enforce the measurement of their number concentration. As reported in Sect. 1, a 10 nm cut-off was chosen to define UFP. In Fig. 4, the total particle number concentration for different cut-off sizes was calculated by integrating the size distribution from different lower limits (2, 5, and 10 nm) to the upper limit of 480 nm. In our dataset, lowering the threshold from 10 to 5 nm would result in an average increase of 14 %, whereas adopting a 2 nm cut-off would lead to a 19 % increase (Fig. 4a). Figure 4b shows the variability of the ratio between the concentration for a certain cut-off size (2, 5, 10 nm) and the total particle number concentration. These considerations highlight the potential impact of measurement thresholds on reported UFP number concentrations and emphasize the importance of detailed measurements of sub-10 nm particles. While the availability and complexity of the instrumentation pose significant challenges to measuring sub-10 nm particles, the dataset presented in this work demonstrates the value of extending the measurements below 10 nm.

The study used meteorological and air pollutant concentration data provided by ARPA Lombardia, the regional environmental agency responsible for managing multiple monitoring stations across the area. For the analysis, data from the Pascal station, situated approximately 250 m from the UNIMI buildings, were utilized. The meteorological dataset included variables such as atmospheric temperature, wind speed and direction, radiation, and relative humidity. The pollutant concentrations included PM₁₀, PM_2.5, NO₂, SO₂, O₃, NO_x, ammonia, and equivalent black carbon (eBC, Savadkoohi et al., 2024).

ARPA Lombardia also provided BLH data from the nearby station of Milano Parco Nord. The BLH was estimated using the Gryning-Batchvarova model for the daytime convective boundary layer (Batchvarova and Gryning, 1991) and the Zilitinkevich model for the nocturnal stable boundary layer (Zilitinkevich and Baklanov, 2002). Both models used turbulence variables that were measured by ARPA Lombardia with a triaxial ultrasonic anemometer at the Milano Parco Nord station. The choice of the appropriate model was based on the assessment of the boundary layer stability, determined from the sensible heat flux, also measured by the ultrasonic anemometer at the same site. Briefly, the Gryning-Batchvarova model describes the daytime convective boundary layer using a simplified analytical approach. The profiles of the main variables are schematized considering that, throughout the boundary layer, each variable assumes a constant value equal to its vertical mean, the entrainment layer is considered to be of infinitesimal thickness, and that, at the entrainment layer, there is a characteristic discontinuity for each variable. For the assessment of the stable boundary layer, Zilitinkevich et al. (2007) developed theoretical models considering simple equilibrium regimes in a step-by-step approach. They applied Large Eddy Simulation to validate their theoretical multi-limit BLH formulation, which reduces to known asymptotic limits in the neutral and nocturnal stable regime. Indeed, the stable and neutral BLH evolution is controlled by factors (e.g., baroclinic shear, large-scale vertical velocity at the top of the boundary layer, non-stationarity of the boundary layer and its horizontal heterogeneity) that are difficult to measure and to use for the validation of the theory.

All data were provided with an hourly time resolution. Using these datasets, we calculated the daily ventilation index (VI), which reflects the potential of pollutants to disperse efficiently through proper ventilation. For each day, this index is defined as: 1VI=mean(ws)⋅max(BLH), where ws is the wind speed, and BLH is the boundary layer height during that day. In line with ARPA Lombardia guidelines, a VI value of 400 m² s⁻¹ was used as threshold to identify stagnant days.

The particle number size distributions in Milan exhibited a clear seasonal cycle, which is illustrated in Fig. 5a and b through the daily median size distribution surface plot per season and the median size distribution per season, respectively. The months of December, January, and February were included in winter; March, April, and May in spring; June, July, and August in summer; September, October, and November in autumn.

During winter, the highest concentrations of particles larger than 50 nm were observed (Fig. 5b). This increase was probably the result of both a decrease in the BLH and an increase in biomass burning emissions (Colombi et al., 2023). Moreover, the typical traffic-related pattern was evident, with marked increases across all particle size ranges starting from 05:00 and 17:00 Central European Time, UTC+1 (Fig. 5a), coinciding with the morning and evening rush hours.

In spring, and particularly in summer, these traffic-related peaks became less pronounced, suggesting an increase in the atmospheric mixing. Additionally, the data revealed a clear midday increase in sub-10 nm particles (Fig. 5a), which was most likely associated with NPF events. This phenomenon, which became more pronounced in the warmer months, was driven by photochemical reactions, enhanced by higher solar radiation and it was, therefore, mostly observed during spring and summer. During summer, we observed the most significant increase in sub-10 nm particle number concentrations, alongside the lowest levels of particles larger than 100 nm (Fig. 5b).

In autumn, the traffic-related peaks reappeared (Fig. 5a) due to the combined effect of the increase in traffic emissions (Colombi et al., 2023) and the decrease in atmospheric dispersion and BLH, becoming again a more dominant factor influencing particle number concentrations. However, the median concentrations across all particle sizes during autumn remained similar to those observed in spring, indicating a seasonal transition towards winter. Overall, though, considering the discontinuities in the data collection (Fig. 2) and the definition of each season, these conclusions may not be representative of each entire season and their comparison has intrinsic uncertainties.

The shape and values of the median size distributions in Fig. 5b are in agreement with those reported for other urban background sites of southern, central, and eastern Europe (Trechera et al., 2023). The comparison between the characteristics of the size distribution surface plots per season (Fig. 5a) in Milan and other urban background sites (Trechera et al., 2023) also does not point out any anomaly. As observed in Milan, several other urban background sites across Europe showed a more pronounced increase in sub-25 nm particles at midday during the warmer months. Higher concentrations in the same size range due to traffic rush hours were also recorded in all urban background sites (Trechera et al., 2023).

Other than this qualitative comparison, a quantitative one was also performed, and the concentrations in the nucleation, Aitken, and accumulation modes measured in Milan were compared with the values reported for other European cities. The average number concentrations for particles in the 10–25, 25–100, and 100–480 nm size ranges were 2642, 4080, and 1819 cm⁻³, respectively. Regarding the accumulation mode, Milan fell within the typical southern European cities, characterized by high concentrations of particles in this size range. The Aitken mode in Milan exhibited a lower average concentration compared to other southern European cities (4800–5900 cm⁻³), but lay at the upper end of the range reported for central European cities, characterized by intermediate concentrations in this mode. Finally, intermediate concentration values were recorded in the nucleation mode in Milan. This comparison, though, should be interpreted with caution as it may be affected by several uncertainties. In fact, while the data presented by Trechera et al. (2023) refer to the years 2017–2019, the data presented in this study cover a single year (2023–2024), characterized by several gaps in the data availability, affecting especially the calculations in the Aitken and accumulation modes. Moreover, differences in the instruments cut-off diameters may further bias this comparison.

The ratio between the average particle number concentration in the nucleation mode (N₁₀₋₂₅) and eBC was used to qualitatively assess the relative contributions of primary and secondary emissions in Milan compared to other European urban background sites. Milan exhibited an intermediate-low N10-25/eBC ratio (∼1444 cm⁻³ µg⁻¹ m³), within the approximate range of 900–4500 calculated for other cities (Trechera et al., 2023). This suggests that primary emissions (traffic) dominated the nucleation mode particles in Milan, whereas in other European sites, photochemistry played a more significant role.

The nanoparticle ranking analysis was applied to characterize NPF. At higher percentile ranks, a midday increase in particle number concentration across all size ranges became clear, indicating NPF (Fig. 6). The process was marked by an initial rise in 1.2 nm particle number concentration, followed by an increase in the concentration of larger particles. This pattern indicates that NPF occurred over a wide area, including Milan itself. At lower percentile ranks, higher concentrations associated with traffic rush hours were evident, but they gradually faded at higher percentile ranks (Fig. 6, panels a to e). This pattern aligned with the seasonal variations in particle size distributions and NPF (Figs. S4, 5a). In fact, lower ranking values ΔN2.5-5, corresponding to weaker NPF, were more frequent during winter (December to February, Fig. S4), when traffic peaks were also more evident (Fig. 5a). Conversely, the strongest NPF events were observed in April and mid-to-high rank values (percentile ranks between 60 and 80) occurred predominantly between June and August (Fig. S4), when stronger atmospheric dispersion minimized the concentration of traffic-related peaks (Fig. 5a).

Our analysis demonstrates that NPF significantly contributed to the UFP number concentration through a growth process that lasted for several hours. As shown in Fig. 7, the concentration of sub-2.5 nm particles increased first around 07:00, followed sequentially by that of 2.5–5, 5–10, and 10–25 nm particles, reflecting a well-defined growth pattern in increasing size order. Accurately distinguishing the contribution of NPF from that of primary emissions is crucial for a proper interpretation of these patterns.

GR were calculated as described in Sect. 2.4.4. The values of 1.8, 2.9, and 9.7 nm h⁻¹ were found for the GR in the size ranges of 3–7, 7–20, and 20–100 nm, respectively. The formation rates J1.5, J3, and J7 are presented in Fig. 8. While J3 correlated with percentile ranks – indicating higher production of 3 nm particles (higher J3) during stronger NPF days (higher percentile rank) – J1.5 remained relatively constant across most ranks. This suggests that clustering, which formed 1.5 nm particles, occurred at the site, but only under certain conditions the particle growth was observed (Kulmala et al., 2013). J1.5 reached higher values only in the 80–100 rank bin, suggesting that clustering was more efficient during strong NPF days. Lastly, J7 did not show a clear increasing trend and was often higher than J3, likely due to the influence of traffic in this size range. This is supported by Fig. 5a, where morning traffic peaks are clearly visible in the 5–10 nm size range. The ratio between J7 and J3 suggests that, for days with rank below the 80th percentile, traffic was a stronger source of particles larger than 7 nm than NPF. During high-rank days (80–100th percentile), when NPF events were stronger, a marked increase in J7 would have been expected as result of a dominant contribution from NPF. However, such an increase was not clearly observed, implying that traffic may have remained the dominant contributor to particles larger than 7 nm even during the most intense NPF days. This result agrees with the discussion in Sect. 3.1 about the relevant role of traffic compared to photochemistry in Milan in the 10–25 nm size range. As mentioned in Sect. 2.4.4, formation rates were calculated only for the days when all the instruments were measuring simultaneously and, therefore, the data availability shown in Fig. 2 should be taken into account when interpreting Fig. 8.

The nanoparticle ranking method allows a continuous analysis of the NPF process in relation to meteorological and dispersion variables and pollutant concentrations. To understand which parameters affected the process, the atmospheric conditions within each bin of 20-percentile of NPF rank were compared. Figure 9 illustrates the relations between CS and ventilation index VI, defined in Eq. (1), and rank as an example. Higher CS corresponded to low-rank days, while a high VI corresponded to high-rank days. NO₂, NO_x, eBC, SO_2, PM_10, and PM_2.5 concentrations reported the same trend as CS, while BLH behaved as the ventilation index (Figs. S5, S6, and S7). Therefore, enhanced NPF was, on average, associated with cleaner air conditions and stronger atmospheric mixing. In particular, intermediate-strong NPF (percentile rank >60) happened mostly during non-stagnant days and when the CS was relatively low (<0.007 s⁻¹ on average). As reported in Sect. 2.4.3, the CS was calculated only for the days when both the SMPS and NAIS provided good data availability. As a result, the CS time series contains several gaps (Fig. 2), which affect Fig. 9a.

Our data allowed a comparison between the environmental conditions and NPF in Milan and in other urban locations. In Milan, the CS varied between 0.01 s⁻¹ (during strong NPF events, Fig. 9a) and 0.03 s⁻¹ (during weak NPF events, Fig. 9a), which is comparable to the values observed in Shanghai (CS between 0.01 and 0.02 s⁻¹ on average; Yao et al., 2018). However, while the particle formation rate at 1.5 nm (J1.5) in Milan remained below 10² cm⁻³ s⁻¹ (averaging around 10¹ cm⁻³ s⁻¹), it reached up to 10³ cm⁻³ s⁻¹ in Shanghai (Yao et al., 2018). This is likely due to differences in the precursor vapor concentrations and atmospheric conditions. However, without precursor vapor measurements in Milan, this hypothesis remains uncertain. GR also differed between the two cities. In Shanghai, the GR was approximately 6 nm h⁻¹ for 3–7 nm particles and 9 nm h⁻¹ for 7–25 nm particles (Yao et al., 2018), whereas in Milan, the values were significantly lower, specifically, 1.8 and 2.9 nm h⁻¹ for 3–7 and 7–20 nm particles, respectively. A similar relation was observed in Nanjing, where both recorded GR and J were higher than in Milan. For example, the average J3 in Nanjing ranged between 7.4 and 13.9 cm⁻³ s⁻¹, while the GR of 10 nm particles was between 13.4 and 14.5 nm h⁻¹, depending on the type of event (Dai et al., 2023).

NPF has also been extensively studied in European cities. In Barcelona, for instance, Brean et al. (2020) reported an average GR of 4.69 and 4.36 nm h⁻¹ for 4.5 and 1.9 nm particles, respectively. The CS in Barcelona was lower during NPF event days compared to non-event days, but it remained below 0.02 s⁻¹ in both cases, slightly lower than the values recorded in Milan. When comparing formation rates, Milan exhibited weaker NPF. While J1.9 in Barcelona frequently fell between 10 and 103 cm⁻³ s⁻¹ (Brean et al., 2020), J1.5 in Milan was mostly limited to the range of 1 to 10 cm⁻³ s⁻¹, indicating a lower particle formation intensity. In Budapest, the GR of 6 nm particles was 7.7 nm h⁻¹ on average, while J6 was 4.2 cm⁻³ s⁻¹, higher than what was observed in Milan in both cases. The CS in Budapest was lower than in Milan during non-event days but in line with Milan values during NPF event days (Salma et al., 2011). Finally, the study by Bousiotis et al. (2021) compared size distributions and NPF characteristics in several urban sites across Europe (Denmark, Germany, Spain, Finland, and Greece), distinguishing urban background and roadside sites. Reported J10 were higher in roadside sites, but overall lower than what was observed in Milan. On average, they remained below 0.1 cm⁻³ s⁻¹ in all sites, except for German roadside sites, where the average J10 was higher but still below 0.2 cm⁻³ s⁻¹. The reasons for these differences may partially reside in the differences across sites, but they are not clear. GR for 10 nm particles was, on average, between 2 and 5 nm h⁻¹, in line with the value found in Milan for that of 7 nm particles (2.9 nm h⁻¹).

If we compare our results to previous studies in the rural areas of the Po Valley, it is clear that lower J1.5 were observed in Milan. Cai et al. (2024) observed an average J1.7 of 10² cm⁻³ s⁻¹ in San Pietro Capofiume during NPF days, which was significantly higher than what was found in Milano (J1.5 was about 3 cm⁻³ s⁻¹). However, the values for J3 and J7 were more similar. GR were also higher than in Milan (around 4 nm h⁻¹ for 3–7 nm particles and around 5 nm h⁻¹ for 7–15 nm particles). The recorded CS was below 0.01 s⁻¹ during both NPF and non-NPF and therefore lower than in Milan, where NPF is possibly more suppressed than in the rural areas.

When comparing all the results, though, it is critical to take into consideration the possible differences in the methodologies for estimating the formation and growth rates, including the slightly different size ranges used in different studies, which contribute to the uncertainty of the comparisons.

The analysis of NPF in relation to the meteorological conditions pointed out that strong wind from northwest was a favorable condition for NPF at this site (Fig. 10). In order to explore further such relation and the characteristics of the air masses that favor the formation of new particles, the Lagrangian particle dispersion model FLEXPART, driven by the meteorological output from WRF simulations, was applied to identify the eventual preferential air mass direction for NPF and its characteristics.

The air mass trajectory density, calculated as described in Eq. (8), emphasizes that north, particularly northwest, was the preferred direction for NPF (Fig. 11). An east-west axis distinctly separated the north and south sectors: air masses arriving in Milan from the north promoted NPF, while those from the south hindered it.

Focusing on the Po Valley only (Fig. 12), it is clear that a lower air mass residence time in the area produced stronger NPF. This agrees with both the anticorrelation between NPF rank and wind speed and with the anticorrelation between NPF rank and pollutant concentrations, as the Po Valley is rich in emission sources. Lower exposure to anthropogenic emissions enhanced NPF in this location, as shown in Fig. 13. Lower air mass exposure to NO_x and SO₂ emissions was associated with higher concentration of small (sub-2.5 nm) particles, to a broader cluster band, extending to 2.5 nm, and to a smaller accumulation mode. On the other hand, at higher NO_x and SO₂ air mass exposure, the cluster particles remained smaller (up to ∼1.5 nm) and had lower concentrations. Furthermore, the accumulation mode reached larger sizes. Overall, these observations indicate that lower air mass exposure to anthropogenic emissions favored the formation of new particles. The air mass exposure to both NO_x and SO₂ emissions anticorrelated with the median ventilation index, which decreased at increasing air mass exposure, supporting the role of atmospheric ventilation (Fig. 13). Considering the data availability described in Fig. 2, the number of data points used in the calculation of the average concentrations shown in Fig. 13 may vary depending on the diameter.

The role of sulfuric acid, which has been identified in previous studies as a critical precursor vapor in the Po Valley (Cai et al., 2024), was investigated through its proxy, calculated as described in Sect. 2.4.5. The sulfuric acid proxy exhibited an increasing trend with the percentile of NPF rank (Fig. 14a), suggesting its potential contribution to the NPF process. No clear correlation between sulfuric acid and SO₂ concentrations was observed (Fig. 14b), indicating that SO₂ was not a limiting factor for sulfuric acid formation in Milan. On the other hand, sulfuric acid showed a clear increase with radiation (Fig. 14b and more clearly, Fig. S8), hinting at the role of photochemical processes for its formation rather than SO₂ availability or a sink effect. Indeed, while on average, a higher sulfuric acid proxy was recorded in correspondence with lower CS (Fig. S8), several cases with low CS and low sulfuric acid were observed and were linked to low radiation. The relative roles of CS and sulfuric acid in NPF were then investigated using the concentration of 2.5–5 nm particles as a proxy for NPF intensity (Sect. 2.4.1). Figure 14c clearly presents an inverse correlation between N_2.5−5 and CS, indicating the relevant role of the CS in inhibiting the NPF mechanism. On average, higher concentrations of sulfuric acid proxy were associated with stronger NPF (Fig. 14a and c). However, given the large variability in the trend, its role is less clear. The gaps in the CS time series due to the limited SMPS data coverage are reflected into the SA proxy time series and may affect Fig. 14.

The results described so far were obtained using the entire dataset regardless of the environmental conditions. However, treating different atmospheric regimes, such as ventilated and stagnant conditions or different seasons together may create biases in the interpretation of the drivers of NPF and hide potentially relevant patterns. To evaluate the robustness of our conclusions in different regimes, we performed an additional stratified analysis separating stagnant and non-stagnant conditions and different seasons (see Supplement) and applying the nanoparticle ranking analysis on each subset. The two analyses (seasons and stagnant/non-stagnant) were performed separately, and the stratifications were not combined due to the limited amount of data.

Despite the differences in background conditions, the main conclusions did not change when analyzing separately stagnant and non-stagnant periods. CS values were generally higher under stagnant conditions compared to non-stagnant ones; however, in both regimes, the CS decreased with increasing NPF rank, indicating that stronger NPF preferentially occurred under lower CS conditions, independently of the level of stagnation (Fig. S9a). SO₂ concentrations showed a less clear behavior and did not appear to limit NPF both under stagnant and non-stagnant conditions (Fig. S9b). Sulfuric acid proxy and J3 increased with NPF rank in both regimes (Fig. S9c, d).

Considering that seasonality may have still introduced some bias in the interpretation of these results (Table S1), a separate study for each season was performed. Seasonal stratification revealed higher CS values in winter compared to the other seasons. In winter and autumn, the CS clearly decreased with increasing NPF rank, while this relation was weaker in spring and summer (Fig. S11a). J3 was more difficult to interpret on a seasonal basis, particularly in summer, due to the limited data availability. Nevertheless, J3 generally increased with NPF rank in all seasons, consistently with the results from the non-stratified dataset (Fig. S11e). SO₂ concentrations were generally higher in winter than in the other seasons due to the enhanced emissions and the weaker dispersion conditions. In winter, SO₂ showed a decreasing trend with increasing NPF rank (Fig. S11c), in agreement with the opposite relation between NPF rank and SO₂ observed in the non-stratified analysis. In spring, summer, and autumn, SO₂ concentrations were lower and did not exhibit a clear trend with NPF rank. Similar SO₂ levels associated with both weak and strong NPF events suggest that SO₂ availability was not a limiting factor for NPF intensity during these seasons. The sulfuric acid proxy did not show a clear relation with NPF rank in most seasons, except for autumn, when an increasing trend was observed (Fig. S11d).

The analysis of NPF after stratifying different atmospheric conditions does not contradict the results obtained with the entire dataset. However, drawing conclusions may be misleading. In fact, the stratification led to a low amount of data per class, reducing the reliability of the results. Furthermore, the NPF intensities in the different groups (seasons, stagnant and non-stagnant) may not be comparable, considering that the nanoparticle ranking was applied separately on each subset (Fig. S10). To assess this, the concentration of 2.5–5 nm particles was also used as proxy for NPF intensity other than the percentile rank (Fig. S11f, g). A larger dataset would allow a more in-depth analysis of how different regimes may affect NPF and of the main drivers of this process in various atmospheric conditions.

In this section, we present an example of NPF day, featuring the characteristics discussed so far (lower CS and eBC concentration, higher BLH, and lower exposure to anthropogenic emissions). Specifically, we focus on 17 November 2023, a day that fell within the 80–100 class of percentile rank (Fig. 15). On this day, local clustering led to an increase in the concentration of sub-3 nm particles starting at 8 am (UTC+1), followed by a subsequent rise in the concentration of particles up to 100 nm in diameter (Fig. 15a), indicating condensational growth. These phenomena were observed in correspondence with a decrease in CS, in eBC concentration, and in air mass exposure to NO_x emissions, as well as an increase in wind speed and BLH (Fig. 15a), suggesting strong atmospheric mixing. Additionally, the air mass trajectory analysis revealed a dominant flow from northwest (Fig. 15b). Oppositely to the average results, SO₂ concentration showed a sharp increase as the event began.

On this day, the phenomenon driving the free tropospheric air masses advection and atmospheric clearing was the Foehn wind, a warm, dry wind descending from the Alps, which brings clear skies and higher temperatures compared to seasonal averages, together with exceptionally low pollutant concentrations in the Po Valley. Specifically, on 17 November 2023, the Foehn wind was identified by the decrease in relative humidity, the daytime median temperature of 17.2 °C (above the daily monthly average of 11.8 °C), and the smooth radiation trend, indicating the absence of cloud cover. The air mass trajectory also confirmed the presence of this wind pattern. The increase in SO₂, the source of which still needs to be confirmed, may have further enhanced the formation of new particles, together with the decrease in CS.

Similar cases have been observed during the campaign but a detailed classification of Foehn wind event days would be needed to further characterize them in relation to NPF. This case study is consistent with the earlier observations that Foehn wind can create favorable conditions for NPF in the Po Valley (Rodríguez et al., 2005) and that it is a significant source of UFP even in urban Milan.