Source apportionment of particle number size distribution in urban background and traffic stations in four European cities

Ultrafine particles (UFP) are suspected of having significant impacts on health. However, there have only been a limited number of studies on sources of UFP compared to larger particles. In this work, we identified and quantified the sources and processes contributing to particle number size distributions (PNSD) using Positive Matrix Factorization (PMF) at six monitoring stations (four urban background and two street canyon) from four European cities: Barcelona, Helsinki, London, and Zurich. These cities are characterised by different meteor- ological conditions and emissions. The common sources across all stations were Photonucleation , traffic emissions (3 sources, from fresh to aged emissions: Traffic nucleation , Fresh traffic – mode diameter between 13 and 37 nm, and Urban – mode diameter between 44 and 81 nm, mainly traffic but influenced by other sources in some cities), and Secondary particles. The Photonucleation factor was only directly identified by PMF for Barcelona, while an additional split of the Nucleation factor (into Photonucleation and Traffic nucleation ) by using NO x concentrations as a proxy for traffic emissions was performed for all other stations. The sum of all traffic sources resulted in a maximum relative contributions ranging from 71 to 94% (annual average) thereby being the main contributor at all stations. In London and Zurich, the relative contribution of the sources did not vary sig- nificantly between seasons. In contrast, the high levels of solar radiation in Barcelona led to an important contribution of Photonucleati on particles (ranging from 14% during the winter period to 35% during summer). Biogenic emissions were a source identified only in Helsinki (both in the urban background and street canyon stations), that contributed importantly during summer (23% in urban background). Airport emissions con- tributed to Nucleation particles at urban background sites, as the highest concentrations of this source took place when the wind was blowing from the airport direction in all cities.

Ultrafine particles (UFP) are suspected of having significant impacts on health. However, there have only been a limited number of studies on sources of UFP compared to larger particles. In this work, we identified and quantified the sources and processes contributing to particle number size distributions (PNSD) using Positive Matrix Factorization (PMF) at six monitoring stations (four urban background and two street canyon) from four European cities: Barcelona, Helsinki, London, and Zurich. These cities are characterised by different meteorological conditions and emissions. The common sources across all stations were Photonucleation, traffic emissions (3 sources, from fresh to aged emissions: Traffic nucleation, Fresh traffic -mode diameter between 13 and 37 nm, and Urban -mode diameter between 44 and 81 nm, mainly traffic but influenced by other sources in some cities), and Secondary particles. The Photonucleation factor was only directly identified by PMF for Barcelona, while an additional split of the Nucleation factor (into Photonucleation and Traffic nucleation) by using NO x concentrations as a proxy for traffic emissions was performed for all other stations. The sum of all traffic sources resulted in a maximum relative contributions ranging from 71 to 94% (annual average) thereby being the main contributor at all stations. In London and Zurich, the relative contribution of the sources did not vary significantly between seasons. In contrast, the high levels of solar radiation in Barcelona led to an important contribution of Photonucleation particles (ranging from 14% during the winter period to 35% during summer). Biogenic emissions were a source identified only in Helsinki (both in the urban background and street canyon stations), that contributed importantly during summer (23% in urban background). Airport emissions contributed to Nucleation particles at urban background sites, as the highest concentrations of this source took place when the wind was blowing from the airport direction in all cities.

Introduction
It has been widely reported that atmospheric particulate matter (PM) has a negative impact upon human health, with 7 million deaths per year attributed to the exposure to air pollution (WHO, 2018). Disentangling the impact on public health of the different sources contributing to PM would allow targeted policies to reduce emissions. Sources of mass concentrations of PM ≤10 µm and ≤2.5 µm in aerodynamic diameter (PM 10 and PM 2.5 , respectively) have been identified and quantified in different cities and regions around the world (e.g. Amato et al., 2016;Pancras et al., 2013;Viana et al., 2008;Wang and Shooter, 2005), but less is known about the sources and their contribution to ultrafine particle (UFP, particles ≤0.1 µm) number concentrations (PNC) (Vu et al., 2015). Previous studies suggest that sources dominating PNC differ from those dominating particle mass concentrations as detailed in Table S1 for the four European cities studied in this work. The quantification of the sources affecting UFP is very important as epidemiological studies suggest that negative health effects may be enhanced with decreasing particle size (Meng et al., 2013;Sioutas et al., 2005), although the associations between UFP and mortality or hospital admissions have been inconsistent in the literature (Kettunen et al., 2007;Lanzinger et al., 2016;Ohlwein et al., 2019;Samoli et al., 2016;Stafoggia et al., 2017;Tobías et al., 2018).
In urban areas, road traffic constitute the main source of UFP (Kumar et al., 2014;Morawska et al., 2008;Shi et al., 2001) but few attempts have been made to quantify its contribution to PNC Friend et al., 2012;Kasumba et al., 2009;Kim et al., 2004;Liu et al., 2014;Ogulei et al., 2006;Pey et al., 2009;Sowlat et al., 2016;Squizzato et al., 2019;Zhou et al., 2004Zhou et al., , 2005. Emissions from vehicles are dependent upon the vehicle technology and the properties of fuels and lubricant oils, as well as the driving conditions (Jones et al., 2012;Kittelson et al., 2002;Lähde et al., 2009;Maricq et al., 2002;Rönkkö et al., 2017Rönkkö et al., , 2014Sgro et al., 2008). Primary particles in the vehicle exhaust include soot particles with mean particle around 30-100 nm (Kittelson, 1998;Maricq et al., 2002) and solid core particles in the nucleation mode, usually below 10-15 nm (Rönkkö et al., 2017(Rönkkö et al., , 2013Sgro et al., 2008;Yao et al., 2005). Undiluted vehicle exhaust emissions, which are at very high temperatures, contain also a variety of different gaseous components, mainly volatile organic compounds (VOCs) and sulphuric acid. Since the saturation ratio of these gaseous compounds rises as the gas cools, these compounds either condense or nucleate to the particle phase immediately after the exhaust discharge to the atmosphere (Casati et al., 2007;Kittelson, 1998;Shi and Harrison, 1999). Which process predominates, condensation or nucleation, depends on the availability of pre-existing particle surface area (condensation sink; McMurry and Friedlander, 1979) along with the dilution and cooling rate (Morawska et al., 2008). Those nucleated particles have been named delayed primary aerosols by Rönkkö et al. (2017) since they are typically present in the particle phase in normal ambient air temperatures. Secondary particles are also generated from gaseous precursors from vehicle exhaust emissions when fully diluted within the ambient air and, driven by photochemistry, are oxidised by reactive species. This oxidation causes VOCs to turn into less volatile species, enhancing secondary aerosol formation by condensation and new particle formation (Gentner et al., 2012;Robinson et al., 2007;Volkamer et al., 2006).
Besides traffic, other sources are known to contribute to UFP. Ports and shipping emissions have been identified as source of UFP. Shipping emissions are characterised by high concentrations of VOCs and sulphur dioxide that result in the formation of secondary particles by nucleation and condensation processes (Kasper et al., 2007). Particle number size distributions (PNSD) from shipping emissions are characterised by an ultrafine mode with mode diameters ranging between 20 and 50 nm (Healy et al., 2009;Kasper et al., 2007). Sulphur content on shipping fuels has started to be controlled, with two areas in northern Europe in which sulphur emissions are tightly limited, including the Baltic Sea. Gas- (Brewer et al., 2016;Yu et al., 2018) and, specially, coal-fired power plants (Wang et al., 2011a) and airports (Cheung et al., 2011) are other relevant sources of ultrafine particles that may affect PNC in urban environment.
Ultrafine PNSD are complex. In contrast to the mass concentration, which is predominantly conservative, particles undergo several processes that modify their PNC and size such as new particle formation (nucleation), evaporation, condensation, deposition, and coagulation (Harrison et al., 2018). Therefore, freshly emitted particles may have a PNSD that may be transformed as these particles move away from the source (Zhu et al., 2002). Accordingly, primary particles would mainly influence the air quality near the emission source, while secondary particles would become more relevant as they travel away from the source to the urban background (UB; Morawska et al., 2008;Yao et al., 2005).
Therefore, there is a need for identification, characterisation, and quantification of the contribution of different sources contributing to PNC. Long-term measurements in different stations provide essential information for understanding the intricate relationship between local emission sources, particle atmospheric transformations, and meteorological processes. Numerous studies have investigated the effect on PNC and PNSD of specific sources in urban areas (Brines et al., 2015;Dall'Osto et al., 2013;Keuken et al., 2015;Zhu et al., 2002). However, long-term PNSD measurements are still scarce (Hofman et al., 2016;Pey et al., 2008;Reche et al., 2011b;Squizzato et al., 2019;Sun et al., 2019;Von Bismarck-Osten et al., 2013;Wang et al., 2011b) since UFPs are not a regulated pollutant. In addition, many different approaches are used to carry out source contribution analysis and direct comparison of results among studies is difficult. However, a number of source apportionment studies with Positive Matrix Factorization (PMF) applied to PNSD have been done before, mainly in the United States Ogulei et al., 2007;Squizzato et al., 2019;Zhou et al., 2004) but also in China (Liu et al., 2014), Australia (Friend et al., 2012), and Europe (Czech Republic: Leoni et al., 2018;Germany: Yue et al., 2008;UK: Beddows et al., 2015).
The aim of this work is to identify sources and processes and quantify their contributions to urban ambient concentrations of PNC, by using the same methodological approach applied to long-term measurements of PNSD in four European cities with varying climatic and emission patterns: Barcelona, Helsinki, London, and Zurich.

Monitoring stations
This study is based on data from four UB stations located in four European cities ( Fig. 1; Table 1) with different climatic conditions, emission sources, and urban morphology. Two street canyon sites (one in Helsinki and one in London) were also evaluated to compare with the sources observed at the UB sites.

Barcelona (Urban Background)
Barcelona is located in the Northeast coast of Spain, in the western Mediterranean Basin. With 1.6 million inhabitants (3.6 million in its metropolitan area) in 2016 (Eurostat, 2018). Barcelona has one of the highest cars densities in Europe (5,500 registered cars km −2 ; DGT, 2018), far above the traffic densities commonly observed in other cities across Europe (1,000-1,500 cars km −2 ). The traffic fleet is characterised by a high proportion of diesel cars (40%) and buses (89% in 2015;DGT, 2018). Moreover, Barcelona holds one of the main harbours in the Mediterranean Basin, which may be a significant source of air pollutants that can be often carried by the sea breeze towards the city. The airport is located in a near city (about 10 km away from the monitoring station), with around 300,000 operations per year (AENA, 2018).
The measurements were carried out at the Palau Reial UB monitoring site (BCN , Table 1) located in southwest Barcelona that is influenced by vehicular emissions from one of the main traffic avenues of the city (at an approximate distance of 300 m) with an average traffic density of 70,000 vehicles/working day.

Helsinki (urban traffic and urban background)
Helsinki is a coastal city situated in southern Finland, at the shore of the Gulf of Finland. It is the largest city in Finland with 0.6 million inhabitants (1.1 million if considering the metropolitan area) in 2016 (Eurostat, 2018). Helsinki's car density is around 1,400 cars km −2 (Statistics Finland, 2018). On average, Finland had a share of diesel vehicles of 26.8% in 2016 (http://www.aut.fi/en/statistics/long-term_statistics/share_of_diesel_cars). Helsinki's port was the busiest passenger port in Europe in 2017 with 12.3 million passengers (Port of Helsinki, 2018). Ships crossing the Baltic Sea must run on fuel with low sulphur content (International Maritime Organization MARPOL regulation). The airport has around 85,000 landings per year (FINAVIA, 2018) and it is about 13 km N from the UB station (HSK).
The SMEAR III (Station for Measuring Ecosystem-Atmosphere Relationships) UB station in Kumpula, Helsinki (HSK , Table 1), is located in an area with different urban land uses varying from allotment gardens to office areas (e.g. University of Helsinki) and single family house areas with relatively low traffic loads. The station is close (about 200 m) to one of the main roads to the city centre with an average traffic density of 50,000 vehicles/day (Järvi et al., 2009).
The traffic-monitoring site in Helsinki is adjacent to Mäkelänkatu and can be classified as a street canyon (HSK_SC , Table 1) with a traffic density of 28,000 vehicles/working day. In its 42 m of width, Mäkelänkatu has six lanes with two tramlines and rows of trees in the middle. The road is flanked by four-and five-storey buildings (height-to-width ratio of 0.4; Rönkkö et al., 2017). HSK_SC is located about 870 m southwest of the HSK site.

London (urban traffic and urban background)
London is in southeastern England (UK). Greater London has 8.7 million inhabitants, making it the largest city in the European Union (Eurostat, 2018). Car density in London is around 1,700 cars km −2 . In 2015, the proportion of diesel cars in the urban areas of England was of 46% in vehicles-kilometres (number of vehicles on a traffic network multiplied by the average length of their trips measured in kilometres, as measure of traffic flow) and the proportion of diesel buses in London was 83% vehicle-kilometres (UK NAEI, 2014). London is surrounded by several airports, some of them over 30 km away. The busiest is Heathrow with around 480,000 movements/year in 2018 and is located approximately 18 km from the UB station at North Kensington.
The North Kensington UB monitoring station (LND, Table 1) is placed in the grounds of Sion Manning School in St Charles Square and is mainly a residential area. The London traffic monitoring station (LND_SC , Table 1) is sited in the kerbside of Marylebone Road, one of the most heavily trafficked of the city with over 80,000 vehicles/ working day. It is a street canyon with six lanes (height-to-width ratio of 0.8) that experiences frequent congestion. The LND_SC station is about 4 km to the east of the LND station. Both stations belong to the London Air Quality Network.  Meteorological parameters for both stations were obtained at Heathrow Airport, including solar radiation (UK Met Office, 2006).

Zurich (urban background)
Zurich is located in northeastern Switzerland and is the smallest of the cities in this study. The city of Zurich has 0.4 million inhabitants (0.6 million including the metropolitan area) and a car density of 2,000 vehicles km −2 . In Switzerland, and presumably also in Zurich, the vehicle fleet consists of 27.2% diesel vehicles, 71.2% gasoline vehicles and 1.6% hybrid and electrical powered vehicles (BFS, 2016).
The measurements were carried out at the Zurich-Kaserne UB station (ZRC, Table 1) that is part of the Swiss National Air Pollution Monitoring Network (NABEL). It is located in a public courtyard in the city centre. The roads surrounding the station have low traffic intensity and the area is not affected by major emissions from industries but it is close to a district with high density of restaurants (west). The biggest train station in Switzerland is located about 300 m away northeast. Zurich airport, with around 270,000 movements per year, is located 10 km north. There is a military base (converted to a civil airport with joint military use in 2014) with very little volume of air traffic. It is located 9 km NE from the monitoring station.

Instrumentation
The instrumentation used for measuring aerosol and gaseous pollutants at the different stations is described in Table 2. For the present study, the data were averaged to hourly values. The periods under study varied depending on the data availability for each site (from 2007 to 2017). Different instruments and measuring configurations were used for PNSD measurements at the different sites, and, thus, the measured size ranges varied: in BCN from 11 to 478 nm (Scanning Mobility Particle Sizer Spectrometer, SMPS TSI 3936), in HSK from 6 to 700 nm (Differential Mobility Particle Sizer, DMPS), in HSK_SC from 6 to 800 nm (DMPS), in LND and LND_SC from 17 to 604 nm (SMPS TSI 3080), and in ZRC from 10 to 487 nm (SMPS TSI 3034). Most of the instruments for measuring PNSD were fitted with a dryer (except the one in Barcelona and Zurich) as recommended by the EUSAAR protocol (Wiedensohler et al., 2012) and were corrected for diffusional losses (except in Zurich). These differences, particularly in the lower size cut, complicate the comparison of the number concentration of smallest particle and total PNC. The SMPS and DMPS underwent several checks for quality control and assurance. On a daily basis, all instruments were checked to ensure they were turned on and working correctly. The impactors and inlets were cleaned on a weekly or biweekly basis. Flow rates were measured at least once a month (twice a month at most of the stations) to ensure the flow was within ± 10%. Once per year, the instruments were either sent for complete maintenance (and the highvoltage supply of the DMA was checked) or participated in a calibration workshop with other SMPS or DMPS (e.g. Gómez-Moreno et al., 2015).
Black Carbon (BC), PM mass (except HSK), and gaseous pollutant (NO 2 , NO, SO 2 , CO, O 3 ) concentrations were also monitored ( Table 2). The instruments for BC and PM monitoring were also checked frequently: the impactors were cleaned at least once per month and the concentrations were compared to gravimetric measures for PM and elemental carbon determinations for BC. Flow is very stable for both types of instruments and were checked at least twice per year in all cities. Both PM and gaseous monitoring are performed according to the European Union standards (Directive 2008/50/EC).

Positive Matrix Factorisation (PMF)
Positive Matrix Factorisation (PMF; Paatero, 1997) is a widely used multivariate data analysis method to identify and apportion the sources of PM or PNSD by analysing the measurements of observed species (or size bins in the case of PNSD) at the receptor site. PMF is a least-squares method that assumes that ambient aerosol X (a matrix of n × observations and m × size bins) can be explained by the product of a source matrix F and a contribution matrix G, whose elements are given by Eq. (1): where p is the number of independent sources, X ij is the measured submicron particle number concentration of the jth size bin in the ith sample, f jk is the concentration of the jth size bin in material emitted by source k, g ik is the contribution of the kth source to the ith sample, and e ij represents the residuals.
PMF is a descriptive model and there are no objective criteria with which to choose the best solution. PMF was performed with Multilinear Engine 2 (ME-2, Paatero, 1999), to identify and quantify the sources of PNSD. ME-2 was used instead of the USEPA PMF 5.0 because the latter software accepts a limited number of observations. The hourly averaged PNSD data were combined with the hourly concentrations of gaseous pollutants (NO 2 , NO, SO 2 , CO, O 3 ). Adding additional species (other than PNSD) can help to separate and identify the sources. It can also decrease the rotational ambiguity because of increased numbers of edge points (Emami and Hopke, 2017;Li et al., 2019). BC was not included in the PMF analyses because the data coverage was low for some of the stations. However, we performed a sensitivity analysis (data not shown) to test the influence of including BC in the factor profiles and contributions and we obtained very similar results. PM mass concentrations were also excluded for three reasons: (1) because they were not available for HSK, (2) ultrafine particles contribute very little to PM mass concentrations and are generally uncorrelated with them, and (3) several different sources may be affecting PM mass concentrations and, thus, the mass values may not add useful source information to PMF as PM composition data would. Although CO and SO 2 were not available for HSK_SC, these species were used for the other sites because UB stations are the focus of this study and the HSK_SC dataset only covered a short period.
PMF requires individual uncertainty estimates for each data value. We followed the methodology established by Ogulei et al. (2007) with little variations. The following equation was used to calculate the measurement uncertainties: where σ ij is the estimated measurement error for size bin or gaseous pollutant j and sample i; α j is a constant for size bin or gaseous pollutant j; N ij is the observed concentration for size bin or gaseous pollutant j and sample i; and N j is the arithmetic mean of the observed concentration for size bin or gaseous pollutant j. We tested values of α between 0.005 and 0.030. Selected α are presented in Table S2. Commonly, α is used as a constant throughout all size bins and pollutants, however, we added higher uncertainty to the lowest and the highest bins of the PNSD as they have been reported to have increased measurement error (Wiedensohler et al., 2018). Thus, we assigned 2*α for the 3% lowest and 3% highest size bins (we had different instruments with different number of bins), and 1.5*α for the subsequent 3% lower and 3% higher size bins. Afterwards, we fitted a spline and used the modelled values as the α j for the PNSD. For the gaseous pollutants, we used a scaling factor (multiplier) of 4 for α which was empirically determined to adjust the distribution of scaled residuals between the reasonable range of −3 and 3 (see below). The overall uncertainty matrix was calculated as: where σ ij is the estimated measurement error (Eq. (2)) and C 3 is a constant. Both α and C 3 were chosen so (1) the scaled residuals were approximately randomly distributed between −3 and 3, (2) the model obtained closest value of the object function (Q, sum of scaled residuals) to the theoretical value, and (3) provided the most physically Table 2 Instrumentation used to monitor particles at the different monitoring stations.  Rivas, et al. Environment International 135 (2020) 105345 interpretable results. Thus, as for α, C 3 was empirically determined through a trial-and-error approach by testing values between 0.05 and 0.15 (values of C 3 optimising the model are presented in Table S2).
Only when missing values corresponded to less than 25% of the number of size bins and gaseous pollutants within a timestamp (that is, at least 75% of the variables had data available), we imputed the concentrations. If no data were available for any PNSD size bin during a specific timestamp, it was excluded from the analysis. The missing cells within included observations were imputed using the 'mice' (Multivariate Imputation by Chained Equations) R package (Van Buuren and Groothuis-Oudshoorn, 2011). The corresponding uncertainties for imputed data were set to twice the imputed value.
The PNSD source profiles and contributions obtained from the ME-2 analyses were scaled to the measured concentration by regressing the measured total PNSD against the ME-2 contribution matrix.
We performed the analyses to all-year dataset. Previous literature suggest performing the analyses by season to account for the substantial season-to-season variability in temperature and solar radiation (Ogulei et al., 2007). We compared all-year results with the results obtained when performing PMF separately by season: summer (June, July, and August), winter (December, January, and February) and transitional period (March, April, May, September, October, and November). We obtained the same number of sources and most of them showed a correlation coefficient > 0.98. However, some differences were observed for specific sources, as shown by some goodness-of-fit measures (Table S3). These differences were mainly due to transfer of contributions between two sources (often of the same nature such as two traffic sources) for one of the seasons during the year. For some stations, carrying out a PMF for each season led to inexplicable strong jumps in the source contributions from the last day of a season to the first of the following season). Thus, we selected to present the results of the allyear dataset as it captured a smoothed season-to-season variability and ensured continuity of the sources throughout the year.

Statistical software
Data management, descriptive statistics, and plots were performed with the R statistical software (v 3.5.1., R Core Team, 2018) and the package openair (Carslaw and Ropkins, 2012).

Results and discussion
Summary statistics for the different pollutants and meteorological data are presented in Table 3 for all monitoring stations. PM 10 , PM 2.5 and NO 2 average concentrations were below the European limit values of 40, 25, and 40 µg m −3 (annual average), respectively, in UB stations from all cities. PNC and PNSD are difficult to compare between stations, as the measurement protocol and, specially, the measured particle size differs considerably. To quantify the effect of the differences in the size ranges, we calculated the total PNC for a reduced common range of approximately 17-480 nm (Table S4) and resulted in a reduction of 45% of the full PNSD range for HSK_SC, 27% for HSK, 26% for ZRC, 17% for BCN with almost the same concentration for the London stations. Thus, when interpreting the source contributions, we should take into account these differences and that these differences will affect mainly the sources in the nucleation mode. Concentrations of BC and the gaseous pollutants that are tracers of combustion processes were highest at the London stations (and particularly the traffic station, LND_SC), followed by HSK_SC, BCN, ZRC, and finally, with the lowest concentrations, the UB station of HSK. The average temperature over the measurement period were lowest in Helsinki, followed by similar temperatures in London and Zurich, and the highest being in Barcelona. As expected, solar radiation increased from north to south, with the lowest average being observed in Helsinki and the maximum in Barcelona.
The datasets for each site were independently analysed by PMF.
Those PMF solutions that had the most physically meaningful profile and temporal behaviour were selected after comparing solutions with different number of factors (Ogulei et al., 2007;Vu et al., 2015). The factors that were common in the different stations, although with slightly different profiles, were Nucleation, two traffic factors (Fresh traffic and Urban, the latter dominated by traffic emissions but influenced by other urban sources including biomass burning in some cities during the cold periods), and Secondary aerosol. In addition, in Helsinki Biogenic contributions were identified as a separated factor (further details in the sources below). For all stations PMF predictions of PNSD correlated very well with the observed values (Fig. S1). For BCN, new particle formation through photonucleation processes had such a high impact that Photonucleation was separated by PMF as a differentiated factor from nucleation particles emitted by road traffic (and nucleation particles from traffic exhaust were included in the Fresh traffic factor, which was specifically labelled as Traffic (nucleation + fresh) for the BCN site). At the other stations, however, the low correlation between traffic tracers such as BC and NO x and the Nucleation factor indicated that Nucleation also included particles generated by photonucleation processes, as there were high concentrations of the Nucleation source under low NOx concentration conditions (Fig. S2).

Splitting of the Nucleation factor into Photonucleation and Traffic Nucleation sources
We developed a methodology (inspired by the one proposed by Rodríguez and Cuevas, 2007) to split the Nucleation factor into two sources: Photonucleation and Traffic nucleation. To this end, we used NO x as a proxy for traffic emissions within the Nucleation factor. Considering that at the morning peak hour most of the Nucleation particles would be from traffic, we multiplied NO x concentration by a scaling factor (the ratio between Nucleation and NO x ) so it matched Nucleation concentrations at morning peak hour (08:00 h local time, except for HSK_SC that was at 07:00 h). The scaling factor was different for each day (day-specific) to account for the possible variations in the NO x to Nucleation ratio due to: (1) long-term changes in the fleet (differences in the fuel proportion and the emission control technologies incorporated in the vehicles; Park et al., 2017;Rönkkö et al., 2013); (2) driving conditions (Wang et al., 2010); and (3) the dependency on meteorological and dilution conditions of particle formation (affecting to nucleation particles) in diluting engine exhaust (Charron and Harrison, 2003;Gidhagen et al., 2005;Rönkkö et al., 2006). For daytime hours (from 08:00 to 21:00 h local time), if solar radiation was over 10 W/m 2 , the product of hourly NO x concentrations by the day-specific factor was assigned to the Traffic nucleation source, while the rest was assumed to be Photonucleation (Photonucleation = Nucleation -Traffic nucleation; Fig. S2). During the night (22 h -07:00 h) all Nucleation particles were assigned to Traffic nucleation as no photonucleation would be expected. In this work, we use the term 'factor' when referring to the direct results from PMF (e.g. for the profile description) and the term 'source' when discussing about the final sources after the splitting of the Nucleation factor.

Traffic size distributions
Regarding the different traffic factors (including the one labelled as Urban) identified at each station, the profiles obtained from this work (Fig. 2) are within those reported at the existing literature. As stated in the reviews by Morawska et al. (2008) and Vu et al. (2015), diesel exhaust emissions are within the size range of 10-130 nm while gasoline emissions are within 15-60 nm. Exhaust plumes are characterised by the emission of primary particles (a carbonaceous mode) and secondary nucleation particles (Morawska et al., 2008). Exhaust primary particles are within the range of 30-500 nm (Casati et al., 2007;Vu et al., 2015) and are mainly composed of agglomerates of solid carbonaceous material (soot: graphitic carbon and lesser quantities of metallic ash with condensed or adsorbed hydrocarbons and sulphur compounds). The carbon core diameter has been reported to be down to 2.5 nm in cars (Sgro et al., 2008) and 10 nm in heavy-duty vehicles (Rönkkö et al., 2013). Heavy-duty vehicles may also emit coarser primary particles within the accumulation mode (100-1000 nm; Morawska et al., 1998). Nucleation particles form from the hot exhaust gases while they cool down and condense to produce large numbers of particles in the nucleation range (< 30 nm) (Morawska et al., 2008). Binary nucleation of H 2 SO 4 -H 2 0 or ternary nucleation of H 2 SO 4 -NH 3 -H 2 O are the main mechanisms of particle formation (Meyer and Ristovski, 2007;Shi and Harrison, 1999). The small sulphuric acid core starts growing by condensation of hydrocarbons (Tobias et al., 2001). In this study, the mode diameters of the profiles of the different traffic factors fall within the abovementioned size ranges (Table 4). The Nucleation factors showed a size range of 7-21 nm and, thus, traffic nucleation particles may be the principal contributor. The lower size range is especially dependent on the lower size-cut of the instrument used for PNSD measurements but in all cities a source with a mode diameter below 25 nm was resolved (Table 4). The size range of mode diameters for Fresh traffic (14-37 nm) may correspond to fresher traffic emissions of core carbon particles with organic compounds condensed and absorbed, including smaller carbon agglomerates. Urban encompassed larger carbon agglomerates (as supported by the correlation of BC and Urban always being higher than for Fresh traffic and Traffic nucleation; Table S5) as well as aged traffic particles that had grown enough to be in this size-range. The latter was corroborated by the daily patterns of Urban concentrations that usually showed a longer and delayed peak in comparison with Fresh traffic (Fig. 3).

Sources in Barcelona (BCN)
Four factors were identified for BCN site. The profiles of the factors are presented in Fig. 2, both for the PNSD and gaseous data. The sources identified from the profiles were Photonucleation (size mode diameter: 13 nm), fresh traffic with a size mode of 31 nm but also including nucleation particles (labelled as Traffic(nucleation + fresh)), a second traffic source mixed with urban background emissions with a size mode of 76 nm (Urban, mostly traffic emissions but slightly influenced by other urban emissions), and Secondary particles with the coarsest particle size (mode: 175 nm; Table 4). The Secondary source showed a bimodal distribution, with a minor peak at 18 nm. A bimodal distribution was also observed by Pey et al. (2009) in BCN by using a completely different approach. Pey et al. (2009) observed a minor peak in the 23-30 nm and a major one at 310-800 nm, with a much higher contribution of the accumulation mode than the nucleation. The bimodal distribution of secondary aerosols has also been observed in other locations (e.g. Gu et al., 2011;Kasumba et al., 2009;Squizzato et al., 2019). Pey et al. (2009) attributed the secondary source to consist mainly of accumulation mode ammonium-sulphate and ammonium nitrate particles. The profiles for the gaseous pollutants also support the source identifications from the size distribution (Fig. 2): Photonucleation and Secondary particles were explained by high contributions from O 3 , while the traffic sources were associated with high NO 2 .
Although photonucleation particles were successfully separated from traffic nucleation particles by PMF in Barcelona, the minor peak at midday and the correlation between NO x and Traffic (nucleation + fresh) (Fig. S3) suggested that the Traffic nucleation factor still included particles generated by photonucleation processes. Following the same methodology detailed above for the splitting of the Nucleation source in the other stations, the difference between the Traffic (nucleation + fresh) and the NO x * factor was assigned to be photonucleation particles. These residual photonucleation particles were added to the Photonucleation source and subtracted from Traffic (nucleation + fresh). With the exception of the source profile, all results presented in this work include the correction for the Photonucleation and Traffic (nucleation + fresh) sources.
The daily, weekly, and monthly patterns for each source are shown in Fig. 3 and were inspected to determine the correspondence with the source identifications. Traffic (nucleation + fresh) and Urban showed a daily pattern coinciding with the typical traffic peaks (Table 1). Traffic (nucleation + fresh) had an average annual contribution of 5207 ± 5468 pt cm −3 (Table 5) and showed the lowest concentrations Table 3 Average (and standard deviation) of pollutant concentrations and weather variables for the periods of study (only for periods when simultaneous PNSD and NO x data was available). For wind direction, the most frequent direction from where the wind was blowing is indicated.  I. Rivas, et al. Environment International 135 (2020)

Fig. 2.
Profiles of the sources including particle size distribution and gaseous species.
I. Rivas, et al. Environment International 135 (2020) 105345 during the summer months (summer average: 3556 ± 2977 pt cm −3 ) and the highest during late autumn (autumn average: 6223 ± 6330 pt cm −3 ). The daily patterns by season are presented in Fig. S4. Similarly, Urban showed the lowest concentrations during August (2352 ± 1186 pt cm −3 ), although the concentrations were more constant throughout the year (2835 ± 2103 pt cm −3 ) than for Traffic (nucleation + fresh) due to the contribution of other urban background sources. Both sources related to traffic were greatest during weekdays and showed the least concentrations on Sunday. Moreover, Traffic (nucleation + fresh) and Urban showed high correlation with BC (r = 0.76 and r = 0.83, respectively; Table S5). Photonucleation showed a peak around midday, coinciding with the greatest levels of solar radiation (r = 0.51, Table  S5), with negligible contributions during nighttime. Photonucleation also showed a small peak at 07:00 of misclassified particles that probably correspond to traffic emissions. Photonucleation did not show a consistent weekly pattern, with similar concentrations throughout the week. Contributions were minimal during the winter months (1506 ± 2690 pt cm −3 , average for 12-14 solar h: 3049 ± 2989 pt cm −3 ) with significant contributions from June to August (3743 ± 5536 pt cm −3 , average for 12-14 solar h: 9153 ± 8554 pt cm −3 ). The Secondary source (675 ± 572 pt cm −3 ) seems to be influenced by traffic emissions since the morning peak and the greatest contributions on Fridays could be seen in the daily and weekly pattern. The correlation coefficient with BC is moderate (r = 0.58). The contributions from the Secondary from our study is much lower than the 2000-6000 pt cm −3 reported by Pey et al. (2009) for BCN in 2004 determined by means of Principal Component Analysis, however, sulphate levels were reduced by a large proportion since 2009 to the study period of this work (Pandolfi et al., 2016).

Sources in Helsinki (HSK and HSK_SC)
Five factors were identified for Helsinki: Nucleation (mode = 11 nm), Fresh traffic (22 nm), Urban (50 nm), Biogenic (100 nm), and Secondary (224 nm). The same factors were identified in the street canyon site, HSK_SC. However, at the HSK_SC the size modes were shifted towards smaller particles due to the proximity to the source for Nucleation (7 nm), Fresh traffic (13 nm), and Urban (45 nm). Although the Biogenic was characterised by the same size mode (100 nm) in both stations, the Secondary showed slightly larger particles (256 nm) at HSK_SC than at HSK (Table 4). Similar to BCN, the Secondary source also showed a bimodal distribution at both Helsinki stations with the minor peak being at around 33 nm in HSK and 30 nm in HSK_SC (Fig. 2). As indicated previously, the Nucleation source was split into Photonucleation and Traffic Nucleation (Fig. S2). The gaseous profiles indicate high contributions of NO 2 to the traffic sources (including the mixed source of Photonucleation and Traffic Nucleation) in both stations (Fig. 2). O 3 was mainly associated with the Biogenic source.
The daily and weekly concentration patterns corroborate the source identifications from the PNSD profiles (Fig. 3). Wood combustion contributed to Urban and also to Fresh traffic during winter, which, besides boundary layer height evolution over the year, would partly explain the higher contributions during the cold periods ( Fig. S4; Ripamonti et al., 2013). Nevertheless, the main source of UFP number concentrations would still be traffic in HSK and especially in HSK_SC. In fact, in HSK_SC, BC attributed to biomass burning was 14% of total BC concentrations (Helin et al., 2018). The average annual concentrations were 1391 ± 1482 pt cm −3 , 1871 ± 2546 pt cm −3 , and 2219 ± 2269 pt cm −3 in HSK and 2811 ± 4050 pt cm −3 , 5636 ± 7056 pt cm −3 , and 4156 ± 3884 pt cm −3 in HSK_SC for Traffic Nucleation, Fresh traffic, and Urban, respectively (Table 5; refer to  Table S6 for average contributions over the same period at HSK and HSK_SC). Regarding the Biogenic and Secondary sources, they did not present a specific daily or weekly pattern, with similar levels throughout the day and the week (Fig. 3). Annual averages were 1001 ± 923 pt cm −3 for Biogenic and 198 ± 219 pt cm −3 for Secondary in HSK and 1734 ± 1439 pt cm −3 and 226 ± 217 pt cm −3 in HSK_SC, respectively. However, the annual pattern showed important differences between these two sources. Biogenic had its peak during the warmer months (Fig. 3) when biogenic emissions (e.g. monoterpenes, isoprene) were at their maximum (Rantala et al., 2016). Biogenic VOC emissions are important precursors for new particle formation (Kirkby et al., 2016;Yan et al., 2018), which may reach the urban environment after they have grown up to around 100 nm. Although biogenic VOC emissions peak in summer, the frequency of new particle formation events is more common during spring and autumn due to the inhibition of new particle formation under high isoprene concentrations (Kiendler-Scharr et al., 2009) and because in cooler temperatures the particle-phase might be favoured by supersaturation. Since we observed the highest concentrations during summer, the Biogenic source may also have the input of particles from polluted air masses from long range transport, which is particularly intense in the summer months due to controlled burning and forest fires from other regions in Eastern Europe   I. Rivas, et al. Environment International 135 (2020) 105345 (Niemi et al., 2009). It may also be mixed with secondary aerosols from anthropogenic origin, as we would expect the levels of Biogenic source to be lower of what we found during the winter when temperatures are often negative. The influence of anthropogenic secondary aerosols on Biogenic is also strengthened by the comparison of the contribution of the sources for the simultaneous periods in HSK and HSK_SC (Table S6), when the Biogenic source is higher in HSK_SC than HSK (we would expect similar levels if there were no influence of anthropogenic and traffic emissions). On the other hand, although concentrations of Secondary were low all year round, they showed a trend with its minimum during the summer months to some extend explained by the evaporation of ammonium nitrate due to the higher temperatures during summer (Pakkanen et al., 2001). The Secondary source may account mainly for anthropogenic emissions, with the total secondary contribution being the addition of the Secondary and Biogenic sources. Photonucleation in HSK (annual average = 313 ± 1044 pt cm −3 ) was higher during the spring (509 ± 1494 pt cm −3 ) and autumn (310 ± 969 pt cm −3 ), which coincides with the periods of higher new particle formation in Finland reported in the literature (Dal Maso et al., 2005;Laakso et al., 2003). By looking at the annual pattern of both HSK and HSK_SC (Fig. 3), we suspect that part of the subsequent growth of nucleated particles may be apportioned to the Urban source since this source showed maxima in spring and autumn (Laakso et al., 2003). Although the methodologies are not directly comparable, our results are in agreement with the cluster analysis by Hussein et al. (2014) for HSK.

Sources in London (LND and LND_SC)
Four factors were selected as the solution for PMF in both LND and LND_SC. The sources were identified as Nucleation (mode = 21 nm in LND), Fresh traffic (37 nm), Urban (81 nm), and Secondary (294 nm). Although we were expecting a shift towards smaller particles in LND_SC due to proximity to the traffic source, we obtained the same or very similar mode diameters for Nucleation (21 nm) and the sources from traffic emissions (34 and 81 nm for Fresh traffic and Urban, respectively). We obtained a much smaller mode for the Secondary aerosols at LND_SC (93 nm; Table 4) but the profile shows a high contribution of particles from around 80 to 300 nm (Fig. 2). The different shape of the profile for the Secondary factor in Marylebone may consist of a mix including also traffic non-exhaust emissions as well as cooking, as the latter was identified to be much larger in LND_SC than LND (Ots et al., 2016). PMF was previously applied to PNSD data from 2011 to 2012 from LND  and four factors were also identified with very similar profiles to ours. Fig. 3 shows the diel patterns for Traffic nucleation, Fresh traffic, and Urban. These sources followed the typical pattern of BC and NO x (common traffic tracers) previously described in literature for LND (North Kensington) and LND_SC (Marylebone; Reche et al., 2011a). In LND, Urban was strongly correlated with BC (r = 0.84; Table S5) while Fresh traffic showed a moderate correlation (r = 0.53) and Traffic nucleation was surprisingly, and unlike what happened at the other sites, not correlated with BC (r = 0.09). For LND_SC, correlation coefficients for BC were stronger (0.52 for Traffic nucleation, 0.72 for Fresh traffic, and 0.84 for Urban) as expected for a street canyon station. Compared to the UB stations in the other cities, LND concentrations of traffic sources were relatively high during the night with a midday local minimum. Moreover, compared to the other cities both LND and LND_SC had stable concentrations of the traffic sources all year round and did not show a minimum over the summer months (Fig. 3). Annual average concentrations (Table 5) were much lower at LND (527 ± 625 pt cm −3 for Traffic Nucleation, 2948 ± 2149 pt cm −3 for Fresh traffic, 1770 ± 1821 pt cm −3 for Urban) than at LND_SC (1451 ± 1242 pt cm −3 , 5087 ± 2903 pt cm −3 , 5037 ± 2903 pt cm −3 , respectively), especially for the source with the smallest particle size which may be associated with fresher emissions (Table S6 shows the annual average for the same periods on both stations). The Urban source may also be affected by emissions from biomass burning, which may contribute particularly to the evening peak during the winter months (Fuller et al., 2014;Young et al., 2015). Urban showed a higher and maintained evening peak during autumn and winter, which was not present during spring and summer (Fig. S4). In LND, Photonucleation was higher during the summer months (398 ± 932 pt cm −3 ) than the rest of the year (annual average: 203 ± 619 pt cm −3 ), with very little contribution during the winter (Fig. S4). The same pattern for Photonucleation was found at LND_SC but with lower contributions (annual average: 165 ± 506 pt cm −3 ; summer: 302 ± 723 pt cm −3 ; winter: 47 ± 195 pt cm −3 ) as photonucleation processes are usually more important under clean atmospheres (Spracklen et al., 2006). The high PNC in LND_SC may have prevented new particle formation; this point is explored more fully by Bousiotis et al. (2019). Besides the fact that London sites had the largest lower size cut-off, the high PNC in London may also explain the lower Photonucleation contribution in comparison with BCN and HSK. Barcelona has considerable pollution levels, however, it experiences very high solar radiation levels and a frequent midday clean up by sea breeze also transporting SO 2 from shipping. On the other hand, Helsinki has lower solar radiation but a much cleaner atmosphere (Table 3). For both London sites, contributions of the Secondary aerosol were stable during the day with the minimum found in the early afternoon in LND (Fig. 3), probably associated with the Table 5 Average (standard deviation) source contributions at the different sites (only for periods when simultaneous PNSD and NO x data was available). Total traffic is the addition of Traffic nucleation, Fresh traffic, and Urban (Traffic (nucleation + fresh) and Urban in the case of BCN).

City
Photo-nucleation (pt cm −3 )  (6441) 589 (551)  I. Rivas, et al. Environment International 135 (2020) 105345 thermal instability of ammonium nitrate and semi-volatile organic aerosols and with better dispersion conditions of higher wind speeds and mixed layer heights. The annual trend followed the one described for nitrate in London (Revuelta et al., 2012), with lower concentrations during summer (also related to nitrate evaporation) and with higher concentrations from February to April. In LND the weekly pattern of the Secondary source showed lower contributions during the weekend (clearly observable when plotting normalised concentrations), which may indicate the influence of local traffic emissions on the secondary particles (also, the correlation with BC reached r = 0.50). Average annual contributions were 184 ± 269 pt cm −3 for LND and 589 ± 551 pt cm −3 for LND_SC. The coarser nature of the Secondary source made it to be the most correlated with PM mass concentrations (r = 0.81 and r = 0.80 for PM 2.5 in LND and LND_SC, respectively).

Sources in Zurich (ZRC)
Similar to previous sites, four factors were identified as contributors to PNSD in ZRC. With the exception of the Secondary factor, the profiles for ZRC were quite similar to those in LND although the mode diameter for Nucleation (15 nm for ZRC) was shifted towards smaller sizes due to smaller lower cut-off of the instrumentation used in ZRC (Fig. 2). The gaseous profile for the Nucleation factor was mainly explained by NO 2 and O 3 suggesting the influence of traffic emissions and the presence of photonucleation particles. Fresh traffic (33 nm) had a similar mode diameter to BCN while for Urban (67 nm) the mode diameter was between the ones found in HSK and BCN (Table 4). The Secondary factor showed a bimodal distribution with the main peak in the coarser mode (246 nm).
The average contributions of Traffic nucleation, Fresh traffic, and Urban were 1621 ± 1309 pt cm −3 , 4906 ± 4626 pt cm −3 , and 2426 ± 1854 pt cm −3 , respectively. Traffic nucleation and Fresh traffic clearly showed the morning traffic peak, while the afternoon peak was followed by Fresh traffic and Urban (Fig. 3). The diel patterns by season indicate that the relative difference between the morning and afternoon peak was much higher during summer and autumn (Fig. S4). This suggests that both Fresh traffic and Urban, were possibly affected by other combustion sources, such as solid fuel burning for heating during the cold period or for recreational activities. The daily pattern by day of the week (Fig. S5) allows identification of the drivers of high concentrations in the afternoon peak as these occurred on Friday and Saturday evenings during the warmer months. There is a recreational area with barbequing near the monitoring station. PMF was not able to separate the charcoal or wood combustion used for the barbeques from the traffic sources.
Traffic emissions are the main contributors to Fresh traffic and Traffic nucleation (and to a lesser extent to Urban) since the concentrations diminish considerably during the weekends. The Secondary source is very stable over the day (annual average: 316 ± 275 pt cm −3 ), with a slightly lower concentration in the early afternoon. Similar to other sites, the greatest concentrations of Secondary aerosols were observed during the colder months, especially February and March, suggesting that ammonium nitrate may be an important component of the Secondary source (since it evaporates during the warmer periods). Minguillón et al. (2012) reported that during wintertime, ammonium nitrate contributed 63.7% of total PM 1 mass concentrations (8.8 µg m −3 ), which diminished to only 1.5% (0.1 µg m −3 ) during the summertime. This result suggests that the Secondary chemical composition may change over the year since there was not as large a reduction in the PNSD sources. Photonucleation contributions showed the expected pattern, with highest levels at midday/early afternoon and during the summer months (summer average: 390 ± 926 pt cm −3 ; annual average: 316 ± 275 pt cm −3 ). Fig. 4 shows the relative contribution of the sources identified by PMF at the different sites. Traffic emissions were by far the highest contributor in all stations, with contributions ranging at maximum (as some traffic sources were mixed with other sources such as biomass burning) from 71 to 91% of the total PNSD. The variability in the absolute average contribution of the combination of traffic sources among the UB sites (ranging from 5245 ± 3480 pt cm −3 in LND to 8952 ± 6281 pt cm −3 in ZRC; Table 5) partly corresponds to the differences on the lower size cut of the measurement instrument. Generally, the lower the size cut, the greater the number of trafficemitted particles included in the analysis. This explains the lowest traffic contribution (in absolute terms) in London, where we would expect the contrary (LND has the highest BC and NO 2 concentrations among the UB sites; Table 3). In addition, the relative contribution of the different traffic sources may also be explained by the influence of other sources to these factors as well as the distance to the road of the monitoring site and meteorology, as these variables would affect the amount of time from emission until measurement and the type of physical processes that the particles undergo. For instance, condensation and coagulation implies a growth of the particles (and a number reduction in the case of coagulation), while evaporation is associated with shrinkage (Backman et al., 2012;Yao et al., 2010). The high contribution of traffic emissions to total PNSD has been consistently reported in literature for urban environments around the globe, including the cities in this study Brines et al., 2015;Dall'Osto et al., 2012;Friend et al., 2012;Liu et al., 2014;Pey et al., 2009;Posner and Pandis, 2015;Squizzato et al., 2019;Vu et al., 2015;Wang et al., 2013).

Relative contributions of the sources
Photonucleation is by far more important in the city with the highest insolation, which is consistent with previous studies (Brines et al., 2015). In BCN, Photonucleation represented on average the 23% of the total PNSD, reaching 35% during the period with higher solar radiation (summer) but being significant during the whole year. In the rest of the UB sites, Photonucleation contributed on average around 3-4% (Fig. 4), reaching a maximum of 7% in LND (summer) and HSK (spring), and a 5% in ZRC (summer). The contribution of Photonucleation in BCN (2586 ± 4310 pt cm −3 ) was approximately an order of magnitude higher than at the other sites: 313 ± 1044 pt cm −3 in HSK, 203 ± 619 pt cm −3 in LND, and 282 ± 795 pt cm −3 in ZRC. Note that HSK and ZRC lower size cuts (6 and 10 nm, respectively) are lower than in BCN (11 nm) while in LND, the lower size is 16 nm.
Generally, Secondary aerosols were the source contributing the least to PNSD (although they would be a large fraction of the mass) due to their regional origin: 3% in LND, HSK, and ZURICH and 6% in BCN. Its relative contribution was generally constant over the year. In HSK, the combination of Biogenic and Secondary added to a total relative contribution of 17%.
Finally, to provide a consistent comparison, Table S7 shows the annual average of the contributions at the UB stations for the same period at the four cities. The relative contributions for the simultaneous period were very similar to the ones observed for the full period of analysis. Fig. 5 shows the polar plots for the different sources and BC, PM 10 , and SO 2 (if available) in the UB stations, indicating the wind speeds and directions that were associated with higher concentrations of each specific source. The polar plots for the street canyons are presented in Fig. S6.

Spatial origin of ultrafine particles
Traffic sources in BCN were mainly of a local origin since they were predominant at low wind speeds. BCN is influenced by a nearby I. Rivas, et al. Environment International 135 (2020) 105345 important avenue with high traffic intensity. BC followed a similar polar distribution than Traffic (nucleation + fresh) and Urban. Although Secondary particles were also associated with low wind speeds, high contributions of this source were also observed with winds from the E blowing both at low and high wind speeds. The behaviour of Secondary particles is broadly mimicking that of PM 10 , corroborating the secondary and regional origin of the Secondary source. SO 2 concentrations were highest for winds blowing from 100 to 180°(especially 160-180°) that is the location of the harbour. Barcelona is registering very low SO 2 levels compared other European cities (Henschel et al., 2013), especially since 2008 when power generation was restricted to only natural gas in the metropolitan area. Thus, currently the main source of SO 2 in the city is shipping. Photonucleation particles were associated with light breezes blowing from the S (180-190°). The airport is located about 10 km SSW (185 -205°) from BCN. Although Photonucleation is associated with wind directions that may come from the harbour and airport, we cannot link their emissions with Photonucleation due to the low wind speeds and low frequency of winds, especially from the direction of the airport (Fig. S7). Traffic sources in HSK were associated with N and S wind components (Fig. 5). Traffic nucleation was particularly associated with N winds. There are several major roads located N that may have some influence on Traffic nucleation, but we would expect a similar or even higher effect (due to particle growth by condensation or coagulation) on Fresh traffic, which is not the case. In this direction there is also located the airport, and air traffic is a well know emitter of huge amount of ultrafine particles in the nucleation mode (Hu et al., 2009;Keuken et al., 2015;Masiol and Harrison, 2014;Mazaheri et al., 2009) that can be detected few kilometres away (Cheung et al., 2011;Hudda et al., 2016). The association with high wind speeds may indicate that nucleation particles have to travel fast in order to be detected in such a small size in our receptor station in the UB. Therefore, there might potentially be a contribution from airport emissions to the Traffic nucleation source. However, the nucleation mode particles in Helsinki might also originate from several other sources, such as wood combustion in fireplaces and sauna stoves, oil-combustion in boilers, and regional nucleation events. Both Secondary and Biogenic were associated with winds from the E and, particularly for Secondary, covering the angle range to the S -SE.
At HSK_SC the local wind direction results from the orientation of the street canyon relative to the prevailing wind. Thus, prevailing winds are associated with NW and SE (Fig. S7). The Biogenic source is associated with N winds (Fig. S6), which, according to the street canyon recirculation dynamics, may actually indicate regional S winds as it did in HSK.
With the exception of Nucleation particles (both Traffic & Photonucleation) in LND, all sources were mainly associated with calm episodes and E winds. This is in agreement with LND being located west of central London and mainland Europe. Urban showed a very local contribution (similar to BC) associated with low wind speeds. On the other hand, Traffic nucleation and Photonucleation were clearly associated with winds blowing from the W -SW sector. Again, although it is difficult to evaluate and quantify, this is pointing towards emission contributions from Heathrow airport (one of the busiest in the world). Moreover, W -SW winds were also associated with clean air masses that favour new particle formation and, therefore, it is difficult to rule out the possible contribution from the airport. Harrison et al. (2019) have also shown an influence of aircraft emissions upon PNSDs at London stations and further analysis of new particle formation events in London is provided by Bousiotis et al. (2019).
At LND_SC, the highest concentrations of traffic sources were observed with E or W winds (same direction as the street canyon) and for winds blowing from the S sector. The street canyon recirculation explains the influence of S winds as the station is located in the southern side of the road and, therefore, receives the local pollution of the road when winds blow from the S .
In ZRC, Fresh traffic and Urban sources seem to be mostly associated with SE winds while Traffic nucleation was mainly associated with winds from the N sector. Secondary particles were mainly associated with local contributions and NE winds. NNE winds are often associated with cold weather forcing the semi-volatile components into the particle phase (particularly ammonium nitrate).
The same results were obtained with the conditional probability function plots (Fig. S8) that indicate the probability of concentrations above the 90th occurring by wind direction and are useful for identify source-areas.

Influence of airport emissions on urban background stations
The polar plots in Fig. 6 were used to identify possible airport influences on the Nucleation particles of the different UB stations. Fig. 6 shows the polar plot for the Nucleation factor (before the splitting into Traffic and Photonucleation) in the first column, the Traffic nucleation source in the second, the Photonucleation source in the third column, and the Photonucleation source for those periods in which there were relatively high Photonucleation concentrations even when the environmental conditions were not favourable for the photonucleation process (i.e. low solar radiation -below 80 W m −2 -during the winter months).
These periods were selected because if photonucleation was low, then airport contributions might be easier to identify. We focused on only the UB stations since the high contribution of traffic emissions in the street canyons might obscure the presence of nucleation particles from the airport.
In Fig. 6, the two dashed lines indicate the angular range of influence of airport emissions: winds blowing from 185 to 205°(SSW) may carry airport emissions to BCN, from 345 to 10°(N) to HSK, from 246 to 260°(WSW) to LND, and 0-22 (NNE)°to ZRC (the military airport has not been considered due to the low air traffic). In all cases, Nucleation particle were observed as being directionally dependent and coincident with the location of city airports. At all the UB stations, Nucleation particles were associated with those wind directions that were from the corresponding airport. ZRC has a more complex topography that would induce funnelling and, therefore, the highest concentration were a bit shifted toward NNW instead of NNE. In BCN, the low wind speed may indicate a local origin of the Nucleation particles (either Traffic or Photonucleation) instead of the airport. Alternatively, both HSK and LND showed the coincidence of the airport wind directions with the greatest contributions for Traffic Nucleation and Photonucleation (under low radiation conditions). However, we note that in HSK there is also several main roads and residential areas with high residential wood combustion emissions at the same direction with the airport. It is difficult to isolate airport emissions contributions without additional tracers; however combining the evidence across the four cities is indicative of airport emissions influencing urban background Nucleation   6. Polar plots showing how contributions of the Photonucleation source were affected by wind direction and wind speed. The area of influence of the wind direction from the airport is within the dashed lines that convey to the airport sign. Fist column corresponds to the Nucleation factor, second column to the Traffic Nucleation (or Traffic (nucleation + fresh) in the case of BCN), third column corresponds to Photonucleation source, and fourth column to the Photonucleation source during periods with relatively high Photonucleation contribution despite unfavourable conditions for photonucleation processes: low solar radiation (< 80 W m −2 ) during the coldest and darker months (Nov-Feb). Wind speed units: m s −1 .
BC highest concentrations were not associated with wind directions from the airport (Fig. 5) and this may indicate that traffic or wood burning emissions are not the main source of Nucleation particles when the wind is blowing from the airport. On the other hand, not identifying high BC concentration from airport direction would be in accordance to aircraft emissions, as aircraft plumes are characterised by very high PNC (especially in the nucleation range) but not BC (Keuken et al., 2015).
Further studies are needed to confirm the potential impact of aircraft emissions and isolate them from other sources.

Conclusions
Positive Matrix Factorization (PMF) was used for receptor modelling the source contributions to long time series of hourly size segregated number particle concentrations at six monitoring stations (four urban background and two traffic stations) in four European cities that were affected by different meteorology and emission patterns: Barcelona, Helsinki, London, and Zurich. We identified common sources across all cities: Photonucleation, traffic emissions (3 sources, from fresh to aged emissions: Traffic nucleation, Fresh traffic -mode diameter between 13 and 37 nm-, and Urban -mode diameter between 44 and 81 nm), and secondary particles. PMF was able to separate the Photonucleation factor only for Barcelona, while a manual split of the Nucleation factor (into Photonucleation and Traffic nucleation) was performed for all the other stations using NO x concentrations as a proxy for traffic emissions.
Traffic emissions were the main contributor in all stations, with a potential maximum contribution ranging from 71 to 94% of PNSD. For London and Zurich stations, no significant variability among seasons was observed. On the other hand, the high levels of solar radiation in Barcelona led to an important contribution of Photonucleation particles (ranging from 14% during the winter period to 35% during summer). Moreover, a source identified as Biogenic emissions was only present in Helsinki importantly affecting both the UB and street canyon stations, particularly during summer (23%) but also during spring (14%) and autumn (12%).
When looking at wind directions that were favouring Nucleation particles, we observed that in most cases the highest concentrations took place when the wind was blowing from the airport location. Particularly, we could easily identify periods when the urban background station in London was affected by emissions from Heathrow. Although less clear, we found that airport emissions might be as well affecting background PNSD concentrations in Helsinki, Zurich, and Barcelona.
This work provided a detailed characterisation of the sources affecting ultrafine particles in four urban environments in Europe, confirming the great contributions from traffic emissions but also highlighting some differences such as the role of photonucleation in high insolation cities. The contribution of the different sources to PNSD will be used in future studies to evaluate the impact of these specific sources on human health.

Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.