University of Simplifying aerosol size distributions modes simultaneously detected at four monitoring sites during SAPUSS

. The analysis of aerosol size distributions is a use-ful tool for understanding the sources and the processes inﬂuencing particle number concentrations (N) in urban areas. Hence, during the one-month SAPUSS campaign (Solving Aerosol Problems by Using Synergistic Strategies, EU Marie Curie Action) in autumn 2010 in Barcelona (Spain), four SMPSs (Scanning Mobility Particle Sizer) were simultaneously deployed at four monitoring


Introduction
Air pollution is a major social concern, especially in urban agglomerations where anthropogenic emissions are an important source of ultrafine particles (UFPs, diameter < 100 nm). These may have a natural or an anthropogenic origin and may be emitted to the atmosphere directly or formed as a result of different atmospheric processes. UFPs are very abundant in number but have little aerosol mass (Harrison and Yin, 2000). Because of their small size they are suggested to be more toxic than coarser particles per unit mass (Davidson et al., 2005;Seaton et al., 1995). Recent epidemiological studies have shown that particle number concentration is directly related to cardiovascular mortality (Atkinson et al., 2010). Additionally, aerosols influence the Earth's radiative balance, either directly or indirectly, through their effect on the albedo and lifetimes of clouds (IPCC, 2007).
Within urban environments, road traffic is found to be the main source through tailpipe emissions (Pey et al., 2009;Kumar et al., 2011). Vehicle exhausts emit both primary particles and gaseous pollutants. Semi-volatile organic compounds can be rapidly converted into aerosols by secondary processes (Charron and Harrison, 2003). However, the variability of particle levels in urban ambient air is not only dependent on the number of vehicles but is also influenced by the geographical, climatological and the meteorological features of the study area (Birmili et al., 2000;Hussein et al., 2006;Olivares et al., 2007).
A large gradient of N is found within urban areas of Europe. In northern European countries N is usually correlated with primary traffic markers during all seasons (Hussein at al., 2004), whereas in the southern European countries the scenario is far more complex. Indeed, Reche et al. (2011) showed that the high insolation registered in Mediterranean cities enhances nucleation events, thus increasing N. It should be kept in mind that the Mediterranean climate is also encountered in other cities worldwide like Los Angeles and Brisbane (Hudda et al., 2010;Cheung et al., 2011). The present work was carried out in Barcelona, a major city located in the NE part of Spain in the western Mediterranean basin (WMB).
The objective of this study was to identify the atmospheric processes and sources affecting the size-selected aerosol concentrations simultaneously detected at four different monitoring sites in the Barcelona area. The unique approach herein presented derives from the spatial distribution of the monitoring sites used, both at horizontal and vertical levels within the city of Barcelona. Four SMPS (Scanning Mobility Particle Sizer) instruments at four different monitoring sites were deployed during the Marie Curie EU Action SAPUSS (Solving Aerosol Problems by Using Synergistic Strategies), allowing us to obtain a large data set characterised by high time resolution (five minutes) and high aerosol size resolution (34 bins in the size range of 15-228 nm).
In order to reduce the complexity of such a large data set, statistical cluster analysis was used to group similarly sized distributions into the same category, while keeping the number of different clusters to a minimum (Beddows et al., 2009). By applying this analysis to particle size distribution measurements taken simultaneously at different monitoring sites, the aerosol variability and transport within such study sites (Beddows et al., 2009;Dall'Osto et al., 2011b) can be studied.
It should be remembered that the SMPS clustering data herein presented correspond only to the SAPUSS intensive field study of one month and are thus influenced by the season (autumn) and the year (2010). A study on the spatial and temporal variability of N >5nm during the SAPUSS study can be found in this ACP SAPUSS special issue (Dall'Osto et al., 2013a). Previous studies on the same study area have focused on yearly data (2004) and can be found elsewhere (Pey et al., 2008(Pey et al., , 2009; for relative clustering analysis see Dall'Osto et al., 2012). Additionally, during this study some important conclusions are drawn on the effect of meteorological parameters on the emissions of primary traffic particles as well as on the correlation of N >5nm with some air quality parameters (NO x , PM x ).

Location
Barcelona is a coastal city located in the northeast of Spain in the WMB. It is confined by the coastal range of Collserola to the north, the Mediterranean Sea to the southeast and two river valleys, the Besòs River to the northeast and the Llobregat River to the west. The city has 1.7 million inhabitants, or around 4 million counting the metropolitan area. The major PM pollution source is traffic as the city has a high vehicle density (6100 cars km −2 ; Amato et al., 2009). The city has a number of complex meteorological scenarios, ranging from stagnant anticyclonic conditions to African dust outbreaks, as well as almost daily sea breeze dynamics. A detailed characterisation of the western Mediterranean basin climatological features can be found in Millán et al. (2000) and in the SAPUSS overview paper (Dall'Osto et al., 2013b). Within the Barcelona region, the SAPUSS measurement campaign took place from 20 September to 20 October 2010. Out of the six monitoring sites, for the purpose of this study we consider the four which were equipped with an SMPS (Dall'Osto et al., 2013b): -The Road Site (RS site ) was located in the car park of Escola Tècnica d'Enginyeria Industrial on Urgell Street, a street canyon with four vehicle lanes (one direction) and two cycling lanes in both directions. This street is representative of the urban traffic related to commercial activity, and during the SA-PUSS campaign the approximate vehicle intensity was 17 000 cars day −1 .
-The Urban Background monitoring station (UB site ) was located in a park of a residential area at the northwest of the city centre, about 80 m a.s.l. It was also close to the busy Diagonal Avenue (9 lane road) that crosses the city from east to west and is primarily used by commuters. It reflects the rush hour traffic peaks and has a traffic volume of about 62 000 cars day −1 .
-Torre Collserola sampling site (TC site ) is found at the Fabra observatory, an astronomical observatory at 415 m altitude above sea level, and located about 450 m (900 m road distance) from the tower Collserola site (tower site; Dall'Osto et al., 2013b). It characterises the suburban environment of the city and is affected by the boundary layer daily cycle and the seamountain breeze circulation.

Size-segregated aerosol concentrations
Four different SMPS instruments with 5 min time resolution were simultaneously deployed at the four sites. Although the use of aerosol drier is advisable (Colbeck et al., 2014;Swietlicki at al., 2008) in future studies, unfortunately it was not possible to use during this campaign. The instrument specifications at each site are as follows.
-RS site : Differential Mobility Analyser (DMA) TSI 3080 and a TSI CPC 3010 (11-322 nm for a total of 511 h). . In order to harmonise the data, they were averaged at hourly resolution to the size ranges of the UB site , in order to obtain a homogeneous data set that could allow an intercomparison between all sites. This resulted in a data matrix of particle size distributions ranging from 15 to 228 nm (39 bins) that contained 2006 h of measurements distributed across the four sites. All SMPS instruments were calibrated and intercompared beforehand, resulting in excellent agreement as shown in Dall'Osto et al. (2013b). They also provided an excellent temporal overlap (85 %). Additionally, total particle number concentrations were obtained by the use of additional CPCs at the three city sites (RS site , UB site and TC site ). At the RS site and TC site the CPC deployed was a buthanol-based TSI Model 3022A with a 50 % cutpoint at 7 nm, while at the UB site and RB site the CPC deployed was a water-based TSI Model 3785 with a lower cutpoint at 5 nm. The CPCs were intercompared before and after the campaign, giving excellent overlap, with uncertainties around 5 % both times (Dall'Osto et al., 2013b). Biswas et al. (2005) intercompared both water-based and buthanolbased instruments and concluded that they showed a similar response, always within the uncertainty of the manufacturer ( ± 10 %).

Other measurements
Meteorological parameters (temperature, relative humidity (RH), wind components, solar radiation and atmospheric pressure) were measured at the four sites described above (RS site , UB site , TC site , RB site ). Gaseous pollutants such as NO, NO 2 , O 3 , SO 2 , and CO were also measured using the

Data analysis
Given the amount of data to be interpreted and the complexity of the study (involving four monitoring sites) a statistical analytical method was applied to the SMPS data set using k-means cluster analysis, in which the particle size distributions were generalised by cluster types (characteristic of an emission or formation process) which facilitated an understanding of the temporal and spatial trends of the size distributions. It classifies spectra with the highest degree of similarity into the same category or cluster, therefore reducing the number of spectra to analyse (Beddows et al., 2009). The cluster analysis was performed on the hourly averaged data of all four sites together (39 size bins and 2006 h), which allowed study of the transport and spatial evolution of aerosols in the urban environment of Barcelona and its region.

k-means clustering analysis
The k-means clustering analysis performed on the SAPUSS SMPS data resulted in nine clusters. Cluster validation indices were used to choose the optimum number of spectra to divide the data as described elsewhere (Beddows et al., 2009;Dall'Osto et al., 2011b). This is solely a statistical optimisation, not accounting for the scientific context in which the data were collected, based on the shape of the spectra.
To reduce the possibility that any clusters combined spectra from two different sources or processes, a higher optimum cluster number (in the range 10-20) was selected in the initial analysis. Having studied the cluster within a scientific context, common clusters were recombined (Dall'Osto et al., 2011b) and for our data set this procedure resulted in a ninecluster solution. The results herein presented summarise all the particle size distributions acquired during SAPUSS at the four monitoring sites (Fig. 1). Please note that the size distributions reported in Fig. 1 are extrapolated to the largest size depending on the site, given the good agreement shown between the harmonised (resulting from the k-means clustering analysis) and the raw spectra. The nine clusters show a very different frequency among the four different monitoring sites (Table 1). This is expected due to the different aerosol sources affecting each site. Such a complex scenario can be broadly summarised in three main aerosol categories: -Three of the clusters are associated with "Traffic" (T clus_1 , T clus_2 and T clus_3 ) and prevailed during 30 % of all measured hours. Within the Traffic category, the differences between clusters are due to the proximity to the traffic source and to the atmospheric processes affecting aerosols after emission, such as evaporation (Dall'Osto et al., 2011a;Harrison et al., 2012). As expected, the RS site is the most affected by traffic emission as it is located close to traffic sources (Table 1). Indeed, T clus_1 and T clus_2 clusters are almost exclusive to the RS site and account for 24 and 47 % of the hours measured at this site, respectively (Table 1). In contrast, T clus_3 is associated with the urban background stations of UB site (22 %) and TC site (14 %), which are more distant from traffic sources. As expected, the regional RB site is not characterised by primary traffic size distributions.
-Three clusters referred to the "Background Pollution" category (UB clus_1 -Urban Background 1; RB clus_1 -Regional Background 1; and RB clus_2 -Regional Background 2) characterised the overall aerosol population for 54 % of the sampling time. They were predominantly found at the background sites of UB site , TC site and RB site . Cluster UB clus_1 was found at all  Table 2. Summary of the lognormal fitting of the 9 clusters separated into the nucleation, Aitken and accumulation modes. Peak maximum values were found between 15 and 24 nm for the nucleation mode, 33-77 nm for the Aitken mode and particles larger than 100 nm correspond to the accumulation mode. The total area percentage for each peak is also indicated.
Type k-means cluster nucleation Aitken accumulation

Special case
Nucleation 15 ± 1 nm (16 %) 28 ± 5 nm (84 %) -Regional Nitrate -52 ± 1 nm (100 %) -Mix -39 ± 1 nm (100 %)four sites and had very dynamic characteristics. It was found more frequently at the UB site and the TC site (around 25 % of hours at each site) in contrast to the 15 % of hours registered at both RS site and RB site (Table 1). On the other hand, clusters describing a Regional Background pollution environment (RB clus_1 and RB clus_2 ) were found more commonly at the SA-PUSS monitoring sites not affected by anthropogenic sources. This is the case of the RB clus_1 cluster, seen at the RB site , UB site and TC site for 22, 19, and 18 % of the time, respectively. RB clus_2 was also found frequently at the RB site (39 %), followed by UB site (17 %) and TC site (15 %).
-Three clusters (Nucleation -NU clus ; Regional Nitrate -NIT clus ; and Mix -MIX clus ) associated with "Special cases" accounted for the remaining 16 % of the aerosol size distribution overall population. The NU cluster was seen primarily at the urban background stations and rarely at the RS site or the RB site . The NIT cluster occurred mostly at the RB site , while the MIX cluster (the least characterised among all) was observed in almost the same proportion at all sites except for the UB site (Table 1). Figure 1 shows the particle size distribution for each of the nine clusters. In order to support the interpretation of this figure, the log-normal fitting modes of each cluster and their modal diameters and mode area percentages are presented in Fig. S1 and Table 2, respectively. Furthermore, Table 3 shows the dominant air mass for each cluster presented. This is achieved following the procedure described in Dall'Osto et al. (2013b), classifying the air mass origin of each day of the campaign as Atlantic (ATL), European-Mediterranean (EUR), North African east (NAF_E), North African west (NAF_W) or Regional (REG). Additionally, the average values of air pollutant and meteorological parameters can be found in Table 4, and the diurnal trends are shown in Fig. 2 should be noted that clusters showing a lower incidence than 30 counts (hours) at any site were not considered. According to the data obtained, each cluster can be described as follows:

Traffic-related clusters
-T clus_1 represents 8 % of the total sample and is exclusively observed at the RS site (24 %). It presents one of the highest N values, showing a bimodal size distribution with a well-defined nucleation size mode at 23 ± 1 nm and a broad Aitken mode at 33 ± 6 nm ( Fig. 1, Table 2, Fig. S1a). It is associated with high concentration levels of traffic pollutants such as BC (3.3 ± 1.4 µg m −3 ), NO (9 ± 7 µg m −3 ) and NO 2 (39 ± 15 µg m −3 , Fig. S3c, S2e, f). Regarding particle mass it shows high PM 10 concentration values (34 ± 15 µg m −3 ) and also high N values in the nucleation mode N 15−30nm (2.1 × 10 3 cm −3 ), as shown in Table 4. It also has the lowest relative humidity (54 ± 16 %) of all clusters at the RS site and occurs mainly in the afternoon and early evening (Fig. 2b).
-T clus_2 prevails during 13 % of the time and is the dominant cluster at the RS site (47 %). Like cluster T clus_1 , it shows a bimodal particle size distribution peaking at 24 ± 1 nm and 34 ± 1 nm, and it has similar concentration values of BC (3.3 ± 1.7 µg m −3 ), NO (8 ± 8 µg m −3 ) and NO 2 (39 ± 18 µg m −3 ). The most important difference between this cluster and the previous traffic cluster (T clus_1 ) is that this one is associated with higher RH conditions (67 ± 11 versus 54 ± 16 %). It also contains less particles in the nucleation mode range N 15−30nm (1.3 × 10 3 cm −3 and 2.1 × 10 3 cm −3 , respectively). This points to an opposite trend between RH and ultrafine particle concentrations, as further discussed in Sect. 4.3. This cluster correlates temporally with the morning rush hour (8 a.m.) and is maintained until the afternoon (2 p.m.). Its frequency rises again coinciding with the evening rush hour (8 p.m.) as can be seen in Fig. 2c.
-T clus_3 prevails 9 % of the time and characterises the traffic environment detected at the urban background stations of UB site (22 %) and TC site (14 %). Like T clus_1 and T clus_2 , T clus_3 also shows a bimodal distribution with one peak in the nucleation size mode and a second in the Aitken mode, although with different size modes (a much reduced nucleation mode at 15 ± 1 nm and broader Aitken mode at 42 ± 4 nm,   respectively; see Table 2). T clus_3 is associated with the highest levels of traffic pollutants at the urban background UB site and TC site , with traffic gaseous average concentrations similar to T clus_1 and T clus_2 (see Fig. S2e, f, g). However, it presents the lowest N concentrations among the three traffic clusters ( Table 4). Furthermore, T clus_3 is related to the predominance of Atlantic air masses. This is in contrast to T clus_1 and T clus_2 , which are found under regional stagnant air mass conditions (see Table 3). T clus_3 occurred mainly during the daylight hours and late evening at UB site , and reaches TC site at midday due to transport by the sea breeze circulation (Fig. 2d). Further consideration on the difference among the three traffic-related clusters is given in Sect. 4.

Background pollution clusters
-Urban Background 1 (UB clus_1 ) is the most prevalent of all clusters (21 % of the time) as it has a significant occurrence at all the four monitoring sites (Table 1). However, it occurs more frequently at the urban background sites (UB site : 28 %; TC site : 26 %). Like the traffic clusters, it exhibits a bimodal distribution with a small nucleation size mode (16 ± 1 nm) and a broader Aitken mode (53 ± 1 nm). Nevertheless, it is important to note that the nucleation mode is less pronounced in comparison to the Traffic clusters and N concentrations are lower (Fig. 1, Tables 2, 4). This cluster is also affected by moderate levels of traffic pollutants: e.g. at the RS site the level of NO 2 reached 25 ± 15 µg m −3 . This background cluster prevails during nighttime at the RS site , likely representing the cleanest conditions at the road monitoring site. By contrast, at the UB site this cluster does not show a clear diurnal variation, confirming its urban background nature (Fig. 2e). It is interesting to note that this cluster was monitored during the morning in the hilly background environment (TC site ) and later on in the afternoon at the regional RB site . This suggests that the urban background pollution (represented by this cluster, and hence named after it) can be transported by the sea breeze circulation from the city centre to the regional background (Fig. 2e).
-The Regional Background Pollution 1 (RB clus_1 ) cluster prevails 15 % of the time and is present at all sites except at the RS site . At the RB site it accounts for 22 % of the time, while at the urban background UB site and TC site represent 19 and 18 %, respectively. This cluster was the only one to have a tri-modal size distribution, with size modes at 20 ± 2, 51 ± 3 and 135 ± 8 nm, the accumulation mode being the dominant one (Table 2). It shows the highest PM concentrations of all clusters for UB site , TC site and RB site (e.g. at UB site PM 10 is 34 ± 12 µg m −3 , PM 2.5 is 25 ± 9 µg m −3 and PM 1 is 18 ± 5 µg m −3 ; Table 4). It is also associated with the highest wind speed values of all clusters at UB site (3.8 ± 2.2 m s −1 ), TC site (5 ± 3 m s −1 ) and RB site (0.8 ± 0.8 ms −1 ). Figure 2f shows that it prevails during the night in TC site , when the site is less influenced by the urban background. At the UB site it occurs regardless of the hour, suggesting that regional background size distributions can also describe the lowest urban background conditions at the UB site .
-The Regional Background Pollution 2 (RB clus_2 ) cluster occurs more often at the regional background RB site (39 %) and then decreases in occurrence as we come close to the city: TC site (15 %) and UB site (17 %). It has a small nucleation size mode at 17 ± 1 nm and a dominant Aitken mode at 77 ± 1 nm. Regarding the diurnal trends (Fig. 2g) it can be observed that it is similar at all four sites, peaking at night. The main differences between RB clus_1 and RB clus_2 clusters is that the first one accounts for aged and long-transport aerosols (high loading of PM mass, Table 4) and is dominated by the accumulation mode (Table 2). By contrast, cluster RB clus_2 presents a broad peak in the Aitken mode with higher N and lower mass concentration levels. Further discussion can be found in Sect. 4.1.

Minor clusters -
The Nucleation cluster (NU clus ) represents only 5 % of all observations and occurs mainly at the urban background UB site and TC site (11 and 6 %, respectively). It has a main nucleation size mode at 15 ± 1 nm and a small Aitken mode at 28 ± 5 nm (Fig. S1g). This cluster prevails under intense solar radiation at both UB site (233 ± 273 Wm −2 ) and TC site (365 ± 285 Wm −2 ) as well as relatively high ozone concentrations at UB site (64 ± 18 µg m −3 ) and TC site (75 ± 13 µg m −3 , Table 4, Fig. S2, S3). The high total N concentrations (1.5 × 10 4 cm −3 at UB site and 1.1 × 10 4 cm −3 at TC site ) and the concentration for the nucleation mode N 15−30nm at both UB site (2.4 × 10 3 cm −3 ) and TC site (2.1 × 10 3 cm −3 ) should also be noted. The diurnal trends also confirm that this cluster is associated with photochemical nucleation events peaking during the afternoon and early evening at the UB site (14-20 h) and TC site (12-15 h), respectively (Fig. 2h). This cluster was found to describe well the nucleation events described in detail elsewhere in this ACP SAPUSS special issue (Dall'Osto et al., 2013a). However, it should be noted that during this study only particles above 15 nm were monitored due to the SMPS configurations. Therefore, the NU clus accounts for the nucleating particles that have grown to such detectable sizes -thus leading to an underestimation of the early stage nucleation processes. It is also of note that the frequency of this NU clus increase in June-August  compared to September-October (this study).
-The Regional Nitrate cluster represents 6 % of the total, and occurs predominantly at the TC site (7 %) and RB site (14 %). It exhibits a unimodal aerosol size distribution peaking at 52 ± 1 nm (Fig. S1h). It is found to peak mainly during nighttime (Fig. 2i). This mode is smaller than a similar k-means cluster (cluster regional, 90 ± 12 nm) found in the clustering analysis of Dall'Osto et al. (2012) for the whole year 2004 in the urban area of Barcelona. In this regard, it is interesting to note that the nitrate cluster of this study was found to occur mainly at the TC site and RB site , the two sites that are away from the urban city centre, suggesting different aerosol size distributions for urban background (Dall'Osto et al., 2012) and regional background nitrate (this study). Additionally, SAPUSS measurements were restricted to the autumn season, whereas the previous study included a whole year of measurements . It is likely that the larger-sized mode of the previous study reflects the wintertime high nitrate mass loadings not monitored during this intensive SAPUSS field campaign.
-The Mix cluster occurs 6-7 % of the time at the RS site , TC site and RB site . It exhibits a unimodal size distribution with a peak in the Aitken mode at 39 ± 1 nm ( Table 2). The temporal trends and the average values of the air quality parameters were not well defined (Fig. 2j, Table 4), likely due to a mix of sources and atmospheric processes describing this factor. This factor cannot be associated with any specific source and was found to be the least well defined of all the nine clusters. It is associated with high concentrations of traffic-related pollutants (NO, CO and black carbon) and SO 2 , but is clearly not heavily influenced by fresh traffic emissions.

Size distributions
The results presented above were expected in the sense that the monitoring sites closest to traffic pollution are the ones most influenced by vehicle exhaust emissions (Traffic kmeans category). In contrast, when moving away from the city centre, the particle size distributions are mainly described by the k-means clusters representative of the background conditions (Background Pollution k-means category). The dominant clusters at RS site (T clus_1 and T clus_2 ) show very similarly size modes in the nucleation and Aitken sizes, centred between 20 and 35 nm and typical of roadside aerosol size distributions (Charron and Harrison 2003;Rönkkö et al., 2007;Dall'Osto et al., 2011a). The finest mode (23 ± 1 nm for T clus_1 and 24 ± 1 nm for T clus_2 ) is well defined (Fig. S1a, b) and can be attributed to particles generated from vehicle exhaust emissions. The Aitken mode, peaking at 33 ± 6 nm and 34 ± 1 nm (T clus_1 and T clus_2 , respectively), is broader than the nucleation ones (see Fig. S1a, b). This mode is somehow in between the position of the modes at around 20 nm associated with nucleation mode particles generated during dilution of diesel exhaust emissions (Ntziachristos et al., 2007) and at around 50-60 nm corresponding to solid carbonaceous particles from diesel exhaust (Shi et al., 2000;Harrison et al., 2011). Out of the two Traffic clusters at RS site , T clus_2 reflects the traffic rush hour diurnal variation (Fig. 2c) and is therefore more representative of fresh vehicle exhaust emissions. By contrast, T clus_1 is seen mainly during daytime (Fig. 2b) and is more affected by other sources and meteorological conditions (lower RH). T clus_1 has a wider nucleation mode area (21 %; see Table 2) whilst T clus_2 shows a higher dominance of the Aitken mode (96 % of the total area). When moving away from the traffic hot spot emission sources (RS site ), the aerosol size distributions describing such sources showed a strikingly different aerosol size mode. This is well seen in our study of cluster T clus_3 , which is the one that best describes the diluted traffic conditions detected at the urban background sites (UB site and TC site ). In this case, the nucleation mode peak is found reduced in diameter by 25 % (at 15 nm) relative to the nucleation mode detected at the RS site . Moreover, there is a loss of area under the nucleation mode (Fig. 1), which also means a loss of particle number within the 15-228 nm size range. This suggests that primary particles originating close to traffic sources (around 20 nm mode, like T clus_1 and T clus_2 nucleation mode peaks) can reduce their sizes by evaporation processes during advection to the urban background site, thus leading to a shift towards smaller-sized modes (Dall'Osto at al., 2011a;Harrison et al., 2012). On the other hand, the modal diameter of the Aitken mode of cluster T clus_3 (42 nm) is larger than the other two traffic clusters (33 nm for T clus_1 and 34 nm for T clus_2 ), suggesting that coagulation and condensation can occur in the Aitken mode. This shows that fine organic carbon (OC) mode aerosols (more volatile) tend to evaporate whereas the solid elemental carbon (EC) aerosols (more stable) do not Harrison et al., 2012).
The size distribution of cluster UB clus_1 suggests that it contains evaporating aerosols (nucleation peak located at 16 nm) but also aged aerosols with an anthropogenic origin (Aitken peak at 53 nm). The latter may also represent the involatile solid graphite particles in vehicle exhaust . This cluster describes the urban background pollution, which can reach the suburban (TC site ) and regional monitoring (RB site ) sites during the afternoon sea breeze circulation (Dall'Osto et al., 2013b). An example of this aerosol transport and evolution of size distributions can be seen for the day 28 September 2010 (Table S1, Fig. S4). By contrast, a very different scenario was found at the RB site , dominated by background clusters (RB clus_1 and RB clus_2 ). They all present much lower N in their size distributions in comparison to the Traffic clusters (Fig. 1). The RB clus_1 cluster is found under Regional air mass conditions; it shows low N and a dominant accumulation mode, thus pointing to aged anthropogenic aerosols, typical of regional recirculation of air masses. In addition, high PM concentrations are measured for RB clus_1 in the urban and rural background stations.
Regarding the minor clusters, the most relevant is the Nucleation cluster, showing that photo-nucleation processes occur in urban environments in southern Mediterranean areas, primarily in urban and suburban background scenarios when the solar radiation is very intense (Pey et al., 2009;Reche et al., 2011;Dall'Osto et al., 2012). The Regional Nitrate cluster appears more frequently at the RB site during nighttime. The Mix cluster was not well defined.

SMPS k-means clustering results explained by cluster proximity diagram during SAPUSS
The results described in Sect. 3.1 are graphically summarised by a Cluster Proximity Diagram (CPD) in Fig. 3. The CPD displays how the clusters are arranged relative to each other based on the similarity of the elements in each cluster measured using the Silhouette Width (Beddows et al., 2009). While k-means clustering matches together the most similar spectra into the nine clusters (Figs. 1, 2), the CPD positions these clusters according to the degree of similarity within each cluster. The more similar the elements within a selection of clusters are, the closer the nodes representing those clusters are placed to each other in the diagram (e.g. T clus_1 , T clus_2 and T clus_3 ). Using the optimum number of clusters (9), the elements of this selection (e.g. T clus_1 , T clus_2 and T clus_3 ) are sufficiently similar to each other to be placed next to each other in the diagram, but they are not sufficiently similar to form a new cluster. Likewise, pairs of nodes furthest apart in the diagram represent clusters whose elements are the most dissimilar (e.g. NU clus and RB clus_1 ). In particular, this is illustrated further in Fig. 3 where the average modal diameter of the clusters increases from left to right. Clusters T clus_1 and T clus_2 are associated with primary traffic aerosols and are positioned in the same vertical area of the diagram. Cluster NU clus and cluster T clus_3 are confined in the smallest modal diameters, in the far left part of the CPD. This is due to the atmospheric sources and the processes affecting cluster NU clus (new particle formation) and cluster T clus_3 (evaporation of traffic-related particles T clus_1−2 ; Dall'Osto et al., 2011a). By contrast, the largest modal diameters detected (right part of CPD, Fig. 3) are associated with regional background clusters (RB clus_1 and RB clus_2 , same vertical position in the CPD). Cluster MIX clus -not well defined -stands in the middle of the CPD and is likely to be a mixture of all sources and processes. By contrast, NIT clus stands in a position close to the RB clusters. Finally, it is interesting to note that cluster UB1 (which is associated with the urban background pollution) is linked to all but two (NU clus and T clus_1 ) of the clusters. This suggests that the sources/processes loading clusters T clus_3 , T clus_2 , MIX clus , NIT clus , RB clus_2 and RB clus_1 all consequently develop and contribute to urban background aerosol. Clusters T clus_1 and NU clus are strong ultrafine aerosol sources which are somehow modified (for example by growth or evaporation) before contributing to the urban background aerosol population.
In summary, the main sources of the smallest ultrafine particles detected during SAPUSS are due to secondary processes (NU clus ) and the evaporation of traffic-related particles (T clus_3 , coming from T clus_1 and T clus_2 ). The lowest particle number concentrations and the highest modal diameters are related to regional background conditions (RB clus_1 , RB clus_2 , NIT clus ). Finally, all these diverse clusters contribute directly into the urban background general aerosol particle spectra (UB clus_1 ), which is indeed at the centre of Fig. 3.

The effect of meteorology on primary traffic emissions and secondary nucleation processes during SAPUSS
The high values of N recorded in the urban area of Barcelona can be mainly attributed to primary vehicle exhaust emissions (Pey et al., 2009). However, Reche et al. (2011) showed that in Barcelona nucleation events can occur in the middle of the day all year round, contributing to an average of 54 % of total N (average of year 2009). Indeed, during SAPUSS the particle number concentrations (N >5nm ) were highly correlated with black carbon (BC, a primary marker for traf- (regional only, regional all, urban). An in-depth study of these new particle formation events during SAPUSS can be found under Dall'Osto et al. (2013a). Overall, during SA-PUSS the city centre of Barcelona was found to be a source of non-volatile traffic primary particles (29-39 % of N >5 nm ), but other sources, including secondary freshly nucleated particles contributed up to 61-71 % of particle number (N >5nm ) at all sites (Dall'Osto et al., 2013a). However, previous studies considering only particles larger than 13 nm found that photochemically induced nucleation particles make only a small contribution to the total particle number concentration (2-3 % of the total; Dall'Osto et al., 2012). The present study considering aerosol size distributions above 15 nm (N >15nm ) also reports a small percentage of N (<2 % of the total number) associated with nucleation events, calculated by considering the percentage of time the Nucleation cluster occurred (5 %; see Table 1) and the nucleation mode area in it (16 %; see Table 2). In other words, within clean Atlantic air masses, nucleation processes strongly affect N >5nm concentrations (Reche et al., 2011;Dall'Osto et al., 2013a). However, such particles often fail to grow above the SMPS detection limit of 13 nm  or 15 nm (this study) in the Mediterranean urban environment.
Less is known on the effect of meteorology on freshly emitted traffic-related ultrafine aerosols in the Mediterranean region. Hence, this section aims to investigate the effect of meteorology on primary traffic emissions. Our objective is to investigate the effect of meteorological parameters on freshly emitted particles from vehicles for a given primary traffic aerosol size distribution. For this purpose, we consider only the traffic hot spot monitoring site (RS site ). We therefore monitor a specific SMPS cluster (T clus_2 , Fig. 1) which best represents traffic emissions and also shows a good correlation with traffic counts at the RS reported in the SAPUSS overview (R 2 = 0.9). We additionally removed from this analysis the days dominated by nucleation events (25 September, 5 October, and 17 October 2010) and rain episodes (11 October 2010), thus obtaining a homogeneous data set representative of the average fresh traffic emissions (26 days in total). In other words, we only considered hourly data characterised by a specific aerosol size distribution (SMPS cluster T clus_2 ) sampled in a road site hot spot (RS site ). This is a unique query which allows us to study how meteorological parameters affect the total N (measured by CPC, N 5−1000nm ) for a given aerosol size distributions (measured by an SMPS, N 15−228nm ).
In order to do so, we plotted the ratio of N measured by the CPC (N >5nm ) and the SMPS (N 15−228nm ) deployed at the road site (RS site ) versus key meteorological parameters (wind speed, solar radiation, temperature and RH). The ratio N >5nm / N 15−228nm accounts for particles with diameters mainly between 5 and 15 nm. Perhaps surprisingly, no meteorological variable was found to give a significant correlation with the total particle number ratio, despite earlier stud-ies (e.g. Charron and Harrison, 2003) finding an inverse relationship to temperature, and a positive relationship with wind speed. It therefore appears likely that other factors such as the road traffic composition and local condensation sink are more important in influencing the nanoparticle number concentration at the RS site . Figure S5 shows hourly values of RH versus N 5−1000 / N 15−228 , where the solid circle points are also coloured as a function of the air mass origin (ATL: Atlantic; REG: Regional; NAF_W: North African west; and NAF_E: North African east). Figure S5 suggests that for a specific aerosol size distribution associated with primary traffic emissions (T clus_2 ), there is a very high variability of ultrafine particles in the range 5-15 nm. However, the trend is not significant (R 2 <0.1) for the hourly values (Fig. S5). These findings highlight the difficulty of establishing meaningful standards for vehicle emissions based upon particle number concentration given the highly remarkable dynamics of traffic-related particles in the urban atmosphere (Dall'Osto et al., 2011a;Fujitani et al., 2012;Li et al., 2013).

Correlations of N with air quality parameters
The current European directive on air quality (2008/50/CE) is based on particle mass although mass concentration limit values do not protect against high N (Atkinson et al., 2010). Figure 4 shows several plots of N 15−30 nm and N 15−228nm versus selected air pollutant concentrations (NO 2 , BC, PM 2.5 and PM 2.5−10 ). Each point shows the average value of N x versus an average of a specific air quality parameter for each of the k-means clusters obtained at each monitoring site.
Average parameters that presented less than 30 total counts for each k-mean cluster were omitted from the diagrams presented in Fig. 4. Figure 4 shows that the current SMPS SA-PUSS data sets can be greatly simplified, allowing a better description of the airborne particle number concentrations and their correlations with other air quality parameters. Figure 4a and b show the NO 2 concentrations correlating with N, given that the most polluted clusters are the Traffic ones (black spots), followed by UB clus_1 , RB clus_1 and RB clus_2 . It should be noted that the main difference between N 15−30 / NO 2 and N 15−228 / NO 2 is given by the location of the NU clus . These clusters show a high average N (2000-2500 cm −3 ) but an intermediate NO 2 concentration (15-25 µg m −3 ), confirming nucleation events are a source of N not directly related to primary traffic emissions (Dall'Osto et al., 2013a; this special issue). A similar conclusion -although less clear -can be drawn if BC is used as an air quality parameter (Fig. 4c, d). The same applies to CO (although not shown). PM 2.5 is regulated by the 2008/50/CE Directive. Figure 4e and f show that RB clus_1 and RB clus_2 clusters are the ones that recorded the highest PM 2.5 levels and lower N concentrations in both cases. UB clus_1 , T clus_1−3 and NU clus show lower PM 2.5 and higher N concentrations progressively, this trend being clearer for the total fraction N 15−228nm (Fig. 4f). Figures 4g and h show the corresponding graphs for PM coarse , the mass concentration of PM between 2.5 and 10 µm. Both figures clearly show three main groups: a first one enclosing the city monitoring sites (UB site , RS site ), a second one associated with the background hill urban site (TC site ) and a third one containing Background Pollution clusters. In both figures, the Traffic and Nucleation clusters associated with the city sites (UB site , RS site ) are located at the top right corner. When considering the same clusters but for TC site , although they still show high N, they contain less coarse particles than at the RS site and UB site , implying the city is a source of urban dust coarse aerosols not found in the background monitoring sites. This clearly suggests that the coarse dust detected in the city mostly arises from anthropogenic sources found in the city (UB site , RS site ) but not in the suburban areas (TC site ). Finally, in the bottom part of the graphs we find the Regional Background clusters. They show low values of N and moderate values of coarse particle mass.

Conclusions
Measurements of particle size distribution were made in the Barcelona urban area during the SAPUSS campaign (20 September-20 October 2010). Four SMPSs were simultaneously deployed at four different monitoring sites: a road site (RS site ), two urban background sites (UB site and TC site ) and a regional background station (RB site ). Measurement size ranges for all monitoring sites were harmonised, resulting in a homogenous data set with particle sizes between 15 and 228 nm at 1 h resolution. A k-means clustering analysis was performed on the combined four data sets, resulting in nine size distributions that described aerosol population. Three clusters account for traffic conditions (30 %), three account for background pollution (54 %) and three described specific special cases (16 %). The traffic conditions influence the sites closest to their sources, while the more distant sites are more influenced by background clusters. Nucleation under high solar radiation conditions is a common feature in southern European cities and contributes to an increase in N, although such particles often fail to grow to sizes above 10-15 nm. This study also clearly shows that evaporation of traffic-related ultrafine aerosols occurs when the air mass moves away from the traffic hot spot. Particles of between 5 and 15 nm show the most complex behaviour. On the one hand, new non-traffic particles formed in cities often fail to grow above 15 nm. On the other hand, 20-30 nm primary traffic particles shrink to smaller sizes soon after emission. Additional studies on the strategies to monitor in a comparable way N 5−15nm levels, as well as on the origin and health effects of this specific size fraction, are therefore suggested in order to support decisions on the potential use of SMPS-CPC technologies for air quality monitoring, because this size range makes a major contribution to total particle numbers.