Organic aerosol components derived from 25 AMS data sets across Europe using a consistent ME-2 based source apportionment approach

Organic aerosols (OA) represent one of the major constituents of submicron particulate matter (PM 1) and comprise a huge variety of compounds emitted by different sources. Three intensive measurement field campaigns to investigate the aerosol chemical composition all over Europe were carried out within the framework of the European Integrated Project on Aerosol Cloud Climate and Air Quality Interactions (EUCAARI) and the intensive campaigns of European Monitoring and Evaluation Programme (EMEP) during 2008 (May–June and September–October) and 2009 (February–March). In this paper we focus on the identification of the main organic aerosol sources and we define a standardized methodology to perform source apportionment using positive matrix factorization (PMF) with the multilinear engine (ME-2) on Aerodyne aerosol mass spectrometer (AMS) data. Our source apportionment procedure is tested and applied on 25 data sets accounting for two urban, several rural and remote and two high altitude sites; therefore it is likely suitable for the treatment of AMS-related ambient data sets. For most of the sites, four organic components are retrieved, improving significantly previous source apportionment results where only a separation in primary and secondary OA sources was possible. Generally, our solutions include two primary OA sources, i.e. hydrocarbon-like OA (HOA) and biomass burning OA (BBOA) and two secondary OA components, i.e. semi-volatile oxygenated OA (SV-OOA) and low-volatility oxygenated OA (LV-OOA). For specific sites cooking-related (COA) and marine-related sources (MSA) are also separated. Finally, our work provides a large overview of organic aerosol sources in Europe and an interesting set of highly time resolved data for modeling purposes.

Abstract. Organic aerosols (OA) represent one of the major constituents of submicron particulate matter (PM 1 ) and comprise a huge variety of compounds emitted by different sources. Three intensive measurement field campaigns to investigate the aerosol chemical composition all over Europe were carried out within the framework of the European Integrated Project on Aerosol Cloud Climate and Air Quality Interactions (EUCAARI) and the intensive campaigns of European Monitoring and Evaluation Programme (EMEP) during 2008 (May-June and September-October) and 2009 (February-March). In this paper we focus on the identification of the main organic aerosol sources and we define a standardized methodology to perform source apportionment using positive matrix factorization (PMF) with the multilinear engine (ME-2) on Aerodyne aerosol mass spectrometer (AMS) data. Our source apportionment procedure is tested and applied on 25 data sets accounting for two urban, several rural and remote and two high altitude sites; therefore it is likely suitable for the treatment of AMS-related ambient data sets. For most of the sites, four organic components are retrieved, improving significantly previous source apportionment results where only a separation in primary and secondary OA sources was possible. Generally, our solutions include two primary OA sources, i.e. hydrocarbon-like OA (HOA) and biomass burning OA (BBOA) and two secondary OA components, i.e. semi-volatile oxygenated OA (SV-OOA) and low-volatility oxygenated OA (LV-OOA). For specific sites cooking-related (COA) and marine-related sources (MSA) are also separated. Finally, our work provides a large overview of organic aerosol sources in Europe and an interesting set of highly time resolved data for modeling purposes.

Introduction
Atmospheric aerosols negatively affect human health (Pope and Dockery, 2006), reduce visibility, and interact with climate and ecosystems (IPCC, 2007). Among particulate pollutants, great interest is dedicated to organic aerosols (OA) since they can represent from 20 to 90 % of the total submicron mass (Zhang et al., 2007;Jimenez et al., 2009). Organic aerosols are ubiquitous and are directly emitted by various sources, including traffic, combustion activities, biogenic emissions, and can also be produced via secondary formation pathways in the atmosphere (Hallquist et al., 2009). Constraining OA emission sources and understanding their evolution and fate in the atmosphere is therefore fundamental to define mitigation strategies for air quality.
Our work is part of the European Integrated Project on Aerosol Cloud Climate and Air Quality Interactions (EU-CAARI), which aims to understand the interactions between air pollution and climate. An introduction about project objectives and an overview on the goals reached within the EU-CAARI project are provided by several papers (Kulmala et al., , 2011Knote et al., 2011;Murphy et al., 2012). The coordinated EUCAARI campaigns of 2008 and 2009 provide significantly more aerosol mass spectrometer (AMS) data sets to analyze in comparison to previous efforts (Aas et al., 2012). For the investigation of the aerosol chemical composition and organic aerosol (OA) sources dedicated studies were performed. Nemitz et al. (2014) discuss the organic and inorganic components of atmospheric aerosols, using AMS measurements performed during three intensive field campaigns in 2008 and 2009. Major contribution to the submicron particulate matter (PM 1 ) mass is provided by the organic compounds, which contribute from 20 to 63 % to the total mass depending on the site. Our work deals with the identification and quantification of organic aerosol sources in Europe using high time resolution data from aerosol mass spectrometer. Here we focus on the investigation of OA sources applying the positive matrix factorization algorithm (PMF) running on the generalized multi-linear engine (ME-2) (Paatero, 1999;Canonaco et al., 2013) to the organic AMS mass spectra from all over Europe.
Currently, only a few studies concerning a broad spatial overview of OA sources are available in the literature. Zhang et al. (2007) investigated organic aerosol sources in urban and anthropogenically influenced remote sites in the Northern Hemisphere, focusing on the discrimination between the traffic-related and secondary oxygenated OA components. Jimenez et al. (2009) presented an overview of PM 1 chemical composition all over the world (including 8 European measurement sites) focusing on the identification of OA sources using AMS data. Ng et al. (2010) provided an overview of OA sources in the Northern Hemisphere, including a broader spatial domain than Europe and a wide range of locations affected by different aerosol sources. Moreover, their major focus was the investigation of the secondary oxygenated components and their aging. Lanz et al. (2010) provided an overview of the aerosol chemical composition and OA sources in central Europe focusing on Switzerland, Germany, Austria, France, and Liechtenstein. In all of these studies, the major fraction of PM 1 was often represented by organics which consisted, for most of the locations, of oxygenated OA; however the contribution of primary sources (like traffic and biomass burning) was not always identified especially in rural and remote places. Our work includes 17 measurement sites all over Europe, comprising 25 unit mass resolution AMS data sets, and represents therefore an unprecedented overview of OA sources in Europe. Moreover, the application of advanced source apportionment methods allow us to overcome limitations of commonly used source apportionment techniques for AMS data, such as the purely unconstrained positive matrix factorization (Canonaco et al., 2013). The positive matrix factorization (PMF) model does not always succeed since the co-variance of the sources might be large due to the meteorology and the relative source contributions which vary too little. This can often be the case at rural and remote sites but it was also shown for an urban background site in Zurich, for which Lanz et al. (2008) pioneered the use of ME-2 for AMS data. Here, for all measurement sites we are able to clearly separate primary and secondary OA components, including hydrocarbon-like OA (HOA, associated with traffic emissions), biomass burning OA (BBOA), cooking (COA) and secondary components (semi-volatile and low volatility oxygenated OA, SV-OOA and LV-OOA, respectively).
In addition, we provide a standardized source apportionment procedure applicable to any measurement site (urban, rural, remote, etc.) guiding source apportionment analysis for on-line measurements. In fact, when applying multivariate methods to AMS data, a critical phase is the evaluation of the results which is strongly affected by subjectivity and obviously depends on the expertise of the researcher. One goal of this work is to facilitate the analysis of the modeler dealing with AMS data; additionally, this strategy might be useful in particular for the analysis of the long-term monitoring network data retrieved with the quadrupole or time-offlight aerosol chemical speciation monitors (ACSM) (Ng et al., 2011b;Fröhlich et al., 2013) A final motivation of our work is to improve the prediction of POA (primary organic aerosol) and SOA (secondary organic aerosol) in regional and global models integrating our European overview of OA sources. Our source apportionment results are suitable for modeling purposes since understanding sources and processes of organic aerosols can substantially improve air quality and climate model predictions. Modeling POA and SOA components is challenging and still critical due to uncertainties in emission inventories and complex atmospheric processing. Including measurements of different OA components will improve the evaluation and constraining of modeling outputs. Our results will help in evaluating the accuracy of emission inventories (especially concerning primary sources) which need better constraints to improve regional and global models (Kanakidou et al., 2005;De Gouw and Jimenez, 2009), while SOA sources obtained from AMS source apportionment could be used to constrain SOA in global chemical transport models (Spracklen et al., 2011).  Li et al. (2013), and Paglione et al. (2013) for the Cabauw 2008 campaign, to Saarikoski et al. (2012) for the San Pietro Capofiume measurements, to Carbone et al. (2014) for the case of Helsinki, to Poulain et al. (2011) for Melpitz, to Dall'Osto et al. (2010) for Mace Head, and to Freney et al. (2011) for Puy de Dome. An overview about PM 1 aerosol chemical composition is provided in a companion paper by Nemitz et al. (2014), where a detailed discussion about measurements setup and data processing is also provided. The average concentrations of PM 1 chemical components as measured by the AMS are also reported in Table S1 in the Supplement. In this paper we focus on the organic aerosols (OA) component which represents the major fraction of submicron particulate matter for most of the sites, ranging between 20 and 63 % of PM 1 (concentration range: 0.6-8.2 µg m −3 ), consistent with the values found by Jimenez et al. (2009) andNg et al. (2010). Table 1 summarizes the average organic concentration for each site and all the seasons and the relative OA contribution to NR-PM 1 as measured by the AMS. Figure 2 represents an overview of the EUCAARI measurement field campaigns focusing on the organic aerosol sources (an analogous plot for the PM 1 chemical composition is reported in Nemitz et al. (2014)). For each site the average organic mass concentration of

Aerosol mass spectrometer measurements
The Aerodyne aerosol mass spectrometer measures sizeresolved mass spectra of the non-refractory (NR) PM 1 aerosol species, where NR species are operationally defined as those that flash vaporize at 600 • C and 10 −5 Torr. Black carbon, mineral dust, and metals usually cannot be detected and quantified by the AMS, while Ovadnevaite et al. (2012) shown the possibility to measure sea salt with the AMS. Several aerosol mass spectrometers were deployed all over Europe during the three intensive EUCAARI field campaigns  , including Q-AMS (quadrupole AMS) (Jayne et al., 2000), C-ToF-AMS (compact time of flight AMS) (Drewnick et al., 2005) and HR-ToF-AMS (high resolution time of flight AMS) (DeCarlo et al., 2006). The general working principle of the AMS is reported below; however the reader should refer to the aforementioned papers for a detailed description of the different AMS types. Briefly, air is sampled through a critical orifice into an aerodynamic lens, where the aerosol particles are focused into a narrow beam and accelerated to a velocity inversely related to their aerodynamic size. Particles are transmitted into a high vacuum detection chamber (10 −5 Torr) and impact on a heated surface (600 • C) where the non-refractory species vaporize. The resulting gas molecules are ionized by electron impact (EI, 70 eV) and the ions are extracted into the detection region to be classified by the mass spectrometer. Details about our AMS measurement quantification and data treatment (e.g., ionization efficiency calibrations, collection efficiency estimation, air corrections, etc.) are described elsewhere . For the evaluation of our source apportionment results, black carbon data obtained from aerosol light absorption measurements performed with an aethalometer or a multi angle absorption photometer (MAAP) were also used in our work where available (see Table S3).

The multilinear engine (ME-2)
Positive matrix factorization (PMF) is the most commonly used source apportionment method for AMS data Ulbrich et al., 2009;Zhang et al., 2011) to describe the measurements with a bilinear factor model (Paatero and Tapper, 1994): where x ij , g ik , f kj and e ij represent the matrix elements of the measurements (x), time series (g), factor profiles (f), and residuals (e). The subscript i corresponds to time, j to m/z, k to a discrete factor and p to the number of factors. The model solution is found iteratively minimizing Q using the least squares algorithm: where σ ij are the measurement uncertainties. The model solution is not unique due to rotational ambiguity (Paatero et al., 2002), in fact the product of the rotated matrix G and F (G = G · T and F = T −1 · F ) is equal to the product of the corresponding unrotated matrix which also provides the same value of the object function Q. In order to reduce rotational ambiguity within the ME-2 algorithm, the user can add a priori information into the model (e.g., source profiles), so that it does not rotate and it provides a rather unique solution (Paatero and Hopke, 2009).
We perform organic aerosol source apportionment using the multi-linear engine (ME-2) algorithm (Paatero, 1999) implemented within the toolkit SoFi (Source Finder) developed by Canonaco et al. (2013) at Paul Scherrer Institute. Similarly to the PMF solver (Paatero and Tapper, 1994), the ME-2 solver (Paatero, 1999) executes the positive matrix factorization algorithm. However, the user has the advantage to support the analysis by introducing a priori information in form of known factor time series and / or factor profiles, for example within the so-called a value approach (see Eqs. (3a) and (3b)). The a value (ranging from 0 up to values larger than 1) determines how much the resolved factors (f j,solution ) and g i,solution ) are allowed to vary from the input ones (f j , g i ), as defined in Eq. (3a) and (3b) (Canonaco et al., 2013). In our work we only constrained the mass spectra represented by f .
For example, if a = 0.1 when constraining a mass spectral profile, all of the m/z's in the fit profile can vary as much as −10 % to +10 % of the input constraining mass spectrum profile.
In our work, a constant a value is applied to the entire constrained mass spectra (MS); however a softer constraining technique is provided by the pulling approach (Paatero and Hopke, 2009;Brown et al., 2012), which is available within the SoFi package (Canonaco et al., 2013) and which is explained in more detail in Canonaco et al. (2014b).
The ME-2 solver is here successfully applied to the time series of the unit mass resolution organic mass spectra measured by the AMS, including for most of the sites m/z up to 200 (for a few sites the analysis was performed only up to m/z 150 due to the low signal to noise ratio (SNR) observed). Data are first averaged to 15-30 minute time resolution and after performing the source apportionment analysis they are averaged to 1 hour for modeling purposes. The error matrix preparation before running the source apportionment algorithm is performed following the procedure introduced by Ulbrich et al. (2009). Briefly, a minimum counting error of 1 ion is applied, m/z with SNR between 2 and 0.2 (weak variables) are downweighted by a factor of 2, while bad variables (SNR<0.2) are downweighted by a factor of 10 (Paatero and Hopke, 2003;Ulbrich et al., 2009). Moreover, based on the AMS fragmentation table, some organic masses are not directly measured but calculated as a fraction of the organic signal at m/z 44 (Allan et al., 2004); therefore the errors of these m/z 44 dependent peaks are downweighted ).

A standardized source apportionment strategy
In this section we provide technical guidelines to perform a standard source apportionment analysis on AMS data in order to identify well known organic aerosol sources, like hydrocarbon-like (HOA), biomass burning (BBOA), cooking (COA) and oxygenated components (OOA), but also sitespecific sources. Our approach is particularly relevant for rural locations where the temporal variability of emission sources is less distinct and where the aging processes are dominant compared to fresh emissions. A detailed description of the main features of these OA sources (source profile, diurnal patterns, etc.) is presented in Sect. 4. Here, we define first our source apportionment strategy and then we provide details about the application of this methodology on the EUCAARI-EMEP data. Finally, some technical examples concerning the data treatment and interpretation are also reported in Sects. 3.2.2 and 3.2.3.

Technical guidelines
Within our work we define a standardized methodology to perform source apportionment on AMS data using the ME-2 algorithm with the aforementioned SoFi toolkit (Paatero, 1999;Canonaco et al., 2013). The sequential steps of the methodology are reported below: 1. Unconstrained run (PMF).
2. Constrain the HOA mass spectrum (MS) with a low a value (e.g., a =0.05-0.1) and test various number of factors.
3. Look for BBOA (if not identified yet): constrain the BBOA MS if f 60 (i.e., the fraction of m/z 60 to the total organic mass) is above background level and check temporal structures like diurnal increases in the evening during the cold season due to domestic wood burning (suggested a value = 0.3-0.5).
4. Look for COA (if cooking not found yet): check the f 55 -f 57 plot for cooking evidence (where f 55 and f 57 are the fraction of m/z 55 and m/z 57 to the total organic mass respectively; see Mohr et al., 2012). Fix it in any case and check its diurnal pattern (the presence of the meal hour peaks is necessary to support it at least in urban areas).
5. Residual analysis: a structure in the residual diurnals might indicate possible sources not separated yet by the model (refer to Section 3.2.3). For each step the residual plots should always be consulted in order to evaluate whether the constrained profile(s) has(have) caused structures in the residuals. If so, the constrained profile should be tested with a higher scalar a value.
6. In general the OOA components are not fixed, but are left as 1 to 3 additional unconstrained factors.
Our approach starts with an unconstrained run, where no a priori information concerning the source mass spectra is added. This first step is important because it reveals the possibility of separation for several OA components with PMF. It also gives the user an idea of the number of possible sources for that site, even though they might not be clearly separated yet. If the HOA mass spectrum is not identified in the first step (e.g., considering from 1 to 5 unconstrained factors), the user should fix the HOA mass spectrum with the a value approach and, to evaluate the presence of this source into the data set, investigate its diurnal pattern and correlation with available external tracers (e.g., black carbon, NOx, etc.). At this step several constrained runs are required varying the number of unconstrained factors (e.g., from 3 to 5) in order to investigate the presence of other possible sources (e.g., BBOA, COA, secondary components and possibly specific site-related factors). Moreover, the user should perform a sensitivity analysis on the a value associated with the HOA MS in order to define a range of possible solutions. A detailed discussion about the sensitivity analysis is reported in Sect. 4.5. If the user is unable to identify a biomass burning related source within step 2, the investigation of the diurnal pattern of a specific organic tracer for levoglucosan and primary biomass combustion species (f 60 = m/z 60 / OA)  can reveal the presence of BBOA at the site (e.g., increasing contribution of f 60 during the evening suggests the use of biomass burning for domestic heating purposes). In addition, it is important to study the variability of f 60 above background levels, which is reported to be 0.3 % ± 0.06 % Aiken et al., 2009;Cubison et al., 2011). Finally, a primary OA source especially important in urban areas is cooking (COA) (Slowik et al., 2010;Allan et al., 2010;Sun et al., 2011;Mohr et al., 2012;. The cooking contribution is not easily resolved even for urban sites due to the similarity of its mass spectrum with the one of HOA in unit mass resolution. So after identifying HOA and BBOA, the user should constrain the COA MS with a rather low a value (e.g., a =0.05). To interpret the retrieved factor as a cooking-related source, its diurnal pattern should show two peaks corresponding to the meal hours at least in urban or semi-urban sites. As demonstrated in Fig. 6 of Mohr et al. (2012), the f 55 vs. f 57 plot can provide further evidence of COA in urban sites strongly affected by cooking activities. In fact, the triangular space defined by Mohr et al. (2012) allows the identification of cookinginfluenced OA for points lying on the left hand side of this triangle which are dominated by f 55 (and therefore cooking emissions) compared to points dominated by the traffic source (lying on the right hand side of the triangle). For specific sites (e.g., coastal locations, etc.) different sources from continental urban and rural locations can be expected. Therefore any a priori knowledge about specific OA sources should be constrained when running the ME-2 engine, to drive the model in finding local sources, often characterized by low contribution in mass and reduced temporal variability. Technical examples are provided in Sect. 3.2.2.
At each step of the discussed methodology, it is important to evaluate how the residuals vary moving from one step to the other, and within a single phase varying the number of factors. After fixing HOA and BBOA (step 3), the investigation of the average diurnal variation of the residuals can highlight the presence of unresolved sources by the model (refer to Sect. 2.3.3 for further discussion).
When using the ME-2 algorithm for fixing source profiles, the user must carefully validate the obtained results since a good solution is not selected based on the possibility to retrieve a constrained profile (which is expected as output of the model), but on several concurrent validation procedures. The toolkit SoFi created by Canonaco et al. (2013) greatly helps in performing all the suggested steps of our source apportionment methodology and provides several metrics to evaluate the quality of the chosen solution (e.g., correlation with external data time series and mass spectra, detailed residuals analysis, explained/unexplained variation plots etc.) and also an efficient comparison of different solutions (see SoFi manual, http://www.psi.ch/acsm-stations/ me-2).

Application to the EUCAARI-EMEP data
The previously mentioned procedure is successfully applied on the 25 available organic AMS data sets and therefore it provides a consistent methodology. Deploying the ME-2 solver allows the discrimination of traffic and biomass burning within the primary sources and of two OOA components for the secondary fraction for most of the sites. In order to perform a value runs within the ME-2 solver, it is necessary to select reference mass spectra to be constrained in the model. Due to the similar features of the HOA and COA mass spectra, in our work we choose the HOA and COA mass spectra identified in Paris by  as a reference, because of the significant contribution of the cooking source to the total OA mass and its strong diurnal pattern at that site. Solutions from other sites may have cooking and HOA mixed to some extent. For the BBOA reference mass spectrum we adopt the one introduced by Ng et al. (2011a) since it is considered representative of averaged ambient biomass burning conditions. A detailed sensitivity analysis investigating the impact of the input MS on the final solution is already ongoing and will be fully addressed in Canonaco et al. (2014a).
Additionally, for the two marine measurement sites (Mace Head and Finokalia), a methane sulfonic acid (MSA) factor is used too (see Sect. S5). First, a relatively clean MSA MS is obtained through an unconstrained PMF run for the Mace Head 2008 late spring campaign (see Fig. S5 of the supplementary material), during which high biological activity is expected (Dall'Osto et al., 2010). As a second step, this MSA MS is used as input to the algorithm for the two The separation of this factor is a challenge for the unconstrained PMF, due to reduced biological activity during early spring in Mace Head and weak marine influence for the site in Crete. Finally, in order to provide a complete overview of the EUCAARI 2008-2009 data, the PMF solution described in this paper for the Finokalia 2009 campaign is reported in this work. Our standardized procedure could not be applied to this data set due to specifics of the data pre-treatment and the presence of unusual local sources.

Technical example of structure in the residuals
As discussed in Sect. 3.2.1, the analysis of the residual structure is fundamental to understand how the model solution varies when adding more factors and which variables and/or events get more explained. Figure 3 shows how the average diurnal profile of the scaled residuals (Q) for Barcelona changes for the 5-factor solution run when constraining HOA and BBOA and when additionally constraining COA. In the first case, the Q diurnal shows two prominent peaks corresponding to the meal hours in Barcelona (Mohr et al., 2012), which suggests the presence of a possible cooking source not resolved yet by the model. Therefore the residual analysis provides an additional good reason to use the ME-2 algorithm to also constrain a cooking source. After constraining the COA mass spectrum in the model, the performance of the model improves since the structure observed in the diurnal profile of the residuals disappears.

Primary and secondary OA source contributions
The standardized source apportionment strategy introduced in Sect. 3.2 is systematically applied to the 25 available AMS data sets, consisting of the AMS matrices with the organic mass spectra over time and the corresponding errors. Table S2 reports the comparison of the number of OA components identified with the a value approach in comparison with the unconstrained run (PMF) , highlighting in red the constrained source mass spectra. The unconstrained PMF often cannot provide a clear separation of OA sources in rural and remote sites (Zhang et al., 2007;Jimenez et al., 2009). This may also happen at urban background sites where the effect of meteorology can still be dominant compared to the source temporal variability (Lanz et al., 2008;Canonaco et al., 2013). In our 25 data sets, unconstrained PMF allows mainly the identification of POA (often including HOA and BBOA in one factor typically characterized by high signal at m/z 44 and 60) and SOA sources (refer to Table S2). Even when HOA is identified, it is often not clean due to the high contribution of m/z 44 (which should be rather small for primary traffic emissions). In some cases it is only possible to separate two secondary oxygenated components, but no primary source is retrieved, although expected. On the contrary, with our approach, primary and secondary OA sources are retrieved for all the analyzed data sets, including traffic (HOA), cooking (COA) and biomass burning (BBOA) as primary sources, and methane sulfonic acid (MSA), semi-volatile and low-volatility oxygenated OA (SV-OOA and LV-OOA) as secondary components. For the Cabauw 2008 and Finokalia 2009 data sets the contribution of local (site specific) sources is also observed. The ME-2 solution for the Cabauw 2008 campaign includes a site specific factor (named here LOA, local organic aerosol) which is interpreted to be hulis-related (humic-like substances), as widely explained in Paglione et al. (2013). These results represent a great improvement in the source apportionment field, since we demonstrate the possibility to identify several pri-  (Paglione et al., 2013), while amines and local sources for Finokalia (Hildebrandt et al., 2011). mary and secondary OA components even at rural locations where the POA factors often contribute less than 10 % of the OA. Comparisons with previously published PMF solutions (mainly from HR-PMF data) for specific sites are reported in Sect. S3 of the supplementary material.
Our methodology combines the advantages of the chemical mass balance and the positive matrix factorization approach. In fact, the a priori knowledge of well-known source profiles (e.g., from primary sources) drives the source apportionment algorithm in finding an optimal solution for the Atmos. Chem. Phys., 14, 6159-6176, 2014 www.atmos-chem-phys.net/14/6159/2014/ model, while less constrained components (e.g., secondary OA) are allowed to freely vary (similarly to the unconstrained PMF case). However, our approach should provide consistent results with the unconstrained PMF case, where an optimal solution could be also identified by the means of other techniques such as e.g., a significant number of seeds, individual rotations or by reweighting specific uncertainties, etc., although requiring often very high time efforts and a lot of expertise on the user side. Figure 4 summarizes the average organic aerosol concentration and the average relative contribution of each OA source for each site (see also Table 2). For all sites and campaigns it is possible to separate a hydrocarbon-like OA factor (average equal to 11 ± 6 % of OA), whose contribution on average ranges from 3 % to 24 % to the total OA mass. The HOA average concentration ranges between 0.1 and 2.1 µg m −3 depending on the site location and campaign. Although Puijo is classified as rural site, it has nearly the largest HOA fraction since located on a hill at 2 km from the city center of Kuopio (population 97000) which is a source of HOA and few point sources (Leskinen et al., 2012;Hao et al., 2013). However, in absolute terms, HOA concentrations in Puijo are rather low (0.2 µg m −3 ), while at sites with high total OA concentrations the absolute HOA amount is higher compared to rural sites.
Biomass burning is identified in 22 data sets and is associated with a mix of domestic heating during cold periods and open fires (e.g., agricultural, forest and gardening waste) and barbecuing activities etc. The BBOA contribution to the total OA mass varies on average between 5 and 27 % (corresponding to 0.1-0.8 µg m −3 ) with an average relative contribution to the total OA mass equal to 12 ± 5 %. At 3 sites (Melpitz spring 2008, Puijo fall 2008 and Finokalia spring 2008) f 60 is close to or below the background values and the BBOA is regarded as negligible. Major contribution to total OA derives from secondary sources, which are classified here based on their degree of oxygenation as SV-OOA and LV-OOA and which contribute on average 34 ± 11 % and 50 ± 16 % to the total OA mass, respectively.
Cooking contributes on average ∼15 % to the total OA mass in Barcelona, consistent with AMS ambient measurements performed in European urban areas like Zurich, Paris, London, etc. (Mohr et al., 2012;Canonaco et al., 2013;Allan et al., 2010). Finally, MSA contributes from 2 % to 6 % to the total OA mass in the two marine sites (Mace Head and Finokalia), similarly to the values reported by Dall'Osto et al. (2010) and Ovadnevaite et al. (2014). Figure 5 is an alternative method to summarize source apportionment results, in fact instead of reporting average concentrations of the sources, it reports the relative OA source contribution vs. the OA concentration for all the rural, marine and urban sites, highlighting the role of specific sources within different concentration ranges (average over 21, 1 and 3 data sets for panel a, b and c, respectively). The number of measurements happening for each concentration bin is reported (black line with markers) and shows a decreasing trend for higher concentration. The last concentration bin includes all data points above that concentration.
For rural sites (see Fig. 5a), the HOA contribution decreases with increasing OA concentrations, while the BBOA contribution is very small for very low concentrations (<1 µg m −3 ), but stable over the rest of the concentration range. No general pattern can be observed for the two secondary components. However the LV-OOA fraction seems to increase at higher concentration. For an urban site like Barcelona (see Fig. 5b), traffic is a significant source both at low and high OA concentrations, while the semi-volatile oxygenated component is rather low. However, the differentiation between SV-and LV-OOA is highly dependent on the oxidation processes in the atmosphere, geographical position of the measurement site, season, meteorological conditions, etc., therefore our conclusions for the Barcelona site might not have general validity. Figure 5c shows the fractional contribution of OA sources as a function of total OA concentration for marine sites. An interesting feature is the high relative contribution of MSA at very low OA concentrations (below 1 µg m −3 ), where both the primary OA sources and the LV-OOA fraction are small. Figure 5 highlights the importance of comparing models and measurements in different concentration ranges instead of only e.g., the average contributions. An obvious example is Mace Head where the contribution of sources at low concentrations from the Atlantic are very different from situations when the station is downwind of European pollution.

Evaluation of results
The interpretation of the retrieved source apportionment factors as organic aerosol sources is based on correlations with external data (see Table S3), the investigation of their diur-nal pattern (Fig. 5) and the source mass spectra comparison with reference ones (refer to Sect. 4.3 for further discussion). However, presenting all details about the evaluation of the source apportionment results for each campaign is beyond the scope of this paper. HOA typically correlates with black carbon, which is co-emitted by the same source; biomass burning correlates with the organic fragment at m/z 60 (org 60 ) which corresponds mainly to the ion C 2 H 4 O + 2 and has been shown to be a good tracer for biomass burning DeCarlo et al., 2008;Aiken et al., 2009). However, in marine environment, m/z 60 is usually dominated by Na 37 Cl (Ovadnevaite et al., 2012). To further evaluate the interpretation of primary sources within the selected solution, source-specific ratios can be calculated (e.g., HOA / CO, HOA/BC and HOA / NO x ) and compared with literature studies. However, in our work this approach could not be systematically applied due to the lack of external data. Bilinear regression (Allan et al., 2010) can be used to estimate these ratios also in the presence of multiple sources; however, this method is more applicable to a single data set rather than an overview of 25 data sets across Europe.
The secondary OA components are compared with the secondary inorganic species: the SV-OOA time series are expected to correlate with nitrate (NO 3 ) due to the higher volatility of this component and its partitioning behavior with temperature, while the LV-OOA time series are correlated with sulfate (SO 4 ) since it represents a less volatile fraction . However, depending on the specific features of the SV-OOA and LV-OOA components, associated with their origin and processing in the atmosphere, their correlations with the secondary inorganic species might be not very high (Table S3). Finally, to further validate our source apportionment results, we investigated the diurnal pattern of the identified sources. In order to remove the effect of boundary layer height evolution, we recommend that users investigate the diurnal patterns of the relative source contributions relative source contribution diurnal pattern in addition to the absolute source contributions. Figure 6 shows the diurnal patterns of HOA, BBOA, SV-OOA and LV-OOA. First, median diurnal patterns for each source referred to a specific site and campaign are evaluated; then mean values (± standard deviation) for the three campaign periods are calculated and reported in Fig. 6. Two peaks corresponding to rush hour times are observed for the HOA daily pattern, while an increasing contribution in the evening hours is typical for BBOA emissions. A rather flat pattern is shown for LV-OOA, although an afternoon increase can be observed for the late spring 2008 campaigns similarly to the expected summertime behavior. Finally, an anticorrelated pattern with temperature is found for SV-OOA. Figure 6 does not report the diurnal pattern of the cooking source since it is identified only for the urban site of Barcelona. The reader should refer to Fig. 3 for the validation of the COA diurnal pattern which is characterized by two peaks corresponding to the meal hours.  Fig. 6, specific m/z express a stronger variability within a source profile compared to others, as later discussed later.

POA and SOA mass spectral variability
The hydrocarbon-like OA (HOA) profile is characterized by peaks corresponding to aliphatic hydrocarbons (including m/z 27, 41, 43, 55, 57, 69, 71, etc.)  . Since this mass spectrum is strongly constrained when running the ME-2 algorithm (a value=0.05), the site to site variability of the characteristic peaks is reduced, as shown by the percentiles in Fig. 7. However, we do not expect this source to significantly vary in terms of MS as demonstrated by the comparison of HOA mass spectra retrieved from ambient measurements (e.g., R 2 = 0.99 between the average HOA MS from Ng et al. (2011a) and the HOA MS retrieved in Paris ) and laboratory experiments (Mohr et al., 2009).
On the contrary, as discussed previously Heringa et al., 2011), the biomass burning mass spectrum is strongly affected by the type of wood, burning conditions, etc., and thus highly variable. For this reason the reference spectrum of BBOA is not constrained very strongly when running the ME-2 model, but we adopt an a value of 0.3 to account for this variability. The characteristic peaks of this source profile are m/z 29 (CHO + ), 60 (C 2 H 4 O + 2 ), 73 (C 3 H 5 O + 2 ) which are associated with fragmentation of anhydrosugars such as levoglucosan ). Major differences in the primary OA mass spectra are observed at m/z 29, 44 and higher masses (e.g., m/z 67, 69, 73, 77, 79, 81, 91).
For the secondary components the major variability is associated with the f 44 to f 43 ratio which provides information about the degree of oxygenation of the considered factor. The LV-OOA factor is characterized by an average f 44 to f 43 ratio equal to 3.3, corresponding to highly oxygenated compounds, while the SV-OOA has a lower ratio (on average equal to 1.1). The f 44 vs. f 43 information is also summarized in Fig. S4, where the SV-and LV-OOA components retrieved for all our data sets are represented within the triangular space defined by Ng et al. (2010). The aging of secondary OA components can be studied considering the evolution in the f 44 (corresponding to the CO + 2 ion) vs. f 43 (mostly corresponding to the C 2 H 3 O + ion) space.
The relative fractions of specific m/z are different between these two secondary components. A comparison of the median SV-and LV-OOA MS reveals that: m/z 91, 105, 107, 109, 115, 117, and 119 are much higher in the SV-OOA MS than in the LV-OOA, while m/z 45, 100, 101, 113 are higher in the LV-OOA MS than in the SV-OOA. This comparison is performed on the normalized spectra from m/z 45 up to 200. No specific tracers for the two components are retrieved in our study.
Using the equation introduced by Aiken et al. (2008) it is possible to estimate the degree of oxygenation of each source making use of the linear relation between the O : C ratio and the fraction of m/z44 of a specific factor. The resulting O : C ratio is 0.13 for HOA, 0.22 for BBOA, 0.41 for SV-OOA and 0.81 for LV-OOA, consistently with AMS high resolution analyses available in the literature Ng et al., 2010;DeCarlo et al., 2010). Figure 8 reports the average fraction of BBOA to the total OA for each site as a function of the average f 60 contribution. For only 3 locations it is not possible to identify a BBOA source, coherently with their corresponding f 60 values below background level (which is expected to be around 0.3 %) (Cubison et al., 2011). A linear relation is found between f BBOA and f 60 (intercept = −0.026, slope=29.34), with an R 2 equal to 0.77, representing the possibility to estimate the amount of BBOA contributing to a site based on the f 60 metric, even before performing a constrained/unconstrained positive matrix factorization run.

Assessment of the BBOA presence
For a few sites with an f 60 contribution close to the background level a small contribution of BBOA to total OA (4 %) is found, representing the uncertainty of our approach, but also to the f 60 background level variability associated with different sites and to the deployment of different AMS. However, in this study the source apportionment including BBOA relies not only on f 60 , but on all mass fragments.
Finally, high BBOA contributions are also observed during rather warm periods (e.g., during the spring 2008 campaign in Helsinki, San Pietro Capofiume, Cabauw) when the domestic heating is not expected. Probable but uncertain sources include open fires, agricultural waste disposal, forest and gardening waste burning which often show their maximum contributions during spring and autumn.

Sensitivity analysis of the a value approach
In order to further evaluate our source apportionment results, we perform a sensitivity analysis varying the a value for the HOA MS, to loosen the constraint for this source and subsequently provide a range of possible reasonable solutions. The HOA MS is initially constrained with an a value of 0.05 because we do not expect it to vary a lot from site to site, as previously discussed. However, releasing the constraint associated with the a value, it is still possible to separate the traffic source for all the sites. Several a value runs are performed increasing its value until the HOA source is not meaningful anymore, based on the features of the HOA MS (e.g., a too high contribution of m/z 44 represented a mixture of HOA with BBOA or secondary oxygenated sources), the variation in the HOA diurnal pattern and, when available, the correlation with external data. For most of the sites an upper range of the a value is found to be 0.2, in accordance with Canonaco et al. (2013) who identified an upper limit of 0.15 for the HOA MS at the urban background site in Zurich for a longer time period. Table 3 summarizes our sensitivity analysis results, reporting for each site the relative contribution of the retrieved OA sources within the a value range of 0.05-0.2 for the HOA MS. The HOA relative contribution does not vary significantly (only by a few percent) within the considered a value range and is sometimes associated with the reapportionment of the other sources (e.g., the contribution of the SV-OOA factor varied accordingly).
Concerning BBOA, an a value of 0.3 is found to give reasonable freedom to the BBOA MS in the ME-2 model, while it is not possible to define a consistent a value upper limit for all the sites. In fact it is difficult to define a criterion to determine when the BBOA factor fails when increasing the a value, due to the variable features of the BBOA MS and the lack of stronger metrics in this study. In our study we present a sensitivity test for BBOA varying the a value in the range 0.2-0.4 and we report the relative contribution of OA sources to total organic as a function of the a value extremes of the investigated range (refer to Table 4). However, if a priori knowledge about wood burning conditions is available for a site, we suggest to constrain the BBOA MS deriving from the same kind of burning conditions, instead of using an average BBOA MS.
Finally, we recognize that the selection of the reference mass spectra to be constrained when running the ME-2 approach is critical and it might affect the source apportionment output. Therefore, in Sect. 6 of the Supplementary Material, the effect of the choice of specific mass spectrum as reference when running ME-2 on the source apportionment output is investigated. However, a future study using more suited data sets with more external constraints on the validity of the retrieved sources will be performed to fully address this important task.  We developed a new standardized approach for source apportionment analysis applicable for aerosol mass spectrometer measurements. Our source apportionment procedure was tested and systematically applied to 25 organic aerosol data sets, demonstrating the possibility to separate the main primary and secondary organic aerosol components also for rural sites. This represents a significant advancement compared to previous literature studies which showed limitations of the unconstrained positive matrix factorization when applied on rural/background site data sets. Our source apportionment strategy is significantly improved through the use of the multilinear engine (Paatero, 1999) and the SoFi toolkit developed by Canonaco et al. (2013). Future applications of our strategy are associated not only with the unit mass resolution aerosol mass spectrometer, but also the high resolution instruments and the aerosol chemical speciation monitor. In the next few years the latter will provide a network of longterm online data about the aerosol chemical composition, often measured at non-urban locations. The investigation of OA sources will require guidelines to overcome instrument-and data-related limitations. This paper provides these guidelines with a structured methodology for a consistent interpretation of OA source apportionment work. Moreover, with our study we are able to describe organic aerosol sources all over Europe, thus improving the actual knowledge on the OA source distribution and representing an important step in the definition of mitigation strategies at the regional scale.
On average primary sources contribute less than 30 % to the total OA mass concentration, while the predominant fraction of OA is associated with secondary formation (mainly SV-OOA and LV-OOA). The traffic contribution is season independent and represents 11 ± 6 % of total OA all over Europe. Biomass burning represents 12 ± 5 % of the total OA mass and might be associated with domestic heating during wintertime and to open fires, agricultural waste disposal, waste burning etc., during the other seasons. Cooking is indeed a relevant source mainly for urban locations (15 %). The control of primary organic aerosol emissions should be performed together with the reduction of the sources of secondary OA (SV-and LV-OOA) in Europe as the latter make the dominant OA fraction, although this task is quite challenging. Finally, coupling European wide measurements and source apportionment results with regional and global models will improve their prediction of POA and SOA components.
The Supplement related to this article is available online at doi:10.5194/acp-14-6159-2014-supplement.
Acknowledgements. This work was funded through the European EUCAARI IP, other collaborating initiatives and through national funding through individual members states to the CLRTAP (Convention on Long-range Transboundary Air Pollution) as a contribution to the EMEP monitoring program. The CEH (Centre for Ecology & Hydrology) and UK contribution, including much of the synthesizing analysis, was funded by the UK Department for Environment, Food and Rural Affairs (Defra). Measurements were further funded by the following national sources: the Spanish Ministry of Science and Innovation, the Swiss Federal Office for Environment, Helsinki Energy, the Ministry of Transport and Communications Finland, the Academy of Finland Center of Excellence Program (project no. 1118615), the German Umweltbundesamt