SIRTA is a well-established atmospheric observatory in the vicinity of the French megacity Paris. The measurement site is located on the plateau of Saclay on the campus of CEA (French Alternative Energies and Atomic Energy Commission) at “Orme des Merisiers” (48.709∘ N, 2.149∘ E, 163 m a.s.l.). Being approximately 20 km southwest of the city centre of Paris, the station is classified as regional background, surrounded mainly by agricultural fields, forests, small villages and other research facilities. The closest major road is located about 2 km northeast. Overviews of wintertime aerosol sources and composition in the Paris region can be found in and .

All 15 instruments were located in the same laboratory, distributed to five separate PM2.5 inlets on the roof of the building. A suite of additional aerosol and gas phase instruments e.g. an Aethalometer for source apportionment of black carbon – for a complete list and description of the inlets and collocated instruments refer to were operated in parallel, providing important data facilitating the validation of sources identified in this study.

The focus of this work lies on source apportionment performed on data recorded with three different but related types of aerosol mass spectrometer: the high-resolution time-of-flight aerosol mass spectrometer (HR-ToF-AMS) was running alternatively in V- and W-mode every 2 min, recording aerosol spectra with a mass resolution of up to MΔM=5000 (W-mode), the time-of-flight aerosol chemical speciation monitor (ToF-ACSM) operating at 10 min intervals with a resolution of MΔM=600 and the quadrupole aerosol chemical speciation monitor (Q-ACSM) with unit mass resolution (UMR) and time steps of ∼ 30 min. All three instruments employ the same operational principle. Aerosol particles are focused into a vacuum chamber by an aerodynamic lens where they are separated from the gas molecules as effectively as possible by a skimmer cone. These particles are flash vaporised on a heated (600 ∘C) inverted cone of porous tungsten. The resulting gas is then ionised by electron impact (∼ 70 eV) and detected by the different ion mass spectrometers (Tofwerk HTOF, Tofwerk ETOF, Pfeiffer Prisma Plus QMG 220 quadrupole). While in the quadrupole mass spectrometer the m/z (mass-to-charge) channels are scanned through at a limited speed of typically 200 msamu-1 (32 data points per amu); the TOF systems measure all ions at every extraction and provide a generally greater mass-to-charge resolving power and sensitivity. Vaporisation can induce thermal decomposition, while electron impact ionisation leads to extensive fragmentation. Both processes reduce the amount of available molecular information. Using fragmentation patterns known from controlled laboratory experiments allows for the determination of the main non-refractory aerosol species (nitrate, sulfate, ammonium, chloride and bulk organic matter).

Each instrument sampled dried aerosol at a similar flow rate of 0.1 Lmin-1 with an additional bypass flow of 2.9 Lmin-1 to reduce particle losses in the lines. Small possible variations of the flows between instruments are taken into account by the standard air beam correction routinely performed on AMS and ACSM data. In the AMS and ACSM systems mass spectral backgrounds must be recorded and this is done differently between the two instruments. The AMS systems use a chopper slit-wheel inside the vacuum chamber to alternate between measurements of aerosol and chamber background (i.e. the particle beam is fully blocked), the ACSM systems use an automated three-way valve switch assembly. This valve is periodically switched between two lines: the air in one line was filtered (“background”) while the other line carries ambient, particle-laden air. All necessary calibrations (ionisation efficiency of nitrate (IE), relative ionisation efficiencies (RIE) of ammonium and sulfate, mass-to-charge axis (m/z), lens alignment, volumetric flow into the vacuum chamber, detector amplification (for more details we refer to the respective publications or the review of ) were performed and monitored on site by the same operators using the same calibration equipment (e.g. SMPS). Since this study is mainly focused on a relative intercomparison of the ME-2 source apportionment, a constant collection efficiency of CE =0.5 was assumed for all instruments for a more detailed analysis see.

The following software packages were used. Q-ACSM: version 1.4.4.5. of the ACSM DAQ software (Aerodyne Research Inc., Billerica, Massachusetts) during data acquisition and version 1.5.3.2 of the ACSM local tool (Aerodyne Research Inc., Billerica, Massachusetts) for Igor Pro (Wavemetrics Inc., Lake Oswego, Oregon) for Q-ACSM data treatment and export of PMF matrices (see Supplement for discussion of changes in most recent software version 1.5.5.0). ToF-ACSM: TOFDAQ version 1.94 (TOFWERK AG, Thun, Switzerland) during acquisition and Tofware version 2.4.2 (TOFWERK AG, Thun, Switzerland) for Igor Pro for data treatment. ToF-ACSM PMF matrices were calculated manually in accordance with the procedures employed in the AMS software SQUIRREL v1.52G (http://cires.colorado.edu/jimenez-group/ToFAMSResources/ToFSoftware/). AMS: standard ToF-AMS data acquisition software v4.0.24 (https://sites.google.com/site/tofamsdaq/) and the Thuner v1.5.10.0 (TOFWERK AG, Thun, Switzerland) to perform the automatic tuning of the ToF-MS voltages during acquisition were employed. Pika v1.12G (http://cires.colorado.edu/jimenez-group/ToFAMSResources/ToFSoftware/) was used for the high-resolution data analysis. The fragmentation table was adjusted according to recommendations in order to take into account air interferences and the water fragmentation pattern.

In the context of this paper, data from various external measurements, namely an Aethalometer, a NOx analyser and a PTR-MS were used to validate factors found by the ME-2 source apportionment. The Magee Scientific Aethalometer model AE33 (; Aerosol d.o.o., Ljubljana, Slovenia) measures black carbon (BC) aerosol by collecting aerosol on a filter and determining the light absorption at seven different wavelengths . Potential sample loading artefacts detailed in are automatically compensated for according to the procedures described in . The absorption coefficient babs depends on the wavelength λ and the Ångström exponent αi, following the relationship babs∝λ-αi.

By exploiting the wavelength dependence, i.e. the Ångström exponent is source-specific , the measured BC can be separated into BC from wood burning (BCwb) and BC from fossil fuel combustion (BCff). To this end a system of four equations has to be solved: babs(λ1)ffbabs(λ2)ff=λ1λ2-αffbabs(λ1)wbbabs(λ2)wb=λ1λ2-αwb babs(λ1)tot=babs(λ1)ff+babs(λ1)wbbabs(λ2)tot=babs(λ2)ff+babs(λ2)wb with absorption coefficients of wood burning and fossil fuel combustion babs, wb/ff at two different wavelengths λ (here: λ1=470 nm and λ2=880 nm) and the corresponding Ångström exponents αwb/ff. According to literature αwb typically lies between 1.9 and 2.2 and αff between 0.9 and 1.1 . More recent studies suggested slightly lower αwb of 1.6–1.7 but this does not affect the overall time trends used for the correlation with sources found by PMF. In agreement with the sensitivity analysis done by for the Paris region, Ångström exponents of αwb=2 and αff=1 were used in the BC source apportionment of this study. The fractions of BC emitted by the respective sources can then be calculated linearly from the total measured BC and the fraction of the corresponding absorption coefficient.

NOx concentrations were measured by a photolytic NO-NO2 analyser (model T200UP NO-NO2, Teledyne API, San Diego, CA, USA) via ozone-induced chemiluminescence. Gaseous methanol and acetonitrile concentrations were detected by a proton-transfer-reaction mass spectrometerf (PTR-MS, serial # 10-HS02 079, Ionicon Analytik, Innsbruck, Austria, ) which is described elsewhere .

For source apportionment (SA) of organic aerosol mass spectral data sets the methods of choice usually are 2-D bilinear models like PMF or chemical mass balance CMB,. In particular, PMF has successfully been used in numerous AMS SA studies . In both methods the organic m×n spectral matrix X, containing m organic mass spectra (rows) with n ion fragments each (columns), is factorised into two submatrices, the profiles F and time series G. The F is a p×n and G is an m×p matrix with p indicating the number of profiles. The residual m×n matrix E contains the fraction of X which is not explained by the current factorisation/model solution and is minimised by the PMF algorithm: X=GF+E.

Within the ME-2 package several cases of PMF are implemented: the traditional unconstrained PMF, PMF with controlled rotations (in many cases this is simply denoted “ME-2”), or fully constrained PMF (a form of CMB). While in unconstrained PMF the algorithm models the (entirely positive) profile and time series matrices F and G with a pre-set number of factors p by iteratively minimising the quantity Q main part of the object function as defined by, the fully constrained (CMB-like) PMF algorithm needs well-defined factor profiles as input and attributes a time series of concentrations to them: Q=∑i=1m∑j=1neijσij2 with eij being the elements of the residual matrix E and σij the measurement uncertainties of ion fragment j at time step i. In many cases, e.g. when two factors have similar time series (e.g. heating and cooking in the evening) or profiles (e.g. traffic and cooking, ), the totally unconstrained PMF has difficulties separating these factors this was already pointed out in former studies, e.g. by. The multilinear engine (ME-2) provides additional control over the rotational ambiguity . Here the solution space is explored by introducing a priori information (e.g. factor profiles) for some (not necessary all) of the factors p. The strength of this additional constraint is set by the so-called a value , which determines how much deviation from the constraint profile the model allows. It ranges from zero to one and can be understood as the relative fraction – by how much each m/z may individually deviate from the a priori profile . In that way, ME-2 covers the whole range of bilinear models from fully constrained (a=0) to completely unconstrained PMF (no a value set). Moving away from the unconstrained solution typically leads to an increase in Q. The magnitude of this increase of Q is used in order to remove solutions whose rotations are not a mathematically adequate representation of the input data set. All factor analyses presented in this study were performed in the robust mode .

Initialisation of the ME-2 engine and analysis of the results was performed using the source finder tool (SoFi v4.6, http://psi.ch/HGdP, ) package for Igor Pro (WaveMetrics Inc., Lake Oswego, Oregon).

As an input, the ME-2 algorithm requires the organic data matrix, the associated error matrix, and the corresponding time and mass-to-charge (m/z) axis. For each instrument the input data were created up to m/z 100 and individually cleaned up. Bad data points were identified by standard diagnostics (airbeam signal, inlet pressure, voltage settings, etc.). A uniform CE=0.5 and a uniform organics RIEorg=1.4 were used for all data sets. The corresponding ionisation efficiency (IE) or, more accurately for the Q-ACSMs, the response factor (RF) calibration values were determined during the first week of the intercomparison study on site and can be found in Table S2. Q-ACSM data were corrected for a decrease in ion transmission at high m/z (≳ 55) according to a standard curve obtained by . For further discussion and recent software updates concerning the relative ion transmission (RIT) calculation for PMF matrices refer to the discussion in the Supplement. To correct for the decay of the detector amplification the airbeam N2 signal at m/z 28 was used (reference value: 1×10-7 A) maintaining the detectors at gain values of around 20 000.

The ToF-ACSM data set exhibited an unusual (exponentially decaying) drift in addition to the drift of the airbeam signals, visible in the always present background signals like the one of stable tungsten isotopes (originating from the ioniser filament). This indicates a change in the IE/AB ratio during the campaign which was confirmed by calibrations at the beginning and at the end. To avoid influence of potential real ambient aerosol trends, a correction function was deduced from the largest signals in the background (m/z 105, 130, 132, 182 and 221, see Fig. S1) and applied to the data set, making the assumption that the IE of ambient aerosol molecules is affected the same way as the molecules in the chamber background. This drift is attributed to transient effects in the electronics occurring after the replacement of the electron multiplier.

A probably too short delay time of the quadrupole scan after a valve switch (125 ms) caused physically not meaningful negative values at the signal channel of m/z 12, therefore the m/z 12 column was removed from all Q-ACSM matrices prior to PMF analysis. m/z channels with weak signals may influence the operation of the PMF algorithm and therefore also the solutions in a suboptimal way because the algorithm may try to apportion nonsensical noise. In order to avoid this the corresponding uncertainty of weak channels can be increased to reduce their weight according to Eq. (6). Table S3 shows a list of down-weighted m/z channels for each instrument. The decision as to whether a channel was down-weighted or not was made individually either because of low signal-to-noise ratio according to the recommendations of or because of spotted outliers with high weighted residuals. Furthermore, the uncertainties of m/z channels that are not directly measured but recalculated from fractions of the signal at m/z 44 via the fragmentation table are adjusted as well according to the recommendation of .

Optimal a values in each case were determined by systematic variation of the a value in relation to increases or decreases of the correlation coefficient R2 of the factor time series with external tracers. The correlations that were maximised for the determination of the best a values were: BBOA factor with BCwb, OOA factor with inorganic SO4 covariance of OOA with sulfate was found at the SIRTA site before by and HOA factor with BCff and NOx. Correlation maxima (R2) are listed in Table . Changes in a value usually affected mainly the correlations of the HOA factor while the correlations of the BBOA and OOA factors were quite stable. On that account two correlations to HOA were made. The sum of the two HOA R2 was maximised. For COA no reliable external tracer was measured. For all factors good correlations with the respective external measurement were reached: BBOA/BCwb: median R2=0.87 (range 0.85–0.94), HOA/BCff: median R2=0.65 (range 0.52–0.73), HOA/NOx: median R2=0.62 (range 0.52–0.77), OOA/SO4: median 0.72 (range 0.51–0.79).

The applied strategy was: increase of a in steps of Δa=0.05 until a maximum R2 (coefficient of correlation between time series of resulting factors and corresponding external tracers) is found. If two factor profiles are constrained, first both a values are varied simultaneously until a maximum R2 is found. From this point, the a value of one of reference profiles is varied independently in both directions (smaller and larger a values) while the a value of the other reference profile stays constant. Again after a maximum R2 is found, the a value of the other reference profile is varied, looking for the maximal correlation with external data (see flowchart in Fig. S8). In this way a large range of a values could be explored for each instrument.

It is to note that of course also the BC source apportionment and other external data used for this sensitivity analysis are prone to uncertainties. The approach detailed above therefore should, if applied elsewhere, always be used with caution, and a sensitivity analysis on the dependence of the results on the input model parameters should be performed. In the presented case the optimisation of a values assured the comparability of the 15 solutions used for the intercomparison of the ME-2 method. A thorough discussion of the uncertainties of the BC source apportionment method and a comparison to other source apportionment methods can be found in .

Figure  shows the time traces of bulk organic matter during the 16 days of simultaneous measurement used for the subsequent ME-2 analysis (16 November–1 December 2013, this corresponds to 550–780 data points depending on data availability of each instrument). The median organic concentration calculated on a point-by-point basis of the 13 Q-ACSMs is displayed as a black line with the interquartile range (IQR) (25–75 percentile) shaded in red and the 10–90 percentile range shaded in grey. The ToF-ACSM time series is shown in green and the AMS in pink. Correlations of ToF-ACSM and AMS with the median of the Q-ACSMs is shown in the two inset graphs. Good qualitative and quantitative agreement between all 15 aerosol mass spectrometers was achieved (R2=0.82–0.99, slope=0.70–1.37, see for intercomparison between Q-ACSMs or Fig.  for comparison of Q-ACSMs to HR-AMS and ToF-ACSM). Average organic matter concentrations during the whole period with 6.9 µgm-3 (range ≈0.7–25 µgm-3) were in the range of typical OA concentrations at this site , providing good boundary conditions (high signal-to-noise and variability) for PMF source apportionment. For a more detailed analysis of the concentration ranges we refer to .

The mass spectrometer discriminates molecular fragments of certain mass-to-charge ratios. The data are then typically displayed as stick plots containing the respective signals for each m/z. The bulk organic signal is calculated from the sum of the sticks (total integrated signal for a given integer m/z) associated with organic molecules or molecular fragments according to known fragmentation patterns detailed in . This is done under the assumption that with constant boundary conditions the fragmentation is constant as well. The sticks in Fig. a represent the median fractions of total organic matter at the respective mass-to-charge ratios for the 13 Q-ACSM instruments during an interruption-free 20 h period (26 November 10:00–27 November 06:00 LT, UTC + 1 h). The IQR and the full range are displayed as boxes and whiskers respectively.

There is significant information remaining in the organic molecular fragments. For example fragments at m/z 60 (mainly C2H4O2+) and m/z 73 (C3H5O2+) mostly originate from primary biomass burning particles . There are exceptions in marine environments where the signal at m/z 60 can also be mainly from Na37Cl, see . m/z 29 (mainly CHO+) as well is often enhanced in wood burning emissions but is also observed from other sources e.g. SOA . The fragments at m/z 43 (mainly C2H3O+) and m/z 44 (mainly CO2+) can help retrieving information about ageing and oxidation state of secondary organic aerosol (SOA) .

The four fragments mentioned above are shown in Fig. b as fraction of the total organic signal for all 15 participating instruments during the 20 h period mentioned above. As already represented in the colour bar of Fig. a it is evident that while most fragments have more or less similar contributions to total organic matter (e.g. f29, f43 and f60 in Fig. b), there is significant instrument-to-instrument variation of the f44. It is to note that the organic signals at m/z 16, 17 and 18 are also calculated from m/z 44 according to the fragmentation patterns highlighting the importance of the f44 variations (see Fig. a). A comparison of the mass spectra after the stick at m/z 44 and all related peaks were removed shows very similar relative spectra (IQR/median <20 % for most m/z, see Fig. S2 in the Supplement). Only m/z 29 which is mostly CHO+ still shows a small increase (see Fig. S2b). This may either indicate a connection to m/z 44 (CO2+) or a small influence of air interferences.

Figure c shows that estimated O : C ratios based on f44 in this study varied from 0.41 to 0.77 for the same ambient aerosol. An elemental analysis of the HR-AMS data however yielded an O : C ratio of 0.38. This is close to the O : C ratio calculated from the formula of for the HR-AMS spectrum (0.42). The consistency of the HR-AMS elemental analysis was confirmed by comparison to a known organic mixture beforehand. As a consequence the “real” O : C value during the intercomparison campaign most likely lies at the low end of Fig. c and the ACSMs overestimate O : C.

The fraction of m/z 44 to total organic matter measured (f44) continuously varies compared to the mean between factors of 0.6 and 1.3 (from 8.5 and 18.2 %, Fig. b). Although the absolute value of f44 that is measured by different instruments is variable, all the instruments measure similar trends for f44. The ratio of f44 between the instruments with even the highest and lowest f44 values, for example, is generally constant over time and does not vary with aerosol composition (see Fig. S3). Moreover, the precision of an individual, stable instrument is good and relative changes observed for any given instrument can be unambiguously interpreted. Thus, source apportionment analyses are not compromised, and indeed are only slightly affected as discussed hereafter.

Measurements of organic standards could be used to calibrate and allow for the intercomparison of the absolute f44 values observed in different ACSM instruments. However, in the absence of these calibrations, caution should be exercised in quantitatively comparing f44 values obtained by different ACSM instruments. This includes application of the f44 vs. f43 “triangle plot” that is widely used to describe oxygenated organic aerosol (OOA) factors and comparisons of O : C values derived from ACSM f44 values.

A direct influence of the vaporiser temperature on this variability is deemed unlikely by ACSM measurements of several ambient aerosols nebulisation of filter extracts, see for method description at different vaporiser temperatures. Relative organic spectra remained constant over a wide range of temperatures (see Fig. S4 and caption) as was already shown for several organic standards by . Also the fragmentation of inorganic molecules remained constant over a range of at least 550±70 ∘C.

The f44 variability is observed to be larger in the ACSM instruments than the AMS instruments . The ACSM and AMS instruments are based on the same particle vaporisation and ionisation schemes (using the identical particle vaporiser), but they are operated with different open/closed or open/filter switching cycles required for background subtraction. AMS instruments are typically operated with a faster switching cycle (<5 s) than the Q-ACSMs (∼ 30 s), which in turn have shorter open times than the ToF-ACSM with the “fast-mode MS” setting employed in this campaign (480 s open/120 s closed). It is noted that a fast filter switching scheme analogous to that of the Q-ACSM has now been implemented for the ToF-ACSM. The different switching times may result in different degrees of sensitivity to delayed vaporisation and pyrolysis artefacts. Efforts to understand and diminish the variability in f44 measured by ACSM instruments are ongoing.

Several publications have demonstrated that higher time and m/z resolution provided by the HR-ToF-AMS in contrast to the UMR of the ACSM result in less rotational ambiguity and provide superior source resolution . Therefore, we first performed a PMF of the HR-ToF-AMS data to determine the likely resolvable factors and their characteristics. High-resolution analysis was performed up to a mass-to-charge ratio of 130 resulting in 355 different organic fragments.

Completely unconstrained PMF analysis yielded four factors: hydrocarbon-like organic aerosol (HOA), cooking-like organic aerosol (COA), oxygenated organic aerosol (OOA) and biomass burning related aerosol (BBOA). Higher numbers of factors resulted in random splitting of already identified factors. However, in the four-factor solution, the HOA and COA factors showed signs of source mixing (mainly with the wood burning related source) like covariance of several factors. An extension of the analysis up to eight factors led to an unmixing of the two factors. Therefore, these clearly resolved HOA and COA factor profiles from the eight-factor solution were extracted, saved and used as anchors in a subsequent four-factor ME-2 analysis with tight constraints of a=0.1 each. The other two factors remained unconstrained. This approach resulted in better correlations with external tracers for all factors than the completely unconstrained four-factor solution. A similar approach of increasing the number of factors in unconstrained PMF and subsequent combination of duplicate factors was used in previous studies . The resulting time series and factor profiles are shown in Fig. a and b. For more details about the PMF analysis of the HR data please refer to Sect. 3 of the Supplement.

Factors 1, 2 and 4 are attributed to POA sources while factor 3 is attributed to SOA. The identification of the factor sources is supported by correlations of profiles to known source spectra, by correlation to time series of the externally measured tracers explained below (see Fig. S5a–d and Table S4) and by identification of diurnal emission patterns (see Fig. ).

Factor #1 (HOA) is dominated by ions related to aliphatic hydrocarbons, e.g. at m/z 41 (C3H5+), m/z 43 (C3H7+), m/z 55 (C4H7+), m/z 57 (C4H9+), m/z 67 (C5H7+), m/z 69 (C5H9+), m/z 71 (C5H11+), m/z 79 (C6H7+), m/z 81 (C6H9+) and m/z 83 (C6H11+) . HOA typically is emitted by combustion engines, e.g. from motor vehicles and believed to mainly come from lubricating oils . The diurnal variation (Fig. ) shows two clear peaks during morning and evening rush hours and the time series correlates well with ambient NOx (R2=0.65) concentrations and fossil fuel-related fraction of BCff retrieved from the Aethalometer (R2=0.68).

The mass spectrum of factor #2, identified as organic aerosol related to cooking activities, shows similarities to the HOA with highest contributions of peaks at similar mass-to-charge ratios (m/z 27, 41, 43, 55, 57, 67, 69, 79, 81, 83) but with a higher contribution of oxygenated species at m/z 41 (C2HO+), m/z 43 (C2H3O+), m/z 55 (C3H3O+), m/z 57 (C3H5O+), m/z 69 (C4H5O+), m/z 71 (C4H7O+), m/z 81 (C5H5O+) and m/z 83 (C5H7O+). This is in accordance with previous publications . Especially the oxygenated fragment at m/z 55 can serve as a good indicator for COA. C3H3O+ is plotted together with the COA factor in Fig. S5b. Its correlation to COA (R2=0.80) is much higher than to HOA (R2=0.38). Also C6H10O+ which was identified as a marker for COA before by and correlates better with the COA factor (R2=0.38) than with the HOA factor (R2=0.23, see grey trace in Fig. S5b). Typical for COA aerosol are the distinctively different (compared to the HOA factor) ratios between m/z 41 and 43, between m/z 55 and 57 and between m/z 69 and 71 . In Fig. S6 the COA factor mass spectrum from this study is plotted side-by-side with the COA factor identified at the same station close to Paris in summer 2009. To date no reliable external tracer number for COA was established but the clear emission peaks during lunch and dinner time in the diurnal variation (Fig. ) are characteristic of clearly resolved COA factors in previous studies and support the present interpretation.

The secondary factor #3 consists of highly oxidised (high f44) organic aerosol (OOA). The diurnal cycle is more or less flat and the overall concentrations are more driven by meteorology than by emissions (see OOA time trace in Fig. a). This is supported by the stronger correlation of OOA to sulfate (R2=0.43), ammonium (R2=0.54), and nitrate (R2=0.47, see Fig. S5d) than for the other three factors (see Table S4). As is frequently the case for winter campaigns, the OOA could not be further separated into oxygenation/volatility-dependent fractions .

The most descriptive features in the mass spectrum of factor #4 identifying it as BBOA are the oxygenated peaks at m/z 60 (C2H4O2+) and m/z 73 (C3H5O2+). They are associated with fragmentation of levoglucosan and other anhydrous sugars which are produced in the devolatilisation of cellulose making it a good tracer for biomass burning emissions . Generally BBOA profiles from different measurement sites are less uniform than e.g. HOA profiles because of the higher variability of fuel and burning conditions . The BBOA factor profiles from this study contain relatively high f44 which may be an indication of ageing and oxidation prior to detection but variations of the BBOA profile can also occur at the source . Similar BBOA spectra were observed before, e.g. in winter in Paris and in Zurich . The diurnal variation shows a steep increase in the afternoon and evening and a subsequent decrease after midnight, corresponding with domestic heating habits. In Fig. S5c the BBOA factor shows very good correlation with BCwb from the Aethalometer (R2=0.90) and to gas-phase methanol (R2=0.76) and a reasonable correlation with acetonitrile (R2=0.48) measured with a PTR-MS. In winter wood combustion is a significant source for primary and secondary methanol .

Overall factor contributions in the analysis of the HR-ToF-AMS data are: HOA 12.7 %, COA 16.0 %, OOA 38.2 %, BBOA 33.1 %. Relative contributions, number and type of factors as well as the fingerprint of factor profiles are in good agreement with results of from winter 2010 at a nearby site.

The amount of factors (four) found in this HR-PMF analysis provides the basis for the analysis of the parallel unit mass resolution (UMR) data sets from the further 13 Q-ACSMs and the 1 ToF-ACSM. The resolving power of the ToF-ACSM is sufficient to resolve a subset of the ions used in the HR-PMF analysis described here . However, the uncertainties associated for inclusion in an HR-PMF study using the ToF-ACSM data are still undetermined. Therefore only UMR analyses of the ToF-ACSM data were performed for this intercomparison study.

PMF analyses were performed individually on all 14 ACSM data sets. The data preparation procedures were described in Sect.  and Table S3. For most instruments, an unconstrained PMF analysis (no additional constraints on any of the factor profiles) could only resolve three separate factors (HOA, BBOA, OOA). The three-factor solutions showed larger instrument-to-instrument variability and less correlation to external measurements for most ACSMs (especially of the HOA factor) than the four-factor ME-2 solutions presented hereafter. Amongst others, these points present a strong argument against the three-factor unconstrained PMF and for an introduction of a COA profile also if the additional information of the HR-AMS PMF was not available in the first place. Contributions and correlations of the three-factor PMF can be found in Fig. S7 and Table S5.

It is noted that although four factors could not be separated by an unconstrained PMF of the ACSM data, several indicators (increased seed variability, residuals of m/z 55, etc.) provide motivation for an extension of the analysis to higher factor numbers using the additional methods implemented in ME-2 to investigate the solution space outside the global minimum of Q (e.g. with profile constraints). In other words, also without the information of the HR PMF it is apparent that the three-factor PMF is not the best possible solution for the ACSMs.

Based on the HR-PMF analysis presented in Sect.  a COA factor was introduced with a variable a value. A verified anchor spectrum from a previous study at the nearby measurement site SIRTA zone 1 of was used (reference spectra from are labelled with the subscript Paris in the following). The HOA factor, if possible, remained unconstrained or was extracted from a previous PMF solution with a higher number of factors similar to the retrieval of the COA factor in the HR-PMF in Sect. . This procedure was favoured because for most ACSM an increase of the factor number produced an HOA factor with similar or better covariance with the time series of NOx and BCff as opposed to the application of external reference HOA spectra. For this purpose unconstrained PMF runs with three, four, five and six factors were performed for each ACSM and the HOA profiles corresponding to the highest combined R2 between factor time series and external data were saved and subsequently used as anchor profiles in the four-factor constrained ME-2 runs. HOA reference profiles retrieved this way are individual for each instrument and denoted HOAindv in the following. A COA factor could not be extracted for the ACSM with this method. The HOA factors in the four-factor constrained ME-2 runs were left unconstrained if their time series correlations with NOx and BCff were better or similar to the constrained case. The two additional factors in the 4 factor constrained ME-2 were left completely free and the results resembled OOA and BBOA for each instrument. Extraction of individual reference profiles directly from the data is not always possible and a more common approach is the adaptation of reference spectra from a database of previous experiments. Therefore the ME-2 results acquired with the use of the database profiles HOAParis and COAParis are shown as well for comparison. The influence of an alternative anchor (see Fig. , top panel, and Sect. ) proved to be small for most ACSMs. However, there are outliers with larger differences in the factor contributions (e.g. #7, #12, TOF) which indicates that by testing a set of reference profiles, if possible, an improvement of the individual source apportionment can be reached. The source apportionment of the ToF-ACSM data produces clearer diurnal trends due to less scatter in the time series and higher temporal resolution compared to the Q-ACSM data. This facilitates source identification. In this study, however, for a clear separation of all four factors without the extra information of HR fitted spectra, the additional controls (e.g. possibility to introduce anchor spectra) of the ME-2 package were necessary for the source apportionment of both, ToF-ACSM and Q-ACSM data. Details about procedures for the selection of optimal a values can be found in Sect. .

Optimised a values for each instrument are shown in Table . In some cases no clear maximum of the temporal correlation to external tracers but a plateau of the correlation coefficient R2 could be found and the largest possible a value is noted in Table . This indicates a stable HOA factor. The COA factor which could not be resolved in the unconstrained PMF of the ACSM data sets is less stable and therefore generally needs a tighter constraint, i.e. a lower a value (see right column of Table ). This is necessary to avoid as much as possible potential mixing of COA and BBOA factors. Similar diurnal cycles of heating and cooking activities (both sources have the highest emissions during the evening hours) pose a risk for factor mixing especially in the Q-ACSM data sets which have lower mass resolution and generally less precision. Two weeks of Q-ACSM measurement result in about 700 mass spectra of which only ∼ 30 are including lunchtime COA emissions and the emission peak of COA aerosol in the evening overlaps with wood burning emissions. In addition COA emissions may be significantly lower and partly transported in contrast to measurements at an urban site. All this may put COA at the edge of ME-2 resolvability. Due to this the Q-ACSM COA factor may still contain some mixed-in BBOA fraction or the other way round. Also the fact that the contribution of the COA factor stays well above zero during the night can be an indicator of some remaining factor mixing which cannot be resolved by ME-2 for this data set, of additional sources emitting COA-like aerosol more permanently like food industry or of regional transport or of the lower mixing height of the planetary boundary layer during night. Due to the first two points, real COA emissions may be somewhat lower than indicated by the COA factor and the factor is named COA-like in the following. For HOAindv a smaller range of a values (a=0.01–0.10; Δa=0.01) was explored to maintain similarity to the extracted profiles.