# Source apportionment of organic gaseous and particulate compounds using a combined positive matrix factorization approach in summer (2020) in the Paris region (France)

Leïla Simon, Olivier Favez, Jean-Eudes Petit, Francesco Canonaco, Jay

Slowik, Caroline Marchand, Valérie Gros

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Leïla Simon, Olivier Favez, Jean-Eudes Petit, Francesco Canonaco, Jay Slowik, et al.. Source apportionment of organic gaseous and particulate compounds using a combined positive matrix factorization approach in summer (2020) in the Paris region (France). Atmospheric Environment, 2025, 354, pp.121269. 10.1016/j.atmosenv.2025.121269. ineris-05067207

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# Source apportionment of organic gaseous and particulate compounds using a combined positive matrix factorization approach in summer (2020) in the Paris region (France)

Leïla Simon<sup>a,b,d,*</sup> ID, Olivier Favez<sup>b,**</sup> ID, Jean-Eudes Petit<sup>a</sup> ID, Francesco Canonaco<sup>c</sup>, Jay G. Slowik<sup>d</sup>, Caroline Marchand<sup>b</sup>, Valérie Gros<sup>a</sup>

## HIGHLIGHTS

* Combined PMF lead to slight mathematic and atmospheric improvements.

* Hydrocarbon-like organics were linked to fresh traffic from the urban sector.

* Cooking-like organics described cooking, aged traffic, and possibly other sources.

* A specific isoprene oxidation factor contributed 11 % to VOC and 4 % to OA.

* Factors corresponding to daytime and nighttime oxidation were resolved.

## ABSTRACT

Gaseous and particulate organic compounds are key components of atmospheric chemistry and better understanding their composition, sources and processes is essential to limit their impacts. Source apportionment using positive matrix factorization (PMF) is customarily performed for such studies. Combining organic aerosol data with their gaseous precursors was shown to be a promising approach, however very rarely attempted so far, to refine their origins using PMF. In this study, co-located continuous proton-transfer-reaction mass spectrometer (PTR-MS) and aerosol chemical speciation monitor (ACSM) measurements were performed at the suburban SIRTA station located in the Paris region. A combined dataset using both instruments during summer (June–August 2020) was then used in an exploratory PMF analysis to investigate the sources and processes of organic compounds, particularly the influences of biogenic emissions and important photochemical reactions on the formation of secondary organic aerosol (SOA) in this period of the year. Specific parameters and evaluation procedures were needed to ensure an equivalent representation of both instruments in the PMF model. A weighing factor was applied to the PTR-MS uncertainties which was controlled and optimized based on the analysis of the modelled scaled residuals. Seven main factors were obtained, describing anthropogenic sources (hydrocarbon-like organics, cooking-like organics), primary biogenic volatile organics, nighttime VOC, oxidized organics, aged organics and a specific isoprene oxidation factor which contributed 11 % to VOC and 4 % to OA. Compared to single-instrument PMFs, more factors were obtained, notably including the cooking-like factor which is not usually resolved using only ACSM data. This method also showed a better mathematical performance for the PTR-MS variables (mean absolute scaled residuals lower for the combined PMF (11.2) than for the PTR-MS-only PMF (38.2)) and a better separation of the factors for the ACSM variables in the combined PMF.

## 1. Introduction

Atmospheric aerosols have significant impacts on health, air quality and climate (Daellenbach et al., 2020; Kroll et al., 2020; IPCC, 2021), which mainly depend on their size and chemical composition. Therefore, to best mitigate their levels and impacts, it is crucial to accurately

investigate their variability, composition, and sources over time. Organic aerosol (OA) is a major component of aerosols and constitutes 23–75 % of submicron particles in Europe (Chen et al., 2022). Primary OA (POA) originates directly from combustion sources such as fossil fuel, cooking activities or biomass burning, while secondary OA (SOA) is formed partly through the condensation of gaseous precursors, namely

<footnote><sup>a</sup> Laboratoire des Sciences du Climat et l'Environnement, CEA/Orme des Merisiers, Gif-sur-Yvette, 91191, France</footnote>

<footnote><sup>b</sup> INERIS, Parc Technologique ALATA, BP2, Verneuil-en-Halatte, 60550, France</footnote>

<footnote><sup>c</sup> Datalystica Ltd, Park innovAARE, Villigen, 5234, Switzerland</footnote>

<footnote><sup>d</sup> PSI Center for Energy and Environmental Sciences, Villigen PSI, 5232, Switzerland</footnote>

<footnote>* Corresponding author. Laboratoire des Sciences du Climat et l'Environnement, CEA/Orme des Merisiers, Gif-sur-Yvette, 91191, France.</footnote>

<footnote>** Corresponding author. INERIS, Parc Technologique ALATA, BP2, Verneuil-en-Halatte, 60550, France.
E-mail addresses: leila.simon@psi.ch (L. Simon), olivier.favez@ineris.fr (O. Favez).</footnote>
volatile organic compounds (VOC), and oxidation/ageing processes in the atmosphere (Hallquist et al., 2009; Kroll and Seinfeld, 2008). Oxygenated OA (OOA), considered as a surrogate of SOA, usually dominates the composition of OA, especially in summer (Chen et al., 2022; Zhang et al., 2019), when the biogenic source can contribute around 30–40 % to VOC concentrations in Paris for instance (Baudic et al., 2016; Airparif, 2022). Among biogenic VOC, isoprene and monoterpenes are known as efficient SOA precursors (Budisulistiorini et al., 2013; Carlton et al., 2009; Han and Jang, 2023; Mahilang et al., 2021). Road traffic and residential (e.g., wood burning) activities are also contributing to VOC levels in urban environments, especially aromatic compounds, which were identified as potential SOA precursors (Li et al., 2021). The involved formation mechanisms include photochemistry, aqueous-phase oxidation, as well as heterogeneous reactions (Xu et al., 2015, 2017; Gilardoni et al., 2016), but the exact sources and processes for the formation of SOA still remain poorly understood.

Positive matrix factorization (PMF) is a widely used approach for source apportionment of ambient pollution. It consists in a bilinear receptor model which resolves measured mass spectral time series as a linear combination of factor mass spectra and temporal variation of their concentrations (Paatero and Tapper, 1994). These factors can be related to emission sources or physicochemical properties or processes. PMF is typically applied to organic mass spectra obtained from online instruments such as Aerosol Mass Spectrometer (AMS, Aerodyne) or Aerosol Chemical Speciation Monitor (ACSM, Aerodyne). It can successfully deconvolve and quantify POA sources based on specific chemical signatures, such as hydrocarbon-like OA (HOA), biomass burning OA (BBOA), cooking-related OA (COA) or coal combustion OA (CCOA) (Chen et al., 2022). However, SOA is usually reported as the main component of oxygenated OA (OOA) and separated based on its volatility as semi volatile OOA (SV-OOA) and low volatile OOA (LV-OOA) or based on its oxidation degree as less oxidized OOA (LO-OOA) and more oxidized OOA (MO-OOA).

The combination of datasets from different measurement techniques was shown to be a promising way to improve the separation and apportionment of OA factors (Crippa et al., 2013a; Healy et al., 2013; Huang et al., 2014; McGuire et al., 2014; Petit et al., 2014; Slowik et al., 2010; Sun et al., 2012). Recent studies have combined AMS/ACSM data with molecular markers from filter measurements (e.g., Srivastava et al., 2019), or with EESI-TOF data (Tong et al., 2022). This allowed some refining of the SOA origins. However, filter measurements have a low temporal resolution (24 h, typically) and EESI-TOF instruments are not easily deployable, nor currently suitable for long-term measurements. Taking advantage of continuous measurements, the first attempt in combining AMS data with co-located organic measurements was achieved with PTR-MS (proton-transfer-reaction mass spectrometer) data. This approach led to additional information on some photochemical processes responsible for secondary OA factors in Toronto (Slowik et al., 2010). This methodology was already applied in Greater Paris during the Megapoli 2009 summer campaign, allowing to resolve SOA factors linked to daytime and nighttime processes (Crippa et al., 2013a). These promising results were appealing for further development of this methodology, albeit challenging as both instruments ought to be balanced in the PMF model, while their specificities must be taken into account.

Near-continuous PTR-MS measurements have been conducted in co-location with ACSM monitoring since January 2020 at the suburban SIRTA facility in the Paris region (Simon et al., 2023). Part of this data is used here for a combined OA/VOC PMF analysis. Compared to previous studies, both mass spectrometers used in this study (i.e., PTR-MS and ACSM) are designed for continuous monitoring using robust but simple techniques, with low mass-to-charge ratio (m/z) resolution from quadrupole spectrometer measurements. Due to the exploratory nature of this work, a 3-month period was selected to investigate various origins of SOA, including significant biogenic sources. This period corresponds to summer 2020, notably comprising short-term heat waves. The

previously developed methods for combining measurements in PMF analysis were adapted with the objectives of improving the PMF analysis for ACSM data and better apportion OA sources. In particular, the addition of VOCs co-emitted by primary sources (e.g., traffic) in the dataset is expected to help separating these sources, and the inclusion of gaseous oxidation products from biogenic emissions could help resolving a biogenic SOA factor.

## 2. Material and methods

### 2.1. Instrumentation

Measurements were conducted at the SIRTA facility (Site Instrumental de Recherche par Télédétection Atmosphérique, 48.71°, 2.16°E, 162 m above sea level), which is located 20 km south-west from Paris city centre (France, Figure S1) and is part of the European Aerosols, Clouds, and Trace gases Research Infrastructure (ACTRIS, https://www.actris.eu/). Long-term in-situ observations of aerosols and reactive gases are provided at this site to characterize the atmospheric chemistry and air quality of the Paris region (Dupont et al., 2016; Petit et al., 2015; Simon et al., 2023; Zhang et al., 2019).

Measurements from a quadrupole aerosol chemical speciation monitor (Q-ACSM, Aerodyne Inc.) allowed for the quantitative assessment of major non-refractory submicron aerosol chemical species, i.e., organic matter (OM), nitrate (NO₃⁻), sulfate (SO₄²⁻), ammonium (NH₄⁺), and chloride (Cl⁻) since end of 2011. The operating principle of the instrument is described in Ng et al. (2011a), while its setup at SIRTA and first years' results are thoroughly described in Petit et al. (2015) and Zhang et al. (2019). Briefly, fine aerosol is sampled through a critical orifice of 100 µm diameter at the inlet of the ACSM's aerodynamic lens. The submicron particles are then flash vaporized at about 600 °C and subsequently ionized with electron impact ionization at 70 eV. Finally, fragments are eventually separated by quadrupole and detected. The time resolution of the ACSM instrument during this study was 30 min, with a scan rate of 0.2s per amu (atomic mass unit) from mass-to-charge ratio (m/z) 12–150 amu. Calibrations of the detector response to a solution of ammonium nitrate were performed regularly (typically every 6 months) and the instrument participated in ACTRIS intercomparisons organised at SIRTA by the Aerosol Chemical Monitor Calibration Centre (ACMCC) in 2013, 2016, 2018 and 2022 (Crenn et al., 2015; Freney et al., 2019). The mass-to-charge ratios of organic species were used as input for the PMF, while the inorganic compounds and total organic matter (OM) were used as external tracers, based on the fragmentation table from Allan et al. (2004).

Co-located VOC measurements were performed using a proton-transfer-reaction quadrupole mass spectrometer (PTR-Quad-MS), which was implemented in January 2020. This technique is described in Lindinger et al. (1998), and its operating conditions at SIRTA are given in Simon et al. (2023). A 6-m ½-inch PFA line enabled sampling at 15 m above ground, with a flow of 8 L min⁻¹ ensuring a residence time of about 3 s. For long-term measurements at SIRTA, the drift pressure (p<sub>drift</sub>) was set to 2.2 mbar, drift voltage (U<sub>drift</sub>) was set to 600 V and drift temperature (T<sub>drift</sub>) was set to 60 °C, resulting in an E/N ratio of 134 Td (ratio of the electric field to the number density of gas in the drift tube).

The PTR-MS was set-up in selection mode, where the monitored mass-to-charge ratios (m/z) were selected prior to the measurements start. A total of 37 m/z were analysed, the first six being for instrumental diagnostic purposes: m/z 21, 25, 30, 32, 37, 55, 31, 33, 42, 45, 46, 47, 57, 58, 59, 60, 61, 63, 69, 71, 73, 75, 79, 81, 83, 85, 87, 93, 97, 99, 107, 111, 121, 137, 139, 147, 151. The time resolution of the measurements was set to 2.6 min, with a dwell time of 5s per mass for the m/z of interest. The correspondence between the m/z and potential compounds was discussed in Simon et al. (2023); the seasonal variability of the contributions, and the attributed compounds for this study, in summer 2020, are summarized in Table S1, as well as their mean detection limit and error.
1-h blank measurements were performed automatically every 13 h, using a Gas Calibration Unit (GCU, Ionimed Analytik, Austria) with a VOC scrubber. The GCU was also used for calibrations about once a month: a VOC standard mixture (Società Italiana Acetilene e Derivati, SIAD, Italy) was injected through the dilution system to perform calibration steps at different volume mixing ratios (VMR, ranging from 1 to 20 ppb). This standard bottle was also validated using a standard from the National Physics Laboratory (NPL, Teddington, UK).

Based on the availability of the data from both ACSM and PTR-MS and the high photochemical activity in this season, the selected and common period ranged from 10th June to August 26, 2020. The calculation of uncertainties for the PMF input matrices for both instruments are given in Text S.1. The hourly averaged datasets of both instruments were first used separately for single instrument PMFs (denoted PMFACSM and PMFPTR-MS), and then gathered for the PMFcombined input, where data points available for only one instrument were discarded. This resulted in a single matrix consisting of 1535 data points and including 73 ACSM variables and 31 PTR-MS variables, corresponding to a data coverage of 84 %. Note that the ACSM was interrupted between August 4th and 12th and therefore this period was deleted from the combined dataset. The timeseries of organic aerosol (ACSM) and methanol, acetone, isoprene, and toluene (PTR-MS) are displayed on Figure S2.

A co-located multiwavelength AE33 Aethalometer (Magee Scientific) provided complementary information on equivalent black carbon (eBC) concentrations and sources, as described in Petit et al. (2015) and Zhang et al. (2019). Using the Aethalometer model, eBC was apportioned into its two main combustion sources, i.e., fossil-fuel (BCff) and wood burning emissions (BCwb) (Drinovec et al., 2015; Favez et al., 2010; Sandradewi et al., 2008; Sciare et al., 2011). The absorption Ångström exponent values in the wavelength range of 470–950 nm used for these calculations were 0.9 and 1.85 for BCff and BCwb respectively, based on Petit et al. (2021).

Nitrogen monoxide and dioxide (resp. NO and NO2) have been monitored since 2013 using chemiluminescence NO2/NO/NOx analyzer (model T200UP, Teledyne API, USA). Since the ozone analyser at SIRTA was not working during this period, ozone data from the AirParif sub-urban station in Les Ulis (2.165 E, 48.68 N) was used here. A comparison with the ozone measured at SIRTA during other periods revealed rather similar ozone levels and variability at both stations (not shown here).

In addition, a measurement campaign took place from 10th April to July 20, 2020, involving a time-of-flight (ToF) PTR-MS (Ionicon, 1000) and two gas chromatography instruments, to analyse a wider range of VOCs that could be used as external tracers. For the PTR-ToF-MS, a heated (50 °C) 16-m PFA sampling line with an inner diameter of 9.53 mm was used to sample at the same height as the PTR-Quad-MS. A pump provided a flow of 22 L min-1, thus resulting in a residence time of about 3 s. The drift pressure was set to 2.3 mbar, the drift temperature to 80 °C and the drift voltage to 411 V, thus resulting in an E/N of 132 Td. A catalytic converter (Zero air generator, Parker, France) enabled to perform blanks manually, once every other working day during the campaign. Calibrations were done about once a month with a standard mixture and using the internal dilution system. The selected PTR-ToF-MS m/z used as external markers were:

* m/z 109.0648: cresol, a nighttime oxidation product of aromatic compounds (Zaytsev et al., 2019)

* m/z 113.0597: dimethylfuranone, a daytime oxidation product of trimethylbenzenes (TMB) and a potential SOA precursor (Li et al., 2021)

* m/z 137.0961: trimethylphenol, a TMB oxidation product and a potential SOA precursor (Li et al., 2021)

* m/z 139.112: nopinone, produced by the oxidation of β-pinene by O3 and OH (Calogirou et al., 1999) + limonaketone, OH oxidation product of limonene (Calogirou et al., 1999)

* m/z 153.127: α-pinene oxide, produced by the nighttime oxidation of α-pinene by O3 (Calogirou et al., 1999)

* m/z 155.106: norpinonaldehyde, produced by O3 nighttime oxidation of terpenes

* m/z 151.112: pinonaldehyde, an oxidation product of α-pinene with OH, NO3 and O3 (Calogirou et al., 1999; Spittler et al., 2006) + limonaldehyde, an oxidation product of limonene (Calogirou et al., 1999)

Two gas chromatographs equipped with FID detectors were also deployed. A C2-C6 airmoVOC and a C6-C12 airmoBTX (Chromatotech, Saint-Antoine, France) were set-up next to the PTR-ToF-MS and connected to a 16m stainless steel sampling line. A calibration was performed on the 26th of June, by sampling an NPL standard containing a mixture of hydrocarbons at 5 ppb.

Meteorological data included temperature, relative humidity, wind speed and direction that were measured by sensors 4 km away from our main measurements (Chiriaco et al., 2018; Haeffelin et al., 2005). Photosynthetically active radiation (PAR) measurements were also provided at this site, as well as mixed layer height, measured by Automatic Lidar and Ceilometer and processed with the CABAM algorithm.

## 2.2. Combined PMF theory

### 2.2.1. PMF principle

The PMF model apportions the observation $x_{ij}$ (here the ACSM and PTR-MS measurements) into a linear combination of a number of factors p for each time step i and variable j consisting of a temporal positive contribution $g_{ik}$ and static combined mass spectrum intensity $f_{kj}$ (Eq. (1)).

$$x_{ij} = \sum_{k=1}^{p} (g_{ik} \cdot f_{kj}) + e_{ij} \quad (1)$$

$e_{ij}$ is the residual matrix, it has the same dimensions as the input matrices and contains the difference between the input data and the modelled solution for each point ij, thereby corresponding to the data that is not modelled by the PMF.

The least-squares algorithm within the multilinear engine (ME-2) solves Equation (1) by iteratively minimizing the parameter Q, which represents the sum of the uncertainty-weighted residuals across the dataset (Paatero and Tapper, 1994, Eq. (2)). Q is typically normalized by $Q_{expected}$ and this Q/Qexp metric is used to infer the improvement of the solution when increasing the number of factors or across different simulations (Canonaco et al., 2013). In Eq (2), $\sigma_{ij}$ corresponds to the measurement uncertainties.

$$Q = \sum_{i=1}^{n} \sum_{j=1}^{m} \left( \frac{e_{ij}}{\sigma_{ij}} \right)^2 \quad (2)$$

Data points with a ratio $\frac{e_{ij}}{\sigma_{ij}} \gg 1$ will have a high impact on the model iteration because they constitute a large part of Q. This can be the case with ambient outliers or electronic noise. To prevent these outliers from driving a solution, the PMF model is generally run in “robust mode”. Outliers are defined at each iteration of the process based on the ratio

$$|\frac{e_{ij}}{\sigma_{ij}}| > \alpha.$$ A value of 4 is recommended for α in the robust mode (Paatero, 1997). The identified outlier points are then dynamically downweighed by the model.

PMF is subject to rotational ambiguity, which leads to different combinations of G and F yielding the same Q values. Some of these solutions could contain mixed or environmentally unreasonable factors. Constraining AMS/ACSM data with a priori information (profile or time series) has been shown to improve the model performance by isolating the more environmentally interpretable PMF runs (Canonaco et al., 2013; Crippa et al., 2014). In the ME-2 algorithm, source profiles can be used as anchors for the PMF ($f_j$), and the a-value approach tells the model how much these current anchors ($f_{j,solution}$) are allowed to relax
over a PMF run:

$$f_{j,solution} = f_{j,anchor} \pm \alpha \cdot f_{j,anchor} \quad (3)$$

a can have values between 0 and 1, with 0 meaning that the profile is fully constrained, at a = 1 the profile is unconstrained; an a-value of 0.2 means that the solution is allowed 20 % deviation from the given anchor profile.

The bootstrap resampling strategy can be used to evaluate the stability of the solution. This methodology randomly generates new input matrices from the input dataset, by randomly duplicating some time points (scans), and deleting others (Efron, 1979). PMF analysis is performed on all these matrices and the variability within a factor of the different and interpretable solutions allows to estimate the statistical random error. Here a bootstrap analysis was performed to ensure the stability of the base case solution, and to assess the PMF errors, by doing a number of repeats (e.g., 200) allowing all a-value configurations and ensuring the stability of the errors.

### 2.2.2. Uncertainty weighting factor

In the case of a combined dataset from two different instruments, the potential systematic biases in their error calculation could impact the value of Q (Eq (2)) differently. Moreover, the stronger internal correlations within the ACSM dataset (due to the important fragmentation associated with the hard ionization technique) compared to the PTR-MS can affect the PMF model by driving the apportionment too. In the case of a PMF analysis using the originally calculated uncertainties, this can result in one of the instruments being well represented while the other being poorly represented by the final PMF model. To avoid this, the instruments' uncertainties were balanced by applying a weighting factor to the error matrix of one of the instruments. This procedure was post-evaluated and the weighting factors were analysed and optimized by monitoring the scaled residuals of both instruments to ensure their approximately equivalent representation (Slowik et al., 2010). This evaluation is detailed in the next section. Here, the weighting factor C<sub>PTR</sub> was applied to the PTR-MS uncertainty matrix σ (Eq (4)), which increased or decreased the contribution of the PTR-MS to Q, up- or down-weighting the PTR-MS data in the PMF solver.

$$\sigma'_{i,j=PTRMS} = \frac{\sigma_{i,j=PTRMS}}{C_{PTR}} \quad (4)$$

$$\sigma'_{i,j=ACSM} = \sigma_{i,j=ACSM} \quad (5)$$

In case the classical robust mode is used for outliers' identification, it would work against this C-value rescaling, as most of the rescaled PTR-MS errors would be tagged as outliers for large C-values and down-weighed accordingly by the robust mode mechanism (Slowik et al., 2010). In SoFi Pro (Canonaco et al., 2013, 2021), a variable-specific robust mode threshold was applied that considered the employed C-values.

### 2.2.3. Instrument weighting procedure evaluation

The first metric developed for the evaluation of balanced solutions consisted in calculating the difference in the absolute scaled residuals ΔE, as they are supposed to be independent of the measuring instrument (Slowik et al., 2010). All the values (Q, ΔE, ...) were calculated in SoFi with the original errors and not the weighted ones to consider changes in Q from the model improvement rather than from C<sub>PTR</sub> rescaling.

$$\bar{\Delta E} = \left( \frac{|e_{if}|}{s_{ij}} \right)_{ACSM} - \left( \frac{|e_{if}|}{s_{ij}} \right)_{PTRMS} \quad (6)$$

ΔE should be close to 0 (±0.25) to prevent one of the instruments to be over- or under-represented in the model (Crippa et al., 2013a).

Recently, a more advanced methodology was developed to ensure similar weight of the instruments by reproducing the scaled residual

histograms obtained for the standalone PMFs (Tong et al., 2022). This method considered the entire scaled residual distribution and not only the mean value, making it more sensitive. To evaluate the residuals behaviour in the combined PMF regarding the standalone one, an F<sub>overlap</sub> metric was calculated which corresponds to the integral overlap between the two probability density functions of both instruments (Eq (7); Tong et al., 2022; Figure S3).

$$F_{overlap} = \int \left( P_{PTR} \left( \frac{e_{ij}}{\sigma_{ij}} \right), P_{ACSM} \left( \frac{e_{ij}}{\sigma_{ij}} \right) \right) \quad (7)$$

This method is particularly suited when a similar behaviour is desired for the scaled residuals of both instruments in the combined PMF as in the standalone ones. In the present case, the instruments could behave differently or better in the combined PMF than in the standalone solutions. Moreover, this method does not always lead to the most environmentally reasonable solution, and other runs should be investigated than those selected by the algorithm (Via et al., 2023). Therefore, we did not necessarily try to reproduce the exact same behaviour as in the standalone PMF, but rather monitor F<sub>overlap</sub> as a main metric in combination with the application of environmental criteria for both instruments, as normally also performed for standalone PMF runs (Atabakhsh et al., 2023; Canonaco et al., 2021; Chazeau et al., 2022; Chebaicheb et al., 2023; Chen et al., 2022; Zografou et al., 2022).

## 2.3. Methodological scheme for the combined PMF

Different steps are needed to first obtain a base case solution, i.e., a preliminary one that is environmentally reasonable, and that will in the end lead to the more robust final solution. These steps are presented in Fig. 1 and discussed based on the relevant C-value metric for this study.

### Step 1: Identification of the thresholds in the C-p space

A large range of C-values was systematically explored, leading to a very high number of different solutions. Here we applied the different methods presented in Section 2.2.3 (Crippa et al., 2013a; Slowik et al., 2010; Tong et al., 2022) and tailored a methodology for our particular dataset. The first step was to identify the thresholds of mathematically possible combinations of C<sub>PTR</sub> weighing values and number of factors p.

The various possible solutions were available in a “C-p space” (Fig. 1), because they were simultaneously dependent of the C<sub>PTR</sub>-value and of the number of factors p (Crippa et al., 2013a; Slowik et al., 2010; Tong et al., 2022). To explore this space and guide the analysis in a specific way, and in order to avoid investigating too many solutions, we first identified the thresholds for the model. The PMF was ran with C<sub>PTR</sub>-values ranging from 10<sup>-9</sup> to 10<sup>10</sup>, and the scaled residuals histograms were investigated (Figure S4). For a C<sub>PTR</sub>-value of 10<sup>-5</sup>, the PTR-MS was poorly modelled, with a very wide histogram (Figure S4a). On the other hand, for a C<sub>PTR</sub>-value of 10<sup>4</sup>, similar histograms were obtained for both instruments (Figure S4b), and they were unimodally distributed around 0. For C<sub>PTR</sub>-values lower than 10<sup>-5</sup>, the PTR-MS variables were not modelled, while for C<sub>PTR</sub>-values above 10<sup>4</sup>, no solution was obtained. Further detailed tests were therefore performed in the C<sub>PTR</sub>-range 10<sup>-5</sup>-10<sup>4</sup>.

### Step 2: Criteria-approach to find best C and p values

Based on the metrics presented in Section 2.2.3, a criteria-approach was used to evaluate the instrument weighing procedure narrowing the C<sub>PTR</sub>-value range of plausible solutions. In this step, the factors were unconstrained because the combined approach was exploratory. The criteria used here, the thresholds applied, and corresponding selected C<sub>PTR</sub>-value are presented in Table 1.

The intrinsic bimodal overlap distribution highlighted two rather distinct types of solutions, i.e., a well-balanced solution state (high
0. Initial C<sub>PTR</sub> and p range

1. Identification of thresholds in the C-p space for modeled and resolved solutions

2. Criteria-approach to find best C<sub>PTR</sub> and p values by monitoring the scaled residuals of both instruments

3. Exploration of single solutions to select the base case

4. Bootstrap analysis to infer the stability of the solution and estimate model error

<figure><img src="image_4.png" /><figcaption>**Fig. 1.** Steps to identify and select a base case for the combined PMF and obtain the final solution (left). Selection of C<sub>PTR</sub> values for the base case (steps 0 to 3) (right).</figcaption></figure>

<table><caption>**Table 1**
Criteria to select the C and p values for the combined PMF.</caption><thead><tr><th>Criteria</th><th>Threshold</th><th>C<sub>PTR</sub> selection</th></tr></thead><tbody><tr><td>Foverlap</td><td>&gt;0.70</td><td>C<sub>PTR</sub> ≥ 0.3</td></tr><tr><td>Total scaled residuals</td><td>[-0.1,0.1]</td><td>C<sub>PTR</sub> ≥ 0.1</td></tr><tr><td>Scaled residuals of m/z 43 (ACSM)</td><td>[-0.2,0.2]</td><td>C<sub>PTR</sub> ≤ 5</td></tr><tr><td>ΔE</td><td>[-0.25,0.25]</td><td>C<sub>PTR</sub> ≥ 0.3</td></tr></tbody></table>

overlap value) and a rather poorly mixed solution state (low overlap value) (Figure S5a and b) and allowed to directly derive a threshold of 0.70 (lower end of the high overlap value) for the F<sub>overlap</sub> criterion (see Section 2.2.3 and Figure S3). Monitoring the total sum of scaled residuals for both instruments allowed to avoid selecting solutions with too high residuals, where too much input variability remained unmodelled. Monitoring the scaled residuals of the key ACSM variable m/z 43 was necessary to ensure that they would not stand out (as discussed in Text S.2), which would indicate that the ACSM was not well modelled, and this was not desirable for a balanced and reasonable solution. As mentioned in Section 2.2.3, ΔE should be comprised between -0.25 and 0.25.

Based on these results, balanced and reasonable solutions were located in a C<sub>PTR</sub>-range 0.3–5. Selected runs are highlighted in blue on Figure S5c for different number of factors, which shows that Q/Qexp varied greatly with C<sub>PTR</sub> in this range, especially between C<sub>PTR</sub> = 0.1–0.5, and C<sub>PTR</sub> = 3–7. Q/Qexp decreased with increasing number of factors, so solutions with higher number of factors were studied. However, 8-factor solutions resulted in split factors (factors 6 and 7 on Figure S6) for which the profiles correlated at 99 % and timeseries at 58 %. Therefore, the 7-factor solutions were further investigated.

### Step 3: Selection and presentation of base case

In the C<sub>PTR</sub> range 0.3–5 and with a p value of 7 as defined by the previous step as more likely to result in a balanced solution, three possible solutions were investigated (for C<sub>PTR</sub> = 0.3, 1 and 5) and the solution for C<sub>PTR</sub> = 1 was preferred, because it was the most balanced one and had the best atmospheric interpretability (Text S.2). This solution resolved a factor that resembled ACSM HOA and contained aromatic VOC, and another one that resembled ACSM COA. Therefore, a

further step to obtain the base case consisted in constraining both these factors and running the model over a smaller C<sub>PTR</sub> range (0.8–2). HOA and COA were first constrained only on the ACSM variables using ACSM/AMS reference profiles from previous measurements at SIRTA (Crippa et al. (2013c) and Fröhlich et al. (2015) respectively). Then, a preliminary combined run was used to constrain all variables of these two factor profiles, to ensure the proportion between ACSM and PTR-MS m/z. The COA factor in this solution had an important contribution of PTR-MS m/z 71, which mainly corresponds to isoprene oxidation products, MVK and MACR (Kroll et al., 2006). In the PTR-MS-only PMF (Text S.3), a separate factor was resolved describing secondary biogenic processes and containing m/z 71. That factor was especially increasing during the beginning of August, a period that is not resolved in the PMF<sub>combined</sub> due to the absence of ACSM measurements. Therefore, biogenic secondary was constrained as a separate factor using PTR-MS m/z 71.

Preliminary results also show that PMF resolved a primary biogenic factor which did not have an important contribution to OA and was not atmospherically reasonable for OA. Similarly, the nighttime factor obtained showed an unreasonable ACSM profile and ACSM residuals were higher when it was included. Since these two factors were expected for VOC and were modelled in PMF<sub>PTR-MS</sub> (which will be presented in Section 3.1 and Text S.3), they were constrained as VOC-only, leading to a preliminary solution that was used for bootstrap.

The base case was obtained with a C-value of 0.9 and consisted of seven factors. These were identified as hydrocarbon-like organics, cooking-like organics, primary biogenic VOC, secondary biogenic organics, nighttime VOC, oxidized organics and aged organics. The factors are discussed for the final solution in the results (Section 3.2).

### Step 4: Bootstrap

To infer the stability of the solution and assess the statistical random uncertainties of the model, the bootstrap approach was used (Paatero et al., 2014). As mentioned, the fingerprint of the first 5 out of the 7 factors was completely or partially constrained. Combined profiles based on preliminary solutions were used as anchors and random a-values were used to limit the rotational ambiguity. The upper a-values used were 0.4 for cooking-like organics and secondary biogenic organics to restrict their degree of freedom while hydrocarbon-like organics,
biogenic primary VOC and nighttime VOC had an upper a-value of 0.7 as they were more stable. Criteria were used to select the best runs out of the bootstrap results and to sort unconstrained factors between each run (Table 2). Sorting unconstrained factors was necessary to average the selected runs and make sure that the same factor was averaged over all runs.

Criteria 1 and 2 evaluated the correlation of hydrocarbon-like organics with external tracers. Here BC and NO₂ were used instead of usual BCff and NOₓ due to their higher correlations with the factor in the preliminary runs. Criterion 3 was used to monitor the ratio between the lunch peak at 1 p.m. (UTC) and the morning baseline at 9 a.m. (UTC) for cooking-like organics, which should be higher than 1. Criteria 5 to 8 were used to reposition the unconstrained factors, oxidized and aged organics. They were sorted based on ACSM *m/z* 43 and *m/z* 44, since the amount of these fragments were different in both factors; which is commonly done to sort LO-OOA and MO-OOA in ACSM PMFs (Chen et al., 2022). On the VOC side, both factors were differentiated by the ratio of *m/z* 33 (methanol) and *m/z* 59 (acetone), which was here used for sorting the factors and is discussed in the results. These criteria thresholds selected 86 % of the solutions.

The mathematical performance of the model for the standalones and combined PMFs was evaluated in terms of Foverlap and Q/Qexp. The comparison of scaled residuals histograms (Fig. 2) shows that the ACSM variables are well represented for both cases, but the histogram is narrower for PMF<sub>ACSM</sub>, suggesting a better apportionment by the model. Q/Qexp points in that direction as well, as it is lower for PMF<sub>ACSM</sub> (0.26) than PMF combined (0.71). On the other hand, the PTR-MS variables seem to be better represented in the PMF<sub>combined</sub> compared to single PMF<sub>PTR-MS</sub>, with lower mean absolute scaled residuals for the combined PMF (11.2) than for the PMF<sub>PTR-MS</sub> (38.2), a slightly narrower histogram and lower Q/Qexp (0.71 vs 0.86).

# 3. Results & discussions

## 3.1. Single-instrument PMF solutions

Text S.3 details the ACSM- and PTRMS-only PMF parametrization and results. The ACSM-only OA PMF resulted in a 3-factor solution: HOA, LO-OOA and MO-OOA. HOA was linked to road traffic, possibly mixed with other sources. LO-OOA describes fresh oxidation with a lower f44 and a more pronounced diel cycle than MO-OOA. Both OOA factors originate mainly from east-southeast and north-east.

Six factors were obtained for the PTRMS-only PMF: traffic, biogenic primary, biogenic secondary, oxygenated, nighttime, and background. The traffic factor contains aromatic VOCs and shows a diel cycle typical of this source (Figure S16). Both biogenic factors contain isoprene, isoprene oxidation products (MVK + MACR) and increase during daytime. The secondary factor contains more oxygenated compounds (methanol, acetone, acetic acid) and increases about an hour later, corresponding roughly to the lifetime of isoprene. The oxygenated factor

<caption>**Table 2**</caption>

Criteria for runs selection during the bootstrap evaluation. Criteria for factor repositioning are in italic.

<table><thead><tr><th>Number</th><th>Factor</th><th>Criterion</th><th>Threshold/<br>Evaluation</th></tr></thead><tbody><tr><td>1</td><td>1-Hydrocarbon-like<br>organics</td><td>R<sup>2</sup><sub>pearson</sub> vs BC</td><td>p-value &lt;0.05</td></tr><tr><td>2</td><td>1-Hydrocarbon-like<br>organics</td><td>R<sup>2</sup><sub>pearson</sub> vs NO<sub>2</sub></td><td>p-value &lt;0.05</td></tr><tr><td>3</td><td>2-Cooking-like<br>organics</td><td>Cooking - like organics[13h]<br>Cooking - like organics[9h]</td><td>&gt;1</td></tr><tr><td>5</td><td>5-Oxidized organics</td><td>Oxidized[ACSM_43']</td><td>&gt; 0</td></tr><tr><td>6</td><td>6-Aged organics</td><td>Aged[ACSM_44']</td><td>&gt; 0</td></tr><tr><td>7</td><td>5-Oxidized organics</td><td>Oxidized[PTRMS_33']</td><td>&gt; 0</td></tr><tr><td>8</td><td>6-Aged organics</td><td>Aged[PTRMS_59']</td><td>&gt; 0</td></tr></tbody></table>

<figure><img src="image_5.png" /><figcaption>**Fig. 2.** Scaled residuals probability histograms for a. standalone PMFs and b. combined PMF.</figcaption></figure>

also increases during the day and is related to photochemical processes and secondary formation from both biogenic and anthropogenic compounds. The nighttime factor contains mainly methanol, acetone, and monoterpenes, it increases at night and in the morning but is difficult to link to a specific source as these compounds originate from various sources and processes. The background factor is also not linked to a single source but rather longer processes, as it contains long-lived species.

## 3.2. Most balanced solution obtained from the combined analysis

In this section, the factors obtained from the combined PMF analysis are presented one by one with figures supporting the discussion of each factor. Fig. 3 shows the chemical footprints, diel cycles and temporal variability of the obtained factors. External data available at the station during this period consisted of inorganic species, meteorological parameters, and *m/z* measured by a PTR-ToF-MS during the first 1.5 months. All R² correlations between the PMF combined factors and external variables are given in Table S2, and some are represented on the diel cycles in Fig. 3c. Residuals associated with this solution are presented in Figure S20.

The scatter plot of ACSM f44 vs. f43 for the factors can give information on their oxidation degree (Ng et al., 2011) and are presented on Fig. 4.

### Hydrocarbon-like organics

The hydrocarbon-like organics factor presents a typical HOA footprint for the ACSM variables (as it was constrained), however the ratios *m/z*41/*m/z*43 and *m/z*55/*m/z*57 are different (i.e., lower) than the ones observed for HOA<sub>ACSM</sub> and previously resolved HOA at SIRTA (Zhang et al., 2019). The corresponding PTR-MS variables comprise mainly aromatic compounds as observed for the traffic factor in the PMF<sub>PTRMS</sub> (Fig. 3b), and the hydrocarbon-like organics factor explains 77 % of toluene, 86 % of C8-aromatics and 62 % of C9-aromatics. The diel profile shows an increase at night and a weaker one in the morning and covaries with BC and NO₂, suggesting the influence of traffic emissions and of the boundary layer. This factor is located at the bottom of the f44/f43 scatter plot (Fig. 4), typical for primary factors, but a bit apart from HOA<sub>ACSM</sub> and HOA from Zhang et al. (2019). As expected, hydrocarbon-like organics correlates significantly with BC and NO₂ (Fig. 3c–Table S2). In addition, a correlation is observed with two PTR-ToF-MS tracers, namely cresol (*m/z* 109.065) and pinonaldehyde + limonaldehyde (*m/z* 151.112), which could be explained by nighttime
<figure><img src="image_6.png" /><figcaption>Fig. 3. Mean factor profiles for a. ACSM variables and b. PTR-MS variables, c. mean diel cycles and d. temporal variability for the PMF<sub>combined</sub> analysis.</figcaption></figure>

oxidation of aromatic compounds and monoterpenes (Calogirou et al., 1999; Zaytsev et al., 2019; Table S2) covarying with this factor. Based on the non-parametric wind regression (NWR, Fig. 5), highest estimated concentrations of hydrocarbon-like organics originate from winds from the north-east, which matches with the main traffic roads and influence from Paris (Figure S1).

• Cooking-like organics

The cooking-like organics factor was initially identified as COA due to the high *m/z* 55 ACSM fragment. AMS measurements attribute the higher *f*55 and *f*57 in COA to the presence of the ions C₃H₃O⁺ and C₃H₅O⁺ (Mohr et al., 2012). The corresponding contributing PTR-MS variables are mainly acetic acid (*m/z* 61) and formic acid (dominant within *m/z* 47 in summer; Simon et al., 2023). Reports of VOC measurements from cooking activities in the Paris region are scarce. In China, acetone, acrolein, *i*-butane and *n*-butane were associated with cooking activities (Sun et al., 2022); laboratory experiments highlighted emissions of aldehydes (acrolein, heptanal, nonanal, ...) as well as acids and alcohols (Klein et al., 2016); and in the United States, long-chain

aldehydes (octanal, nonanal), as well as fatty acids (heptanoic, octa-
noic, nonanoic and decanoic acids) were identified (Coggon et al.,
2024). The latter study also associated acetic acid and acrolein with
cooking activities. Acetone and acetic acid have various sources in the
summer and cooking activities could contribute to their concentrations
in our study, *i*-butane and *n*-butane are also emitted by the traffic source,
and the PTR-Quad-MS sensitivity was too low for the detection of
long-chain aldehydes and fatty acids. The diel variability shows a lunch
increase, a slight decrease in the afternoon and an increase in the eve-
ning, suggesting cooking activities, as was observed in preliminary runs.
The diel cycle is less marked than in stations closer to the source, such as
in the centre of Paris (Crippa et al., 2013b). A COA-like factor has pre-
viously been detected at SIRTA using high mass resolution spectrometry
during the 2009 Megapoli campaigns (Crippa et al., 2013a,b,c). How-
ever, the significance of such a factor has always been questioned in
following PMF studies using only ACSM measurements since then at
SIRTA (Fröhlich et al., 2015; Petit et al., 2014, 2015; Zhang et al., 2019,
2020), highlighting a possible important added value of the combined
PMF approach. Nevertheless, this factor shows a low but significant
correlation with dimethylfuranone (*m/z* 113.060, R² = 0.43, Fig. 3c), an
<figure><img src="image_7.png" /><figcaption>Fig. 4. Scatter plot of f44 vs. f43 for all PMF<sub>combined</sub> and PMF<sub>ACSM</sub> factors, as well as the PMF<sub>ACSM</sub> factors from Zhang et al. (2019).</figcaption></figure>

oxidation product of trimethylbenzenes (Li et al., 2021), which are mainly emitted by traffic but could also come from cooking activities (Crippa et al., 2013a). This factor may thus be explained by the covariation of cooking emissions, aged traffic and rapid gas-phase oxidation of anthropogenic compounds. This factor is also located at the bottom of the f44/f43 scatter plot (Fig. 4), but closer to HOA<sub>ACSM</sub> and HOA from Zhang et al. (2019) than hydrocarbon-like organics. The NWR plot (Fig. 5) shows the highest concentrations from the east and does not

point to a specific origin, suggesting that this factor might not come from a single source.

### Primary biogenic VOC

As discussed before, this factor was only resolved for the PTR-MS variables and represents primary biogenic emissions of VOC. Indeed, it contains isoprene (m/z 69), a small fraction of its oxidation products (m/z 71) and monoterpenes (m/z 137), similar to the PMF<sub>PTRMS</sub> biogenic factor (Fig. 3b). Its diel profile shows an increase during the day, in agreement with the isoprene emissions correlated to temperature and solar radiation (Figure S17). The NWR plot (Fig. 5) suggests that the highest estimated concentrations of this factor are coming from the south, especially for stronger winds, which could indicate that the source is located further away from the site. In fact, the Rambouillet forest is located around 19 km away in the south-west of the site (Figure S1), which is a distance that a wind of a speed of 8 m/s can travel in less time than the lifetime of isoprene. Parks and forests are also located in the south-east of the site.

### Secondary biogenic organics

This factor is characterized by a typical OOA profile with high levels of m/z 43 and m/z 44. The PTR-MS variables in this factor include mainly m/z 71, corresponding to oxidation products from isoprene (MKV + MACR); m/z 61, corresponding to acetic acid; m/z 33 – methanol and m/z 59 – acetone, similar to the corresponding PMF<sub>PTR-MS</sub> profile (Fig. 3b), but with a higher contribution from m/z 71. The diel cycle shows an increase during the day about 1 h after primary biogenic starts increasing, corresponding to the lifetime of isoprene (Atkinson, 2000). This factor correlates with dimethylfuranone and somewhat with nopinone + limonaketone (m/z 139.112, Fig. 3c–Table S2), indicating a temporal covariation of the photooxidation of primary biogenic and anthropogenic compounds. The f44/f43 plot (Fig. 4) shows this factor in the right hand side, in agreement with what is expected for biogenic-influenced OOA (Canonaco et al., 2015; Chen et al., 2022; Heringa et al., 2011; Ng et al., 2011). Obtaining a biogenic secondary factor associated with oxidation products of isoprene is a promising result and suggests that oxidation products of monoterpenes could be used as tracers to extract a specific factor linked to these processes, but their higher m/z makes the detection difficult with PTR-Quad-MS. The

<figure><img src="image_8.png" /><figcaption>Fig. 5. Non-parametric wind regression plots obtained for each of the PMF<sub>combined</sub> factors. The circles indicate the wind speed in m/s, and the colour indicates the joint probability in the first plot, and the estimated factor concentration (µg·m⁻³) in the other ones. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)</figcaption></figure>
NWR plot (Fig. 5) suggests that highest concentrations of this factor originate from the south-east of the region, which could correspond to processed biogenic emissions from forests like Fontainebleau, which is located about 45 km from SIRTA (Figure S1).

## Nighttime VOC

As for primary BVOC, the nighttime VOC factor was a PTR-MS only factor with mainly *m/z* 33 (methanol), *m/z* 59 (acetone) and *m/z* 137 (monoterpenes), similar to the PMF<sub>PTR-MS</sub> one (Fig. 3b). The diel profile is the opposite of the daytime profiles, with a small increase in the morning, a strong decrease during the day and a subsequent increase in the evening. This shape can be explained by daytime consumption of the VOCs and higher boundary layer, while nighttime levels can be due to the boundary layer decrease and/or to emissions of methanol, acetone and monoterpenes at night. As for the nighttime factor in the PMF<sub>PTRMS</sub>, this factor can be associated with different sources, biogenic and anthropogenic such as solvent use and personal care products, and processes. The NWR plot (Fig. 5) does not point to a specific direction for the highest concentrations, probably due to the long lifetime of methanol and the ubiquity of the sources associated with the factor.

## Oxidized organics

This factor presents a typical ACSM LO-OOA profile with high levels of *m/z* 43 and *m/z* 44. Other fragments have a small contribution, like *m/z* 41 and *m/z* 55, underlining the fresh oxidation of this aerosol. The PTR-MS variables in this factor include mainly *m/z* 33 (methanol) and *m/z* 59 (acetone). The diel cycle of oxidized organics shows a decrease in the morning, which could be linked to some partitioning into the gas phase as the temperature increases, as well as the boundary layer causing dilution of the compounds (Crippa et al., 2013c). The subsequent increase in the afternoon could result from photochemical production of compounds with a lower volatility. The factor concentration further increases in the evening, due to the lowering of the boundary layer, and to the potential nighttime chemistry leading to production of more oxidized gas- and particle phase compounds. This factor is located close to the LO-OOA<sub>ACSM</sub> factor on the f44/f43 plot, although somewhat towards more oxygenated aerosol (Fig. 4). Oxidized organics correlate significantly (Table S2) with dimethylfuranone, nopinone + limonacetone (*m/z* 139.112) and α-pinene oxide (*m/z* 153.107), indicating potential influence from the oxidation of biogenic and aromatic compounds. Separating the dataset into daytime and nighttime did not allow to further specify sources for both periods, which highlights the need for including source-specific tracers in both gas and particulate phases in future PMF modelling. The NWR plot of this factor (Fig. 5) shows that the highest concentrations seem to come from the south-east, similar to the biogenic secondary factor, hinting at its biogenic influence, but important concentrations also originate from the north-east, associated with traffic and anthropogenic emissions, suggesting that this factor was not able to separate biogenic and anthropogenic sources.

## Aged organics

This factor presents a typical ACSM MO-OOA profile with a higher level of *m/z* 44 than in oxidized organics. The PTR-MS profile includes mainly methanol and acetone as well, but the acetone-to-methanol ratio is higher, suggesting a more aged factor due to acetone having a longer lifetime than methanol (61 days vs 12 days; Atkinson and Arey, 2003). In addition, the diel profile shows important background concentrations but also some daytime oxidation to counter the dilution from the boundary layer dynamics. The f44/f43 plot shows that this factor is situated on the upper end, close to MO-OOA<sub>ACSM</sub> (Fig. 4) and MO-OOA from Zhang et al. (2019). Finally, it does not significantly correlate with any external tracer (Table S2) and the NWR plot shows high concentrations coming from all directions, with higher ones from the east,

similar to the oxidized organics factor (Fig. 5).

## 3.3. Comparison with standalone PMFs

The contributions of each factor to the respective component (OA or VOC), as well as the error on these values, are presented for PMF<sub>ACSM</sub>, PMF<sub>PTRMS</sub> and PMF<sub>combined</sub> in Fig. 6. For organic aerosol, the contribution to hydrocarbon-like organics is much lower (2.8 %) than the contribution of HOA in PMF<sub>ACSM</sub> (10.3 %) which was similar to previous observations in summer (Zhang et al., 2019). The difference between PMF<sub>ACSM</sub> and PMF<sub>combined</sub> can be explained by a “split” of HOA into hydrocarbon-like organics and cooking-like organics, as the sum of their contributions matches the 10 % HOA in PMF<sub>ACSM</sub>. However, cooking-like organics contributes more in the PMF<sub>combined</sub> than hydrocarbon-like organics, but COA was not resolved in PMF<sub>ACSM</sub>, highlighting the difficulty of clearly resolving these sources in a suburban station. In addition, the diurnal cycle of HOA was pointing to a rather mixed traffic source. The low contribution of hydrocarbon-like organics to OA could also be attributed to less traffic in summer, especially in 2020 as activities were still impacted by COVID-19, as well as high oxidation of primary compounds in summertime. The “split” of HOA is further illustrated on Fig. 7 representing the timeseries of PMF<sub>ACSM</sub> factors with their respective OA PMF<sub>combined</sub> factors summed. In addition, the correlations of HOA and hydrocarbon-like organics with external traffic tracers (BC, NO₂ and alkanes measured by gas chromatography; Table 3) show a higher R² value for hydrocarbon-like organics with gaseous compounds compared to HOA, and a similar value for BC. It could also suggest that the hydrocarbon-like organics factor is related to a more specific source than HOA<sub>ACSM</sub> or to emissions, as the concentrations drop to the baseline after a peak, while HOA and cooking-like organics could describe more aged/accumulating processes and/or sources further away from the measurement site (Fig. 7). The NWR plots also suggest a more specific source for hydrocarbon-like organics, as its plot points specifically to the northeast origin, while cooking-like organics and HOA plots are wider. This underlines the difficulty of HOA to precisely represent the temporal variability of

<figure><img src="image_9.png" /><figcaption>**Fig. 6.** Contribution of PMF<sub>ACSM</sub> and PMF<sub>combined</sub> factors to total OA, and of PMF<sub>PTRMS</sub> and PMF<sub>combined</sub> factors to total VOC. Values in brackets indicate the error estimation from the bootstrap analysis.</figcaption></figure>
<figure><img src="image_10.png" /><figcaption>Fig. 7. Time series of the PMF<sub>ACSM</sub> and corresponding PMF<sub>combined</sub> factors (OA component) summed.</figcaption></figure>

<table><caption>**Table 3**
Correlations of HOA<sub>ACSM</sub> and hydrocarbon-like organics from the PMF<sub>combined</sub> with BC and some gaseous external tracers.</caption><thead><tr><th>R<sup>2</sup><sub>pearson</sub></th><th>BC</th><th>NO<sub>2</sub></th><th>i-butane</th><th>n-butane</th><th>i-pentane</th><th>n-pentane</th><th>n-hexane</th></tr></thead><tbody><tr><td>HOA (PMF<sub>ACSM</sub>)</td><td>0.57</td><td>0.31</td><td>0.37</td><td>0.40</td><td>0.37</td><td>0.46</td><td>0.22</td></tr><tr><td>Hydrocarbon-like organics (PMF<sub>combined</sub>)</td><td>0.53</td><td>0.74</td><td>0.83</td><td>0.80</td><td>0.74</td><td>0.79</td><td>0.64</td></tr></tbody></table>

primary traffic, as has also been shown in winter at SIRTA (Petit et al., 2014; Srivastava et al., 2019; Zhang et al., 2019).

Due to the short lifetime of its main contributing VOCs, the biogenic secondary factor is considered as a “less-oxidized OOA” from an OA point of view. Therefore, biogenic secondary and oxidized organics are summed to be compared to LO-OOA<sub>ACSM</sub> in terms of contributions (56.8 % (±1.6) vs 46.5 % (±1.1), Fig. 6) and temporal variability (Fig. 7). Aged organics contribute 33.4 % (±0.5) to OA while MO-OOA<sub>ACSM</sub> contributes 43.2 % (±0.8). This suggests that the combined PMF apportions the oxidized factors somewhat differently than the ACSM-only PMF, and these contributions are more similar to the results from Zhang et al. (2019), who highlighted a more important contribution of LO-OOA in summer (56 %) than MO-OOA (26 %). The sum of biogenic secondary and oxidized organics shows a pronounced temporal variability, with an important increase when the temperature increases especially at end of June, while aged organics has a less marked variability, in agreement with its more processed nature. This difference is less marked on the PMF<sub>ACSM</sub> OOA factors, where MO-OOA<sub>ACSM</sub> also increases significantly during the warmer periods. This suggests an underestimation of LO-OOA in favour of MO-OOA during periods of high oxidation by the PMF<sub>ACSM</sub>.

Correlations of the factor timeseries with the other factors' timeseries for both methods are provided in Table S3 and Table S4. The intercorrelations R² of the PMF<sub>ACSM</sub> factors range between 0.55 and 0.78, suggesting that they are not well separated from each other. These intercorrelations can also be explained by the strong internal covariation of the ACSM variables. On the other hand, for the PMF<sub>combined</sub> solution, no significant correlation (R² > 0.40) is found between the factors, suggesting that this method separates them better. These different elements suggest a better understanding of OA from a PMF combining ACSM and PTR-MS than from ACSM data alone.

Regarding volatile organic compounds, most of the factors have similar contributions in both PMFs (traffic vs. hydrocarbon-like organics, biogenic primary, nighttime, and background vs. aged organics). The biogenic secondary factor from PMF<sub>PTR-MS</sub> has been apportioned as

biogenic secondary (11 %) and part of cooking-like organics and oxidized organics in the PMF<sub>combined</sub>, while the oxygenated factor in PMF<sub>PTRMS</sub> was partly attributed to cooking-like organics and partly to oxidized organics. The secondary biogenic factor seems to be more specific of isoprene first oxidation in PMF<sub>combined</sub>, with higher f71 (0.21 vs 0.11 for PMF<sub>PTR-MS</sub>) and higher factor's correlation with ambient temperature (R² = 0.35 vs 0.06). It also seems to better describe particle phase processes (higher correlation with OM, R² = 0.40 vs 0.21), while the factor's correlation with m/z 139 is similar for both solutions (R² = 0.36 and 0.38). The lower contribution of the secondary biogenic factor in the combined PMF is linked to a lower contribution from methanol, acetone and acetic acid, with methanol and acetone contributing to oxidized organics and acetic acid to cooking-like organics. Despite being summertime, the contribution of biogenic primary to total considered VOC in the PMF<sub>combined</sub> is not higher than 12 %, which is due to the site type and important atmospheric oxidation. In comparison, considering at least 32 % of total biogenic in PMF<sub>PTR-MS</sub> (9 % primary and 23 % secondary, with contributions of the biogenic source to the oxygenated, nighttime and background factors that cannot be ruled out) and more than 23 % in PMF<sub>combined</sub> (12 % primary, 11 % secondary, part of oxidized organics and probably of aged organics), results are similar to the 30 % contribution previously apportioned in Paris (Baudic et al., 2016). Differences in both PTR-MS PMFs are also attributed to the period in the beginning of August not being included in the PMF<sub>combined</sub> due to the absence of ACSM data.

Overall, even though the ACSM factors seem better apportioned mathematically in a single-instrument PMF, they can find more environmental meaning in the combined PMF. The PTR-MS variables were mathematically better apportioned in the combined PMF and an additional factor was obtained compared to the respective standalone PMF, while 7-factors solutions for the PMF<sub>PTR-MS</sub> resulted in systematic splitting. Eventually, the addition of the PTR-MS variables helped in the apportionment of the OA component.
## 4. Conclusions

A combined positive matrix factorization source apportionment was performed for the first time on a unified ACSM-PTRMS UMR dataset and for a full season (summer 2020). The present exploratory work highlighted the difficulty of combining data from two different instruments and of objectively choosing the most mathematically correct and environmentally reasonable solution. The development and use of a combination of criteria, manual inspection and constraints was essential to guide the model towards a balanced solution and we presented here a step-by-step methodology useful for future studies facing similar challenges. The solution obtained and presented here consisted of 7 factors, 5 combined (i.e., hydrocarbon-like organics, cooking-like organics, biogenic secondary organics, oxidized organics and aged organics) and 2 PTR-MS only (biogenic primary VOC, and nighttime VOC). Hydrocarbon-like organics was linked to fresh traffic mainly originating from north-east, where Paris and the main roads are located. Cooking-like organics was associated with a mix of cooking activities, aged traffic, and possibly other anthropogenic sources. The primary biogenic VOC factor described daytime concentrations of biogenic compounds, while secondary biogenic organics described fresh oxidation of the primary biogenic factor, leading to the simultaneous formation of secondary gaseous compounds and BSOA. A VOC factor describing gaseous nighttime processes from different sources was identified but it was not associated with simultaneous formation of SOA. Finally, oxidized and aged organics described respectively fresh and aged oxidation of both gaseous and particulate organic compounds. These were separated by their relative amounts of ACSM *m/z* 43 and *m/z* 44 and PTR-MS *m/z* 33 (methanol) and *m/z* 59 (acetone).

Improvements from this method compared to single-instrument PMFs were mainly observed for the OA component, resulting in a better separation of HOA, LO-OOA and MO-OOA. HOA was separated into hydrocarbon-like organics and cooking-like organics, while oxidized and aged organics provided a better separation of OOA between fresh oxidized and more processed OA than LO-OOA and MO-OOA from PMF<sub>ACSM</sub> as their correlation was lower in the PMF<sub>combined</sub>. For the VOC analysis, results were similar for both methods for most of the factors, but mathematical improvements were observed, with lower mean absolute scaled residuals and lower Q/Qexp value obtained for the PMF<sub>combined</sub> compared to the PMF<sub>PTR-MS</sub>. Interestingly, the secondary biogenic and oxygenated factors appeared to be apportioned into biogenic secondary, cooking-like organics & oxidized organics in the combined analysis. The biogenic secondary organics factor from the combined PMF describes more specifically isoprene first oxidation as its fraction of MVK + MACR is higher than in the PMF<sub>PTRMS</sub>. However, please note that the conclusions and apportionments presented here need to be reinforced, as they were established over a relatively short period of time. Therefore, a perspective that this analysis offers, now that the method is tailored for this kind of dataset, is to perform a combined PMF on data from other seasons, especially during cold months to better apportion SOA from wood burning activities. Data from mass spectrometers with a better resolution than UMR (e.g., PTR-TOF-MS and ACSM:X) could help better apportion OOA as well as performing combined, rolling PMF allowing for time-dependent factor profiles, particularly interesting for OOAs, oxidized organics, aged organics and secondary species.

### CRediT authorship contribution statement

**Leïla Simon:** Writing – original draft, Visualization, Methodology, Investigation, Formal analysis, Data curation. **Olivier Favez:** Writing – review & editing, Validation, Supervision, Investigation, Funding acquisition, Conceptualization. **Jean-Eudes Petit:** Writing – review & editing, Validation, Supervision, Investigation, Funding acquisition, Data curation, Conceptualization. **Francesco Canonaco:** Writing – review & editing, Software, Methodology, Investigation. **Jay G. Slowik:**

Resources, Methodology, Investigation. **Caroline Marchand:** Supervision, Project administration, Funding acquisition. **Valérie Gros:** Writing – review & editing, Supervision, Project administration, Funding acquisition, Conceptualization.

### Fundings

This work has benefited from the support of the research infrastructure ACTRIS-FR registered on the Roadmap of the French Ministry of Research. This research has been supported by the H2020 ACTRIS-2 project (grant no. 654109) and the following related projects.

### Declaration of competing interest

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

### Acknowledgements

The authors would like to thank François Truong and Roland Sarda-Estève for the obtention of the PTR-MS dataset. We would also like to thank Anna Tobler for her help on using SoFi.

## Appendix A. Supplementary data

Supplementary data to this article can be found online at https://doi.org/10.1016/j.atmosenv.2025.121269.

### Data availability

Data will be made available on request.

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