Hygroscopic properties and mixing state of aerosol measured at the high-altitude site Puy de Dôme (1465 m a.s.l.), France

A Hygroscopicity Tandem Differential Mobility Analyser (HTDMA) was used to evaluate the hygroscopic properties of aerosol particles measured at the Puy de Dome research station in central France, periodically from Septem-ber 2008 to January 2010, and almost continuously from Oc-tober 2010 to December 2012. This high-altitude site is ideally situated to allow for both the upper part of the planetary boundary layer and the lower free troposphere to be sampled. The aim of the study is to investigate both the influence of year-to-year, seasonal and diurnal cycles, as well as the influence of air mass type on particle hygroscopicity and mixing state. Results show that particle hygroscopicity increases with particle size and depends both on air mass type and on season. Average growth factor values, GFs, are lowest in winter (1.21 ± 0.13, 1.23 ± 0.18 and 1.38 ± 0.25 for 25, 50 and 165 nm particles, respectively) and highest in autumn (1.27 ± 0.11, 1.32 ± 0.12 and 1.49 ± 0.15 for 25, 50 and 165 nm particles, respectively). Particles are generally more hygroscopic at night than during the day. The seasonal and diurnal variations are likely to be strongly influenced by boundary layer dynamics. Furthermore, particles originating from oceanic and continental regions tend to be more hygro-scopic than those measured in African and local air masses. The high hygroscopicity of oceanic aerosol can be explained by large proportions of inorganic aerosol and sea salts. Aerosols measured at the Puy de Dome display a high degree of external mixing, and hygroscopic growth spectra can be divided into three different hygroscopic modes: a less-hygroscopic mode (GF 1.7). The majority of particles measured can be classified as being in either the less-hygroscopic mode or the hygroscopic mode, and only few of them have more-hygroscopic properties. The degree of external mixing, evaluated as the fraction of time when the aerosol is found with two or more aerosol populations with different hygroscopic properties, increases with particle size (average yearly values are 20, 28 and 45 % for 25, 50, and 165 nm particles, respectively). The degree of external mixing is more sensitive to season than to air mass type, and it is higher in the cold seasons than in the warm seasons. With more than two years of nearly continuous measurements , this study gathers the results from one of the longest data sets of hygroscopic growth factor measurements to date, allowing a statistically relevant hygroscopic growth parame-terization to be determined as a function of both air mass type and season.


Introduction
Atmospheric aerosol particles affect the Earth's climate in various ways. As a direct effect, they scatter and absorb solar radiation. In addition, some aerosols can be activated to form cloud droplets, and will thereby indirectly impact the radiation budget of the planet. The impacts of aerosol particles on the climate are subject to many uncertainties, which are linked to their physical and chemical properties (IPCC,

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2013). Both the direct and indirect effect on radiation is influenced by aerosol particle hygroscopicity, meaning that hygroscopicity is a key parameter to better understand and estimate aerosol radiative impacts and aerosol-cloud interactions. Chemical compounds may be present in aerosol particles as internal mixtures (all particles of a given size have the same chemical composition), or external mixtures (particles of a given size are divided into several sub-populations of different chemical composition). The mixing state of the aerosol particles may have an impact on the way they interact with water vapour (i.e. on their indirect effect), and on the way they interact with solar radiation (i.e. on their direct effect).
Hygroscopic properties and mixing state of atmospheric aerosol particles can be studied in detail using a Hygroscopicity Tandem Differential Mobility Analyser (HTDMA). This instrument selects a narrow range of particle diameters (D 0 ) from a polydisperse aerosol, and exposes the selected particles to a well-defined elevated relative humidity, which is normally 90 % (RH90). Due to water uptake, the diameter of the selected particles will increase (D), and a hygroscopic growth factor (GF) can be calculated. The mixing state of aerosol particles can be evaluated from hygroscopicity measurements, when a population of particles selected at a given diameter falls into different hygroscopic modes, pointing to the presence of different aerosol populations for this size.
An overview of HTDMA data on atmospheric aerosol reported up to September 2007 has been summarized in a review article by Swietlicki et al. (2008). Historically, most data have been obtained during intensive field campaigns, covering only a few weeks to some months of measurements. Marine, rural and urban environments have been studied rather extensively over the last 20 years (see e.g. Swietlicki et al. (2008) and references therein), while measurements at high-altitude sites, i.e. away from local sources and periodically in the free troposphere (FT), are more rare. Measurements at high-altitude sites are important when considering the climatic effect of tropospheric clouds, which are largely formed on FT aerosol. For the formation of convective clouds (e.g. cumulus), boundary layer (BL) aerosols also play an important role. Up until now, HTDMA measurements at high-altitude sites have been studied at the research station Jungfraujoch in the Swiss Alps (3580 m a.s.l.) Sjögren et al., 2008;Kammermann et al., 2010), the Izaña baseline observatory station on the island of Tenerife in the northeastern Atlantic (2367 m a.s.l.) (Swietlicki et al., 2000) and the Monte Cimone observatory in northern Italy (2165 m a.s.l.) (Van Dingenen et al., 2005).
The Puy de Dôme research station (pdD) in central France is ideally situated for measurements of various types of air masses. Located at 1465 m a.s.l. it lies in a region which allows for both the upper part of the planetary boundary layer (PBL) and the lower part of the FT to be sampled, depending on meteorological conditions. In this study, the aim is to investigate aerosol hygroscopic properties and aerosol parti-cle mixing state, away from direct sources at a background site. The work presented covers data collected in periods from September 2008 to January 2010, and almost continuously from October 2010 to December 2012. This is, to the authors' knowledge, the first study that investigates hygroscopic properties of particles measured at a high-altitude site almost continuously over more than two years. This allows for detailed analysis of the influence of year-to-year and seasonal cycles, diurnal patterns and air mass types on particle hygroscopicity.

Measurement site
The Puy de Dôme research station (pdD) is located at the top of Puy de Dôme, 1465 m a.s.l. in central France (45 • 46 N, 2 • 57 E), 16 km west of the city of Clermont-Ferrand (396 m a.s.l., about 140 000 inhabitants). The site has been defined as a rural background site (Putaud et al., 2004) and as a high-altitude site (Asmi et al., 2011). According to Henne et al. (2010), the site is representative of western European air masses over a large scale. The station surrounding area is mainly dominated by fields and forests. Meteorological parameters such as wind speed and direction, temperature, relative humidity, radiation (global, UV and diffuse), atmospheric trace gases (O 3 , NO x , SO 2 , CO 2 ), particulate black carbon (BC) and aerosol particle number concentration are monitored continuously. The site is often used for investigations of cloud microphysical properties, cloud chemistry and aerosol-cloud interactions (Wobrock et al., 2001;Sellegri et al., 2003;Marinoni et al., 2004;Asmi et al., 2012), due to frequent formation of clouds (> 50 % of the time from November to March). Boundary layer heights (BLHs) over several seasons have been calculated from model outputs (Venzac et al., 2009) or retrieved from remote sensing measurements . BLH retrievals were cross-checked using meteorological parameters  and in situ aerosol measurements (Venzac et al., 2009). Both studies indicate that in winter, spring, and at night during summer, the site is more often influenced by FT or residual layer (RL) air masses, compared to the summer season (Venzac et al., 2009;Boulon et al., 2011).

Instrumentation
The Hygroscopicity Tandem Differential Mobility Analyser (HTDMA) system used in this study is designed and built at the Laboratoire de Météorologie Physique (LaMP). The instrument includes silica gel dryers, two Differential Mobility Analysers (DMAs), a humidifying section, and a Condensation Particle Counter (CPC). First, a polydisperse aerosol is sampled at a flow rate of about 0.6 L min −1 . This aerosol is dried to less than 30 % RH, using silica gel diffusion driers. The first DMA (DMA1) alternatively selects six different dry Selected particles are subsequently exposed to 90 % RH, using a humidification system. The humidification system consists of a Nafion membrane exposed to humid air generated by bubbling the air through distilled water (18 Ohm). RH is measured and controlled by a dew point mirror placed on the second DMA (DMA2) sheath loop. The particle diameter increases as a result of water uptake, and the resulting particle size (D) is measured with DMA2, while the particle concentration is measured by the CPC. The ratio of D to D 0 is defined as the hygroscopic growth factor (GF). The particle concentration measured by the CPC as a function of GF is referred to as the measurement distribution function (MDF). An MDF covering the whole GF range can be obtained by changing the diameter selected by DMA2 gradually or in discrete steps, while keeping DMA1 at a constant dry size. The first and the second DMA are operated using a closed-loop/vacuum pump set-up. A critical orifice and mass flow controllers are used to control the sheath aerosol flow rate at 3 L min −1 . The system is confined and cooled by Peltier systems ( T close to ±5 • C). The accuracy of the RH sensors of the HTDMA at the pdD is regularly checked using pure ammonium sulfate, which has a well-known GF value at 90 % RH. Intercomparisons performed during a EUSAAR workshop (Duplissy et al., 2009) showed that the average variability of measurements compared with other HTDMA instruments is less than 1 %. The humidification system presented a stability of ±3 % RH in normal conditions.

Data inversion and fitting procedure
In this work, growth factor probability density functions (GF-PDFs) are obtained from the measured GFs following the procedures given by Gysel et al. (2009). The method uses a full TDMA transfer forward function in combination with a χ 2 minimization algorithm, which has been tested on HTDMA data (Gysel et al., 2007;Allan et al., 2008). A piecewise linear inversion approach was used, with the centre of the first and the last inversion bins set to GF = 0.7 and GF = 2.5, respectively. The resolution chosen was GF = 0.15. All GF-PDFs measured in the range 87 % < RH < 93 % were recalculated to RH = 90 % according to Eqs. (3) and (6) in Gysel et al. (2009). Data acquired at lower or higher RH were ignored and scans that show particle counts less than 1 cm −3 are not included in the analysis.
The HTDMA at the pdD is calibrated using ammonium sulfate, which has well-documented hygroscopic parameters. With a resolution GF = 0.15 chosen for the fit, the spread in data obtained by ammonium sulfate is σ < 0.05. According to Sjögren et al. (2008), GF-PDFs showing σ ≤ 0.10 indicate an internal mixture, or a quasi-internal mixture with limited spread of growth modes. In contrast, GF-PDFs with σ ≥ 0.15 are considered externally mixed, or quasi-internally mixed with substantial spread of growth factors. These mixing state criteria were followed to evaluate data also in this work.
Hygroscopic growth factor distributions are quite complex at the pdD, often with two and sometimes three hygroscopic modes observed simultaneously. This indicates a high degree of external mixing and the influence of multiple sources of particles at the site. When the distribution is multi-modal, the average GF provided by the TDMAinv program is not sufficient to fully describe the different hygroscopic modes of individual GF-PDFs. All data are therefore further interpreted using a Matlab program developed at LaMP. By describing the obtained GF-PDF as a superposition of multiple Gaussians, the growth factor GF, spread σ and number fraction NF of particles in each hygroscopic mode can be identified for every scan individually. This means that when the GF spread in the DMA transfer is higher than expected (σ > 0.10), two different hygroscopic modes are searched to explain this spread. The aspect of this type of analysis, with a strict mode-fitting procedure for each individual GF-PDF, enables a more accurate idea of the aerosol mixing state. Figure 1 is an example of a bimodal growth factor distribution obtained from the TDMAinv program, where the software provides an average GF of 1.38 and a spread σ of 0.18. The different modes are identified using the Matlab program and a fit of multiple Gaussians on a single GF spectrum analysis. In this example, a first GF mode is identified at GF 1.00 and σ 0.07 and a second at GF 1.37 and σ 0.09.
Further, hygroscopic kappa values κ, as introduced by Petters and , are calculated according to where a w is the water activity at which the GF was measured. According to Köhler theory (Köhler, 1936), a w is obtained by where σ s is the surface tension of the solution droplet (here assumed to be pure water), v w is the partial molar volume of water in solution, R is the universal gas constant, T is the temperature, and D is the diameter of the droplet. Given the nature of Eq. (1), negative kappa values are nonsensical, but are in fact present in Fig. 1 due to uncertainties associated with the DMA transfer functions.

Air mass back trajectory calculations
Back trajectories for air masses arriving at the pdD were calculated using HYSPLIT (HYbrid Single-Particle Lagrangian Integrated Trajectory) (Draxler and Hess, 1998). Trajectories were calculated for the arrival pressure 850 hPa at the height of the pdD every 6 h, going back 72 h in time, and were classified as continental, African, oceanic or oceanic modified as  Asmi et al., 2012). The classification "oceanic modified" refers to air masses originating from the ocean, which have travelled over the continent and are thus influenced by continental sources. In addition, air masses predominantly circulating above continental France were classified as local.

Results and discussion
In the first stage of data analysis, the general behaviour of the hygroscopic properties of particles is studied as a function of all sampled particle sizes (25, 35, 50, 75, 110 and 165 nm). Then, focus is put on the analysis of the hygroscopic growth and mixing state of particles with dry sizes 25, 50 and 165 nm. These sizes of aerosol particles are representative of the nucleation mode (25 nm), the Aitken mode (50 nm) and the accumulation mode (165 nm) at the pdD (Venzac et al., 2009). Table S1 in the Supplement gives the total number of successful scans for each particle size, split by calendar month. Based on literature, BC and mineral dust can be considered almost hydrophobic with a GF less than 1.05 (Weingartner et al., 1997;Vlasenko et al., 2005), while biomass burning aerosols can have a wide range of GFs increasing up to 1.65 (Cocker et al., 2001;Pagels et al., 2003). These very high values were measured after the biomass burning particles have had some time to mix with secondary inorganic ions, and much lower GFs were measured closer to the source. The main inorganic ions (NO − 3 , SO 2− 4 and NH + 4 ) can be associated with ammonium sulfate or ammonium nitrate, which have GFs around 1.7 Prenni et al., 2003;Wise et al., 2003). GFs of secondary organic aerosol (SOA) range between 1.07 and 1.14 (Virkkula et al., 1999;Saathoff et al., 2003;Baltensperger et al., 2005) and up to more than 1.65 for aged SOA in simulation chamber studies (Duplissy et al., 2011). The GFs of organic compounds may vary between about 1.0 and 1.7 (Peng et al., 2001;Wise et al., 2003;Chan and Chan, 2003;Prenni et al., 2003Prenni et al., , 2007Koehler et al., 2006;Huff Hartz et al., 2006). SOA formed from the terpenes α-pinene and β-pinene have been reported to have GFs between about 1.03 and 1.18 (Saathoff et al., 2003;Varutbangkul et al., 2006;Prenni et al., 2007). Finally, particles composed of sea salt or sulfuric acid are very hygroscopic with GFs higher than 2.0 Koehler et al., 2006).

Year-to-year and seasonal variability
In order to provide an overview of particle hygroscopicity, average GF-PDFs were calculated for each continuous measurement year (2011 and 2012). As observed in several studies (see e.g. Swietlicki et al. (2008) and references therein), there is a distinct increase in hygroscopicity with increasing particle diameter (Fig. 2a). Nucleation mode particles have average GF values of around 1.1-1.2, while particles in the Aitken mode cover a larger range of GFs and show more variability than those in the nucleation mode. In 2011, the GF peaks at around 1.1, and in 2012 it has increased to about 1.2. Finally, accumulation mode particles cover GFs from less than 1.0 to over 2.2 and show more variability between 2011 and 2012. In the accumulation mode, the GF-PDF is often bimodal with a first mode located close to 1.0 and a second mode between 1.4 and 1.6.
The size-dependent hygroscopicity solely due to the aerosol composition can be addressed by plotting κ-PDFs as a function of particle diameter, calculated for 25, 35, 50, 75, 110 and 165 nm (  distribution concept as described by Su et al. (2010). Both in 2011 and 2012, the aerosol hygroscopicity is increasing with increasing particle size independently of the Kelvin effect from 50 nm to larger sizes. There is also a tendency of the nucleation mode particles to be slightly more hygroscopic than the Aitken mode particles. Years 2011 and 2012 are on average very similar, with more dispersion in the hygroscopicity of the accumulation mode particles during 2012. Seasonal variations in particle hygroscopicity were assessed using data from 2008, 2009, 2010, 2011 and 2012. In 2008, data were only collected in September, while 2009 includes wintertime and springtime measurements. In 2010, winter and autumn are represented, but neither spring nor summer. In 2011 and 2012, measurements took place over all seasons. Winter at the pdD stretches from December to February, spring from March to May, summer from June to August and autumn from September to November.
Monthly median hygroscopic GFs and κ values were calculated from the GF-PDFs and are displayed in Fig. 3, while Table 1 gives seasonal averages. Fig. 3 shows that aerosol hygroscopicity is lower in winter than during summer. It is also observed, from the large error bars, that the variability is higher in winter than in summer. Particles in the nucleation mode do not show any strong seasonal variability, as the average GF is roughly constant throughout the year. Aitken and accumulation mode particles are generally most hygroscopic in autumn and least hygroscopic in winter. Weingartner et al. (2002), Sjögren et al. (2008) and Kammermann et al. (2010) studied hygroscopic properties at the FT site Jungfraujoch (JFJ) in the Swiss Alps (3580 m a.s.l.). In the first two studies GFs were measured at 85 % RH, but could be extrapolated to 90 % RH. In winter, when the JFJ  (Swietlicki et al., 2000), which have large contributions of anthropogenic emissions, were reported to be bimodal, and no average GFs were presented. GFs reported from JFJ are compared to those measured in this study in Table 2. The yearly averages measured by Kammermann et al. (2010) are close to those observed at the pdD. This is also the case for the summertime values given by Sjögren et al. (2008) and Kammermann et al. (2010). However, wintertime GFs measured by Weingartner et al. (2002) and Sjögren et al. (2008) are much higher than those observed in this work, while those given by Kammermann et al. (2010) are more similar. Overall, GFs measured at JFJ are generally higher than those measured at the pdD. A likely explanation to this could be that the JFJ site is located at a higher altitude than the pdD station, and is thus less influenced by the advection of pollution aerosols from the PBL. Indeed, opposite to observations at the pdD, Kammermann et al. (2010) found that PBL influence has no effect on the annual mean hygroscopicity of the aerosol measured at JFJ, although GFs are significantly lowered during the short periods with PBL influence.

Atmos
GF-PDFs measured at the pdD were averaged over each season in Figure 4a. For particles in the nucleation mode, the shape of the GF-PDF is similar for all seasons, peaking between 1.1 and 1.2. Aitken mode particles are characterized by a wide range of GFs, especially in the cold seasons. The distribution function peaks at a lower GF in winter and in summer (GF peaks at about 1.1) than during other seasons (GF peak 1.1-1.3). For accumulation mode particles, the shape of the GF-PDF strongly depends on the season. In winter and in autumn two modes are clearly visible, with a first mode located between 1.0 and 1.1 and a second mode around 1.5-1.6. The occurrence of this nearly hydrophobic mode in winter lowers the average GF as reported in Table 1. The very low GF values observed here point to either BCrich biomass burning aerosol or BC-rich particles associated with other combustion sources, such as fossil fuel combustion aerosol, which have had little time to mix with secondary inorganic ions.
Again, the hygroscopic properties of aerosol solely due to their chemical composition can be investigated using the κ-PDF as a function of particle size. Figure 4b indicates that the higher hygroscopicity of nucleation mode particles relative to the Aitken mode particles observed on the yearly average is mainly seen in autumn and winter. Otherwise the particle hygroscopicity, as well as the external mixing degree, is increasing with particle size for all seasons. The appearance of a more-hygroscopic and a less-hygroscopic mode at larger particle sizes is mainly observed during autumn and winter.
The observation of several hygroscopic modes in the GF-PDFs measured at the pdD indicates a high degree of external mixing that needs to be characterized. Each of the individually retrieved GF-PDFs was examined in more detail using the Gaussian fitting procedure described in Sect. 2.3.1. Briefly, when the spread in a single GF-PDF was σ > 0.10,  two different hygroscopic modes were searched to explain this spread. This procedure allowed identification of several hygroscopic modes with a specific median growth factor GF, GF spread σ and number fraction NF found in each mode. The calculated median GF of each mode was then attributed to one of three hygroscopic classes. Mode 1 represents lesshygroscopic material with GFs lower than 1.3, i.e. BC and organic material. Mode 2 corresponds to hygroscopic particles with GFs between about 1.3 and 1.7, e.g. ammonium sulfate and mixtures of ammonium sulfate and organic material. Mode 3 is the more-hygroscopic mode, with GFs higher than 1.7. These are particles most likely composed of sea salt and modified sea salt. Modified sea salt refers to sea salt that has been modified by other species in the air, for example condensation of secondary continental species. It should also be mentioned that particles with relatively high GF values may still contain BC if the inorganic ion volume fraction is very high; it is not possible to assess whether a small BC core is present using this method. Table 3 gives the average GF of each hygroscopic mode and the frequency of occurrence (FO) of that mode, i.e. the fraction of scans in which you find particles in mode 1, mode 2 or mode 3, respectively. The data show that the less-hygroscopic mode (mode 1) is most important for nucleation and Aitken mode particles, occurring in 86 and 84 % of all scans, respectively. For accumulation mode particles, the hygroscopic mode (mode 2) is strongest, with a FO of 79 %. The average GFs of each hygroscopic mode (GF1, GF2, GF3) are roughly the same for all particle sizes; only the FO changes. Table 4 shows the frequency of external mixing split by season, i.e. the percentage of scans that display two or more modes. At the pdD, the aerosol is found as an external mixture from 16 to 67 % of the time, depending on both particle size and season. It is clear that the degree of external mixing increases with particle size, and that it is higher in the cold seasons than in the warm seasons. During winter, the boundary layer height is more frequently at the height of Puy de Dôme, so that aerosol measurements are made at the interface between the PBL and the FT. Therefore, during the winter months, the change in aerosol sources results in a large variation in GF values. Sjögren et al. (2008) used the GF spread (σ ) for individual scans to conclude that wintertime aerosol measured at JFJ is predominantly internally mixed. Nonetheless, the authors did find a small GF mode at about 1.0-1.2, in addition to the main mode. The mode was less pronounced for 50 nm particles than for 100 nm particles, which is coherent with the trend of the degree of mixing with particle size seen at the pdD. Similar to the pdD, the JFJ summertime aerosol showed a more homogeneous distribution. Kammermann et al. (2010) also found that 50 nm particles were characterized by a broad peak including the full range of particle compositions. Particles larger than 75 nm were more clearly bimodal, again in agreement with the pdD trend showing a higher degree of mixing with larger particle size.
Monthly average GFs and NFs of particles in each hygroscopic mode, measured at the pdD, are displayed in Fig. 5. Overall, less-hygroscopic particles are dominating in wintertime, but their relative number fraction (NF1) decreases as spring arrives and the number fraction of hygroscopic particles (NF2) increases. The nucleation mode is dominated by less-hygroscopic particles throughout the whole year (NF1: 57-88 %), although the hygroscopic mode contributes significantly (NF2: 11-43 %). More-hygroscopic particles are Atmos. Chem. Phys., 14, 9537-9554, 2014 www.atmos-chem-phys.net/14/9537/2014/ present only at very low number fractions (NF3: < 1 %). The Aitken mode mostly contains less-hygroscopic and hygroscopic particles. Hygroscopicity is lowest in winter (NF1: 61-79 %, NF2: 20-34 %, NF3: < 5 %) and highest from late spring to early autumn (NF1: 39-56 % NF2: 21-59 %, NF3: < 2 %). The accumulation mode is most sensitive to seasonal variations. The less-hygroscopic mode is dominant only during winter months (NF1: 43-63 %, NF2: 28-47 %, NF3: 3-24 %). As spring arrives, this fraction decreases (NF1: < 38 %) and the hygroscopic fraction increases (NF2: 51-83 %). In autumn, the less-hygroscopic fraction slowly begins to increase again. The more-hygroscopic mode only contributes low number fractions throughout the year (NF3: 5-10 %), with a maximum fraction present during winter. This observation is in agreement with a more efficient longrange transport of sea salt particles to the site in winter . Figure 5 also shows that for nucleation and Aitken mode particles the average GF in the less-hygroscopic mode (GF1) increases in the warm season, while the GF of hygroscopic mode (GF2) and the morehygroscopic mode (GF3) remains more or less the same. In the accumulation mode, GF1, GF2 and GF3 show no significant variation throughout the year. Freney et al. (2011) suggest that low-volatility oxygenated organic aerosol particles (LV-OOA) measured at the pdD in winter are related to aged biomass burning emissions, whereas organic aerosol particles measured in summer are linked to biogenic sources. The hygroscopicity of particles originating from biomass burning can vary significantly (Pagels et al., 2003), but they are globally less hygroscopic than organic particles originating from biogenic sources. This change of organic sources from winter to summer would explain the increase in GF1 from winter to summer in the nucleation and Aitken modes. Bourcier et al. (2012) and Freney et al. (2011) found that the fraction of BC measured at the pdD is low (< 5 %), while the organic fraction, which could also contribute to the number fraction of less hygroscopic particles, varies between 23 % (Freney et al., 2011) and 48 %  in winter. In summer, the organic fraction contributes to at least 55 % (both studies) of the total mass concentration. Thus, it seems like the organic fraction is only variable in wintertime, leading to variable values of hygroscopicity. In winter, the PBL height is close to the pdD height during daytime, meaning that the pdD site can be either in the PBL or in the FT. Furthermore, higher fractions of biomass burning aerosol have been identified at the site during winter (Crippa et al., 2014). Asmi et al. (2012) characterized Cloud Condensation Nuclei (CCN) properties at the pdD and report that aerosol properties, and likely also their sources, are different between summer and winter. During summer, the authors measured less-aged organics, possibly from biogenic sources. Wintertime organics had a higher organic aerosol m/z ratio to total organics (f 44 ), suggesting more-aged organics.
The seasonal variations of the contribution of different hygroscopic fractions are likely linked to both the seasonal variation of the vertical transport of air masses from the PBL to the pdD site and to seasonal changes in aerosol composition. This vertical transport may also be discussed in the light of the diurnal variations of the hygroscopic fractions in the aerosol.

Diurnal variability
Particles measured at the pdD show a clear diurnal variation, with a higher GF measured at night-time than during the day, as illustrated in Fig. 6. For all particle sizes, the median GF is highest in late night/early morning, and lowest around midday. This diurnal variation is due to the less-hygroscopic fraction that increases during the day, while the hygroscopic fraction decreases. It is likely the result of the site being in the RL or FT at night, hence being exposed to long-range transport and aged aerosol particles. During the day, there are more air masses arriving from the PBL with a larger contribution from anthropogenic emissions that are less hygroscopic. It is also possible that the partitioning of ammonium nitrate and/or other nitrates at lower temperatures contributes to the higher GF values at night. The diurnal variation is most pronounced for nucleation mode particles. Nucleation and Aitken mode particles may originate from anthropogenic emissions transported from the PBL or from new particle formation and growth occurring at the site. New particle formation (NPF) events are frequently observed at the pdD during the day (Venzac et al., 2007;Boulon et al., 2011;Rose et al., 2013). Boulon et al. (2011) and Rose et al. (2013) suggest that the nucleated particles grow from condensation of organic compounds, which are likely less hygroscopic. Thus, NPF events will lead to an increase in the less-hygroscopic fraction, which could explain the observed diurnal variations at the site.
Hygroscopicity data are further segregated into night (00:00-06:00 UTC) and day (09:00-15:00 UTC), and are split into seasonal averages in Fig. 7. The diurnal changes are observable over all seasons and all particle sizes. In winter, the daytime increase in the number fraction of lesshygroscopic particles (NF1) is smaller than during the other seasons. This is consistent with observations by Rose et al. (2013), who report that NPF events are less frequent in winter (NPF event frequency 17 %) than in spring, summer and autumn (NPF event frequency 26, 27 and 24 %, respectively).

Influence of air mass origin
Air masses were sorted according to their origin in order to investigate the influence of long-range transport on the aerosol hygroscopic behaviour measured at the top of the pdD. Back trajectories were calculated from the HYSPLIT model (Draxler and Hess, 1998) every 6 h, going back 72 h in time, and were classified as either continental, African, oceanic, oceanic modified or local according to the boundaries defined in Fig. 8. The colour coding represents the number of back trajectories arriving at the pdD with a 1 • × 1 • resolution over the measurement period September 2008-December 2012. The origin of a back trajectory is defined as a function of the number of hours spent over each sector by an air mass. Hygroscopicity data treated in this work arrived Atmos. Chem. Phys., 14, 9537-9554, 2014 www.atmos-chem-phys.net/14/9537/2014/ from air masses that were 36 % oceanic, 29 % African, 19 % continental, 10 % oceanic modified and 6 % local. Figure 9 shows that there is a seasonal variation in the frequency of continental air masses. For example, the contribution of continental air is substantial throughout most of the year, but in July and August those air masses are rarely present. Local air masses are most frequent from late spring to early autumn. This is in agreement with the observation of a higher PBL in the warm seasons, in which the winds are weaker. Table 5 shows the frequency of external mixing split by air mass origin, i.e. the percentage of scans that display two or more modes simultaneously. Particles in the nucleation and Aitken mode have the highest degree of external mixing for oceanic and oceanic modified air masses (21-39 %) and the lowest for local air masses (14-20 %). Accumulation mode particles show different behaviour, with the degree of external mixing being highest for continental air masses (54 %) and lowest for oceanic and oceanic modified air masses (40-  42 %). The degree of external mixing is less sensitive to air mass type than to season. For example, the frequency of external mixing in the accumulation mode varies from 31 % in summer to 67 % during winter, while it only varies from 40 % in oceanic air masses to 54 % in continental air masses.   , 2005). Accumulation mode particles in African air display a high degree of external mixing also in this study, although dust events have not been individually identified.
Median GFs and average NFs measured at the pdD are displayed as a function of air mass origin in Fig. 10. Taken as an average over the whole measurement period, the hygroscopic variability as a function of air mass trajectory is not obvious. Nucleation and Aitken mode particles originating from the oceanic and continental regions tend to contain slightly higher fractions of the hygroscopic mode than those measured in African and local air. In the accumulation mode, oceanic and oceanic modified air contains much larger fractions of more-hygroscopic particles than the other air masses.
When oceanic modified air masses are measured at the pdD they contain marine air internally mixed with aged anthropogenic and less-hygroscopic particles, thus resulting in a more-hygroscopic mode with an average GF less than that of sea salt (GF3 ∼ 1.80). A GF of 1.8 can represent aged sea salt particles, either by displacement of sea salt chloride by nitric acid, or by mixing of NaCl with less-hygroscopic particles such as ammonium sulfate or ammonium nitrate (Gard et al., 1997). According to Bourcier et al. (2012), modified oceanic air measured at the pdD contains one of the largest fractions of inorganic anthropogenic compounds and sea salt aerosol to total mass. Sellegri et al. (2001) and Piazzola et al. (2012) also show that sea salt is aged principally Atmos. Chem. Phys., 14, 9537-9554, 2014 www.atmos-chem-phys.net/14/9537/2014/ with NO − 3 rather than with organics. This would explain the high hygroscopicity of particles in modified oceanic air compared to those in other air masses. In fact, aerosols in oceanic modified air masses are generally more hygroscopic than in oceanic air masses. At first glance this is surprising since sea salt is the most hygroscopic of all salts, but the observation confirms that oceanic air masses at the pdD contain a high fraction of organic particles, as reported by , Bourcier et al. (2012), Freney et al. (2011 and Asmi et al. (2012). Since the hygroscopic properties of organic material can be highly variable, they can partly explain the variation in GF and κ observed in oceanic air masses in wintertime. Further, Asmi et al. (2012) observed, by CCN measurements, that oceanic particles measured at the pdD are less hygroscopic in oceanic air masses than in oceanic modified air masses, due to very high organic fractions (up to 60 %) measured in oceanic air. In contrast, continental European air masses contained less organics in winter, which Asmi et al. (2012) explained by suppression of biogenic activities.
Local air masses tend to be dominated by a less-hygroscopic mode, and a hygroscopic mode (NF1 + NF2 > 85 %). Here, the less hygroscopic aerosol particles are likely originating from fresh anthropogenic emissions (BC and primary organics), and the hygroscopic mode corresponds to aged anthropogenic particles (secondary organic and inorganic compounds). Continental particles should show the same hygroscopic properties as the local ones in the accumulation mode (most representative of long-range transport), but they are more hygroscopic than the local ones for the nucleation and Aitken modes, presumably due to ageing of the fresh combustion particles. Particles in African air have hygroscopic properties somewhere between local and continental air.
In order to investigate whether the seasonal variation previously observed is due to the variability of air mass origin, data are further divided into seasons in Fig. 11. As described in Sect. 3.1, nucleation mode particles do not show any apparent seasonal general trend (without air mass splitting). This could be because the individual seasonal trends are opposite for continental and local air, compared to oceanic modified air. The continental and local aerosol is more hygroscopic in the colder season, as the hygroscopic particle fraction (NF2) increases at the expense of less-hygroscopic particles (NF1). The opposite trend is seen in oceanic modified air masses, in which particles are less hygroscopic in autumn and in winter. The other air masses do no not show a marked seasonal cycle. A similar behaviour can be seen in the Aitken mode, with the exception that the wintertime aerosol is less hygroscopic also for oceanic and African air masses. The hygroscopic behaviour of accumulation mode particles is more difficult to describe. Continental accumulation mode particles display the same seasonal trend as smaller particles (nucleation and Aitken), with higher hygroscopicity in the cold season. For all other air masses, particles are least hygro-scopic in winter, as observed for the general trend (without air mass splitting). Oceanic and oceanic modified particles are most hygroscopic in spring, while the GFs of African and local particles peak in autumn. Venzac et al. (2009) found that the seasonal variability in aerosol sources at the pdD was predominant over the continent compared to marine aerosol sources. Freney et al. (2011) andBourcier et al. (2012) suggest that the atmospheric particle composition at the site is strongly influenced by both season and air mass origin. For example, Freney et al. (2011) found that the highest nitrate and ammonium mass concentrations at the pdD were measured during winter/spring, in periods when oceanic and oceanic modified air masses dominated. This would explain the high GFs seen in accumulation mode particles in those air masses, as the accumulation mode is most representative of chemical analysis.

Hygroscopic growth factor parameterization
Parameterizations giving the GF as a function of RH can be found in different forms (e.g. Zhou et al., 2001;Rissler et al., 2006). In this paper a parameterization is derived from GF measurements conducted at the Puy de Dôme at RH = 90 %. This parameterization is similar to the one of Zhou et al. (2001), which was previously used in several papers (Laakso et al., 2004;Hõrrak et al., 2008) and is available for RH up to 90 % and for particles in the size range 10 to 420 nm. In particular, this kind of parameterization was previously shown to retrieve very satisfying GF estimations for RH in the range 60-90 % and for particles smaller than 300 nm at the Puy de Dôme (Rose et al., 2013). For lower RH or larger particles, the model is likely to slightly overestimate the GF. The parameterization is a continuous one-parameter function GF = 1 − RH 100 γ , where γ is a dimensionless parameter which can be parameterized as a function of particle dry size, d p : γ = −a × d p 1 nm − b. Parameters a and b for all seasons and air mass origins are given in Table 6.
Also found in Table 6 are the kappa values, κ, for each particle size and for all seasons and air mass origins. These values have been calculated following Petters and Kreidenweis (2007). The parameterization and the kappa values are issued from a long-term data set, and are therefore considered reliable for future use in studies in which the hygroscopic properties should be taken into account, such as for calculations of condensational sink or for calculations of size distributions at ambient humidities, useful for calculations of optical properties. The parameterizations and kappa values are representative of western European aerosol in remote sites (Henne et al., 2010).

Conclusions
HTDMA data of aerosol particles measured at the Puy de Dôme research station (France, 45 • 46 N, 2 • 57 E, Figure 11. Variations in hygroscopic growth factor (GF), kappa value (κ) and number fractions (NF) measured at RH90 as a function of air mass origin and season for particles in the nucleation mode (left panels), Aitken mode (middle panels) and accumulation mode (right panels). The figures show the median GF value, with the bottom and top sides of the box giving the 25th and 75th percentiles, and the extremities the 10th and 90th percentiles. The coloured bars illustrate the NF of particles found in each hygroscopic mode. 1465 m a.s.l.) were evaluated over the time period September 2008 to December 2012. The aim was to investigate the influence of year-to-year and seasonal variability, diurnal cycles, and air mass types on particle hygroscopicity and to use these data to develop a parameterization that can be applied to take into account the water uptake of particles in the calculation of the condensational sink or optical properties of aerosols at Puy de Dôme in particular, and in western continental Europe in general.
Results show that particle hygroscopicity increases with particle size and depends both on air mass type and on season. Average GF values are lowest in winter (1.21 ± 0.13, 1.23 ± 0.18 and 1.38 ± 0.25 for 25, 50 and 165 nm particles, respectively) and highest in autumn (1.27 ± 0.11, 1.32 ± 0.12 and 1.49 ± 0.15 for 25, 50 and 165 nm particles, respectively). Moreover, particles are generally more hygroscopic at night-time than during the day. The seasonal and diurnal variations are likely linked to the seasonal and diurnal variation of the vertical transport of the PBL layer to the site. The hygroscopic variability as a function of air mass origin is not obvious, although particles originating from the oceanic, modified oceanic and continental sectors tend to be more hygroscopic than those measured in African and local air. The high hygroscopicity of oceanic and modified oceanic aerosol can be explained by larger proportions of inorganic aerosol and sea salts.
The GF-PDFs of particles measured at the pdD often display two and sometimes three modes simultaneously, indicating a high degree of external mixing at the site. Growth spectra are therefore divided into three different hygroscopic modes, two of which are found in the majority. Depending on particle size, a less-hygroscopic mode (GF < 1.3) or a hygroscopic mode (GF 1.3-1.7) dominates the aerosol, while a more-hygroscopic mode (GF > 1.7) is normally only present Atmos. Chem. Phys., 14, 9537-9554, 2014 www.atmos-chem-phys.net/14/9537/2014/ Table 6. Parameterization giving the growth factor (GF) as a function of relative humidity (RH), and the kappa value κ for each particle size, including standard deviations.

GF derived κ Season
Air mass origin a × 10 −4 b × 10 −2 25 nm 50 nm 165 nm All All 5.08 7.63 0.16 ± 0.08 0.16 ± 0.10 0.28 ± 0.14 Winter All 4.09 7.13 0.14 ± 0.10 0.14 ± 0.13 0.29 ± 0.14 Spring All 5.48 7.23 0.15 ± 0.09 0.16 ± 0.09 0.30 ± 0.11 Summer All 5.09 7.50 0.15 ± 0.09 0.15 ± 0.07 0.29 ± 0.17 Autumn All 4.95 9.28 0.20 ± 0.10 0.19 ± 0.09 0.23 ± 0.15 All Oceanic 5.51 7.68 0.16 ± 0.10 0.16 ± 0.09 0.26 ± 0.15 All Oceanic modified 6.40 7.78 0.16 ± 0.80 0.16 ± 0.09 0.29 ± 0.14 All African 4.59 7.12 0.14 ± 0.80 0.14 ± 0.08 0.21 ± 0.12 All Local 5.15 6.90 0.16 ± 0.11 0.14 ± 0.09 0.25 ± 0.14 All at lower number fractions. The degree of external mixing, i.e. the percentage of HTDMA scans that display two or more modes at the same time, increases with particle size (average yearly values of about 20, 28 and 45 % for 25, 50 and 165 nm particles, respectively) and is higher in the cold seasons than in the warm seasons. This is likely a result of higher number concentrations of combustion aerosols emitted from heating devices in the PBL in winter and autumn. The degree of external mixing is less sensitive to air mass type than to season. Ultimately, parameterizations of hygroscopic growth factors and kappa values are calculated for given seasons and air mass types. These parameterizations and kappa values are needed for future calculations of wet aerosol size distributions, which are more useful than dry aerosol size distributions and essential for comparisons of in situ and remote sensing data.
The Supplement related to this article is available online at doi:10.5194/acp-14-9537-2014-supplement.