A field campaign was conducted at the high-alpine research station Jungfraujoch (3580 m a.s.l. in central Switzerland) from 12 June to 6 August 2016. Additional results are included from measurements conducted during the Cloud and Aerosol Characterization Experiment 2010 (CLACE2010) campaign at the same site during the same period of the year (19 June 2010 to 17 August 2010). The exact same instruments were used during both campaigns. Over the last 20 years, the Sphinx laboratory at the Jungfraujoch has hosted numerous field experiments on aerosol-related research (Bukowiecki et al., 2016), specifically addressing aerosol–cloud interactions during CLACE campaigns (e.g. Sjogren et al., 2008; Zieger et al., 2012), new particle formation (e.g. Bianchi et al., 2016; Tröstl et al., 2016), and continuous characterization of aerosol properties and trends (Collaud Coen et al., 2013). In 1995, the aerosol monitoring became part of the Global Atmosphere Watch (GAW) programme of the World Meteorological Organization (WMO). Further environmental research comprises for example a thorough study of the aerology and air mass dynamics around this site (e.g. Poltera et al., 2017), which is important to understand aerosol transport phenomena.

The Jungfraujoch is located on a mountain pass oriented in the direction southwest–northeast between the Jungfrau (4158 m a.s.l) and Mönch (4107 m a.s.l.) peaks. Owing to this, two main wind directions are observed from the southeast and the northwest. The relative proximity of the Jungfraujoch to lower-altitude pollution sources as well as its presence within clouds about 40 % of the time (Baltensperger et al., 1997) makes it an appropriate site to study black-carbon–cloud interactions. According to Herrmann et al. (2015), free tropospheric (FT) conditions prevail for 39 % of the time at the Jungfraujoch but only around 20 % in summer. Pollution injections from the planetary boundary layer (PBL) increase the number concentration of particles larger than 90 nm from typical levels under FT conditions of around 40 up to 1000 cm-3; these injections are the dominant source of CCN at the Jungfraujoch in summer, when mostly liquid clouds form (mixed-phase clouds can occur in the case of low temperatures).

The occurrence of in-cloud conditions during the campaign was determined with the LWC measurements of the PVM. The criterion for defining a cloud event was a minimum LWC of 0.1 g m-3 for at least 1 h. Cloud events typically lasted 2 to 15 h. Very short periods (a few minutes) during the cloud events, during which the LWC dropped below 0.1 g m-3, were likely caused by entrainment of dry air near the edge of a cloud and were excluded from the analysis. Cloud presence was independently confirmed based on significant differences in the particle number concentrations measured behind the total and interstitial inlets. In total, 24 cloud events were sampled in 2016 (see Table S1).

As discussed below, aerosol hygroscopicity and cloud peak supersaturation often varied substantially over the full duration of a cloud event. Therefore, stable periods within a cloud event were identified as periods with limited variability in key aerosol and cloud parameters. Sometimes even two distinct stable periods were identified in a single cloud event, resulting in a total of 11 “stable cloud periods” from the CLACE2016 campaign which were chosen for further detailed analysis (see Table 1). The analyses of three stable cloud periods extracted from the CLACE2010 campaign are also shown. Combining both campaigns, these periods add up to a total duration of 14.1 h.

For in-cloud conditions, we define the size-dependent activated fraction, AF(DX), as the number fraction of particles with diameter DX that formed a cloud droplet. The activation spectrum is inferred from size distribution measurements behind two different inlets. A first option is to use the interstitial (int) and total inlets (tot), e.g. as done by Hammer et al. (2014b): AFintDX=dNtotdlogDXDX-dNintdlogDXDXdNtotdlogDXDX. Here, dNYdlogDX is the particle number size distribution with respect to diameter DX measured behind the inlet type “Y”, where “X” is a placeholder indicating the diameter type, i.e. dry particle mobility diameter, dry particle optical diameter or BC core mass equivalent diameter.

Alternatively, the activation spectrum is inferred from the data measured behind the PCVI inlet and the total inlet: AFPCVIDX=dNPCVIdlogDXDXdNtotdlogDXDX. The activated fraction typically follows an S-shape curve, as seen in Figs. 2 and 3, starting with null activation at sufficiently small diameter and reaching a plateau value at sufficiently large diameters. We define the threshold dry diameter for activation to cloud droplets, Dhalfcloud, as the diameter at which the activated fraction reaches half of the activated fraction at the plateau.

We use the term “activated fraction” in the context of particle number, whereas we use the term “scavenged fraction” when presenting mass fractions of particulate matter incorporated into cloud droplets relative to the total aerosol. Size-resolved activated fraction and scavenged fraction of BC are identical in the special case of choosing the BC core mass equivalent diameter for the diameter scale. However, activated fraction and scavenged fraction integrated over a certain diameter range are not identical due to the different size dependence of the weighting factor when integrating number or mass.

The equilibrium size of an aerosol particle under subsaturated relative humidity (RH) conditions and its activation threshold to a cloud droplet at supersaturated RH conditions depend primarily on the particle dry diameter (Ddry) and chemical composition. The Köhler theory (Köhler, 1936) describes equilibrium vapour pressure (RHeq) over a solution droplet by combining the Kelvin effect, capturing the influence of size, and Raoult's law, capturing the influence of particle composition. Parameterizing Raoult's law is complicated by nonideal interactions between water and solutes and by the presence of both inorganic and organic compounds in internally mixed particles. Petters and Kreidenweis (2007) proposed the use of a single hygroscopicity parameter κ to describe Raoult' law, i.e. to describe the dependence of water activity on solution concentration for a given particle composition. This approach, commonly referred to as the κ-Köhler theory, allows the equilibrium supersaturation over the solution to be expressed as a function of droplet diameter, Ddrop: SSeq(Ddrop):=RHeqDdrop-1=Ddrop3-Ddry3Ddrop3-Ddry31-κexp⁡4.σs/aMwRTρwDdrop-1, where ρw and Mw are the density and the molar mass of water, respectively; σs/a is the surface tension of the solution–air interface (hereafter assumed to be equal to the surface tension of pure water); R is the universal gas constant; and T is the absolute temperature. From Eq. (3), it follows that SSeq has a global maximum at the droplet diameter above which the particle is considered to be activated to a cloud droplet. Equation (3) further implies an unambiguous relationship between the dry diameter of a particle, its hygroscopicity parameter κ and the maximum supersaturation. Knowing two of these parameters makes it possible to infer the third one using Eq. (3) and numerical approaches. For example, knowing the supersaturation and κ implies a critical dry diameter above which all particles activate to cloud droplets.

The combination of total CCN number concentration at a defined supersaturation, measured by the CCNC in a polydisperse set-up, with total particle number size distribution, measured by the SMPS, makes it possible to infer the critical dry diameter of the ambient aerosol for the supersaturation set in the CCNC (Kammermann et al., 2010b). This approach was applied for the first time at the Jungfraujoch by Jurányi et al. (2011) under the assumption that the aerosol is internally mixed. Specifically, the particle number size distribution was integrated from the maximum diameter to the diameter at which the integrated particle number concentration is equal to the simultaneously measured CCN number concentration. The lower limit of integration matching this condition corresponds to the critical dry diameter for CCN activation, DcritCCN. As the CCNC was repeatedly stepped through a sequence of four different supersaturations between 0.70 % and 0.35 %, this provided the relationship between the supersaturation and corresponding critical dry diameter for CCN activation of the ambient aerosol. This was converted to the corresponding relationship between particle dry diameter and the hygroscopicity parameter κ based on Eq. (3). Figure 4a and b show these relationships for two example cloud periods. The data points are located along the dotted lines because only two free parameters are left in the κ-Köhler theory for a fixed supersaturation applied in the CCNC.

The activation of aerosol particles in an ambient cloud depends on the peak supersaturation reached during cloud formation. We applied the method introduced by Hammer et al. (2014a) to retrieve the effective peak supersaturation (SSpeak) of clouds observed at the Jungfraujoch. Briefly, the half-rise threshold diameter for activation to cloud droplets (Dhalfcloud) during a cloud event was inferred from the SMPS particle number size distribution measurements behind the total and interstitial inlets as explained in Sect. 3.2 and shown in Fig. 2. The corresponding SSpeak of a cloud was then retrieved by inputting this Dhalfcloud and the corresponding CCNC-retrieved aerosol hygroscopicity parameter κ (Sect. 3.4) into the κ-Köhler equation (Eq. 3). In the present study, the hygroscopicity parameter was, on average, found to be independent of particle size (Fig. 6), while it varied in time (Fig. 5b). Therefore, we simply considered the moving average, κsmooth (black open circles in Fig. 5b), of the time-resolved κ values at different particle sizes to be representative of the κ value at the diameter Dhalfcloud. This is slightly different from the approach chosen by Hammer et al. (2014a) and Motos et al. (2019), in which case the size dependence was considered by interpolation or extrapolation of size-dependent κ values to the diameter Dhalfcloud (at the expense of time averaging over a whole CCNC measurement cycle).

The apparently circular calculation in the above approach, i.e. using the κ-Köhler theory to obtain a value of the hygroscopicity parameter and then reusing this value in the κ-Köhler theory, is required to account for the temperature difference between droplet formation processes occurring in the CCN counter and at cloud base. Cloud base temperature, Tcloudbase, which was used as input to the κ-Köhler equation during CLOUD2016 but not CLOUD2010 because of the need of a PVM, was not directly measured. Instead it is chosen to be equal to the dew point corresponding to the total water content at the Jungfraujoch with a correction for the pressure difference between the Jungfraujoch and the cloud base (see Hammer et al., 2014a).

The critical supersaturation for droplet activation is calculated for individual BC-containing particles detected by the SP2 behind the different inlets, following the approach described in Motos et al. (2019). Briefly, the approach entails combining κ-Köhler theory (Sect. 3.3) with the ZSR mixing rule as introduced by Petters and Kreidenweis (2007). The calculation requires the total particle diameter, the volume fractions and corresponding hygroscopicity parameters of each of the components of the particle. We treat the BC-containing particles as two-component particles with total size (and volume) taken from the optical diameter of the particle measured with the SP2 (Sect. 2.2.2). The BC volume is inferred from the rBC mass measured by the SP2. The κ value of BC is chosen to be zero as BC is insoluble. The κ value of the coating is assumed to be equal to the mean κ value inferred from the CCNC measurements at all supersaturations during the cloud event under investigation (the size dependence of the κ values inferred by the process described in Sect. 3.4 was typically small, thus justifying this type of averaging). The κ value of the mixed particle is calculated as the volume-weighted mean of the κ values of the BC core and its coating (ZSR mixing rule). For the CLACE2010 campaign, the κ values were taken from the annual data set of κ values at the Jungfraujoch published by Jurányi et al. (2011), with interquartile ranges used for error propagation. These theoretical calculations of BC-containing particle critical supersaturation are based on the assumption of spherical core–shell morphology – a simplification that is tested in the BC activation closure presented below.

The PCVI, described in Sect. 2.2.1, was not operational during all but two cloud events due to technical issues linked to flow rate adjustments and icing of the inlet (Table S1 in the Supplement). During the cloud events on 22 July and 4 August, when the PCVI functioned, the input and output flow rates were set to 11.8 and 1.5 L min-1, respectively, resulting in a calculated particle enrichment factor in the outflow of 7.9 (ratio of input to output flow rate). Particle losses along the PCVI inlet line were estimated to be as high as 67 % based on total concentration measured by the CPC behind the total inlet compared to the concentration measured with the PCVI-inlet CPC when bypassing the PCVI during out-of-cloud conditions. The transmission efficiency of the PCVI was around 45±5 %, based on laboratory tests prior to the campaign. These PCVI corrections for enrichment factor, line losses and transmission efficiency were applied to the raw number size distributions measured behind the PCVI, as illustrated in Fig. 3a. The absolute uncertainties in the corrected cloud droplet residual number size distributions were considerable as the loss corrections amount to a factor of ∼7 in total. Nevertheless, good agreement with the total number size distribution was reached for large particle diameters, where most particles are activated to cloud droplets. Furthermore, the size-dependent activated fractions inferred from PCVI and total inlet data agreed well with those inferred from the interstitial and total inlet data (Eqs. 1 and 2, respectively; shown in Figs. 3b and S2b). This shows, firstly, that the PCVI and the interstitial inlets indeed sampled exclusively cloud droplet residual and interstitial particles, respectively; and, secondly, that the interstitial- and PCVI-based approaches provided consistent results with respect to measured threshold diameters for activation to cloud droplets.

In the present work, the uncertainties associated with MAAP- and SMPS-derived scavenged fractions are based on propagating differences between measurements conducted behind the interstitial and total inlets during out-of-cloud conditions, immediately before and after each cloud event. The same approach applies for SMPS-derived activated fractions of the total aerosol (and the corresponding activation diameter Dhalfcloud) and SP2-derived activated fractions of BC-free particles. Uncertainties related to the SP2-derived activated fractions of BC-containing particles result from the propagation of Poisson-based counting uncertainties related to the BC core number size distributions with a sample volume uncertainty assumed to be 5 %.

The uncertainties in the retrieval of κsmooth were estimated using the deviation of κ values around the moving average of these values representing κsmooth (see Sect. 3.5 and Fig. 5). A Monte Carlo simulation was used to propagate the uncertainties estimated for Dhalfcloud and κ to SSpeak. These uncertainties are listed in Table 1.

The aerosol properties observed during this study will not be discussed in detail as several comprehensive data sets of the Jungfraujoch aerosol observations have already been published (e.g. Bukowiecki et al., 2016, and references therein). By contrast, only limited data on BC properties have been published at the Jungfraujoch so far (e.g. Liu et al., 2010; Kupiszewski et al., 2016), but a more comprehensive manuscript on this topic is currently in preparation (Motos et al., 2019). Here, we focus only on the aerosol properties that are directly relevant for determining the activation behaviour of BC in clouds.

The hygroscopicity parameter κ was inferred for the bulk aerosol from the polydisperse CCN measurements combined with the size distribution measurements using the method described in Sect. 3.4. This provides a time series of κ values as shown in Fig. 5b for the 31 July–1 August cloud event. These κ values are representative of different particle diameters because the CCN measurements were done at different supersaturations. The aerosol hygroscopicity varied during the cloud event. However, the short-term fluctuations were sometimes dominated by random noise due to limited counting statistics from the low particle number concentrations, e.g. during the first part of the cloud event shown in Fig. 5 from about 16:00 to 22:00. By contrast, the size dependence at a given time was often small, e.g. during the last part of the 31 July–1 August event after 02:00 on 1 August. Results for two more cloud events are shown in Fig. 4. The first event (Fig. 4a) is an example where κ varied strongly over the cloud period, while the second event (Fig. 4b) is representative of the conditions during the campaign, i.e. rather stable hygroscopicity. In both of these and other cases, temporal variability typically dominated over size dependence. This justifies the use of a simple running mean of κ data points from all supersaturations (i.e. neglecting the size dependence) in the further data analysis of droplet activation processes in clouds (see also Sect. 3.5).

The statistics of aerosol hygroscopicity over the whole CLACE2016 campaign are shown in Fig. 6. Mean values of κ≈0.25 and the interquartile range overlap well with the range of aerosol hygroscopicity observed at the Jungfraujoch during previous long-term campaigns (Kammermann et al., 2010a: mean κ of 0.24 over 13 months; Jurányi et al., 2011: mean κ of 0.20 over 17 months; Schmale et al., 2018: mean κ of 0.29 over 35 months). This indicates that CLACE2016 was representative in terms of aerosol hygroscopicity.

The size distribution measurements behind the total and interstitial inlets were used to determine the size-resolved fraction of particles that activated to cloud droplets during cloud events (Eq. 1; Sect. 3.2). The half-rise threshold diameter (Dhalfcloud) for droplet activation was then inferred from these data as illustrated in Fig. 2. The resulting time series of Dhalfcloud during the 31 July–1 August cloud event is shown in Fig. 5c, with 6 min time resolution. Large variations of Dhalfcloud, by a factor of 2 or more, were found during this and most other cloud events.

The κ-Köhler theory was then used to infer the effective cloud peak supersaturation (SSpeak) from the time-resolved Dhalfcloud and κ values (see Sect. 3.6 for details). The variations in Dhalfcloud translate to variations in SSpeak by factors of up to 4 during individual cloud events (see Fig. 5d for the 31 July–1 August cloud event). Such variations in SSpeak are primarily driven by variations in atmospheric dynamics (i.e. updraft) at the cloud base and to a lesser extent by the number concentration of potential CCN, as demonstrated for the Jungfraujoch site by Hoyle et al. (2016). Variations in effective cloud peak supersaturation are a priori unrelated to the cloud LWC (Fig. 5a and Table 1), which depends only on the air parcel's height above the cloud base. The tendency of convective clouds (mostly of the cumulus type) to create highly spatially and temporally variable supersaturations was reported by Politovich and Cooper (1988). Such clouds form by convection of warm air in contact with mountain faces and are often found in mountainous regions in summer.

Table S1 shows that the variations in SSpeak were large during all cloud events. In order to study the activation of aerosol particles to cloud droplets under well-defined conditions, only continuous in-cloud periods with limited variability in SSpeak were retained for further analysis. Additional criteria were sufficiently stable values of hygroscopicity, particle number concentrations and BC mass concentration. A total of 14 stable cloud periods adding up to a total of 14.1 h of in-cloud measurements were identified (11 from CLACE2016, 3 from CLACE2010).

The size-resolved activated fractions averaged separately for all stable cloud periods of the CLACE2016 campaign are plotted in Fig. 7. The mean peak supersaturation, indicated for each period by the line colour, decreases monotonically with increasing activation threshold diameter. This is not surprising as the SSpeak value of each stable cloud period was calculated from the Dhalfcloud value. However, it does imply that variations in Dhalfcloud were mainly driven by variations in updraft velocities and resulting supersaturations, whereas differences in aerosol hygroscopicity only caused minor additional modulation of Dhalfcloud. The key parameters for each selected cloud period are summarized in Table 1, including the droplet number concentration inferred from the difference in particle number concentration between the total and the interstitial inlet, as well as the median number concentration of potential CCN, i.e. particles with a mobility diameter larger than 90 nm (N90; e.g. Hammer et al., 2014a). SSpeak ranged from 0.15 % to 0.96 % and Dhalfcloud from 39 to 150 nm. The selected periods of in-cloud measurements are representative of clouds typically encountered at the Jungfraujoch in summer. This is shown with Fig. S1, in which the SSpeak values observed during CLACE2016 are compared with results from previous studies at the Jungfraujoch. The distribution of SSpeak during CLACE2016 largely overlaps with the temporally more extensive observations reported by Hammer et al. (2014a). Furthermore, the systematic difference between northwestern and southeastern wind direction, explained with differences in orographic uplifting by Hammer et al. (2014a), was also found during CLACE2016.

The scavenging of BC, i.e. the mass fraction of BC incorporated into cloud droplets, has previously been investigated at the Jungfraujoch. Cozic et al. (2007) applied the same combination of interstitial and total inlets to determine the scavenged fraction of BC (based on eBC mass measured by two MAAPs), as well as the scavenged fraction of the total aerosol (derived from SMPS measurements). They found close agreement between the scavenged fractions of BC and that of the total aerosol for warm clouds with temperature at Jungfraujoch (TJFJ) above -5 ∘C, i.e. high correlation and almost identical values on average. Such close agreement is a priori not expected because BC is insoluble in water; however, the authors attributed it to the high degree of internal mixing of BC in the aged aerosol at the Jungfraujoch. Figure 8a presents an equivalent analysis of BC and total aerosol volume scavenged fractions for the CLACE2016 data set of this study, which confirms the close agreement. Note that the MAAP-derived eBC mass-based scavenged fractions are consistent with SP2-derived rBC mass scavenged fractions. However, the eBC data were chosen for Fig. 8 as they are available at higher time resolution because the SP2 was switched between three inlets.

Going a step further, we examined the dependence of the scavenged fractions on SSpeak by colouring the data points in Fig. 8a accordingly. The fact that data points are systematically ordered by colour indicates that the scavenged fractions of both BC and the total aerosol volume are primarily controlled by variations in SSpeak, as previously suggested by Ohata et al. (2016). Indeed, plotting the same data set as scavenged fraction against log(SSpeak) in Fig. 8b reveals an S-shaped relationship for both the total aerosol volume and BC, which is well represented by manually fitted Hill equations (green and black dashed lines). Scavenged fractions are on average equal for BC and the total aerosol, as already shown in Fig. 8a, and reach values of 50 %, 75 % and > 90 % at supersaturations of 0.13 %–0.17 %, 0.25 %–0.31 % and > 0.55 %, respectively. This implies that the peak supersaturation at cloud formation must be considered to correctly describe the fraction of BC incorporated into cloud droplets through nucleation scavenging, as also shown by Ching et al. (2018) using particle-resolved model simulations. For example, the systematic difference in the mean SSpeak between northwesterly and southeasterly wind conditions at the Jungfraujoch, as shown in Fig. S1, results in systematic differences for the scavenged fractions of both BC and the total aerosol volume. This result also confirms that nucleation scavenging is the dominant mechanism resulting in the incorporation of particles (BC-free or BC-containing) into cloud droplets at the Jungfraujoch. If impaction, a process unrelated to SSpeak, were to dominate, we would not observe such a relationship between the scavenged fractions and SSpeak.

The SS dependence of the scavenged fraction of a hypothetical, internally mixed aerosol with log-normal size distribution and size-independent hygroscopicity (composition) will follow a Hill curve such as the dashed lines in Fig. 8b. Variations in modal size would shift the position of the Hill curve, whereas deviations from the log-normal size distribution shape would distort the shape of the curve. Similarly, variations and size dependence of aerosol hygroscopicity would also modulate the scavenging curve but are probably too small to cause modifications to the same extent. Such variations are the reasons for the substantial scatter around the Hill curves in Fig. 8b. The reverse conclusion is that size distribution and mean hygroscopicity must be known to accurately describe the supersaturation dependence of the scavenged fraction.

The scavenged fraction of BC mass is only expected to be equal to the total aerosol volume scavenged fraction for all peak supersaturations if BC contributes an equal fraction to the aerosol volume at any particle size and if the critical activation diameters of the BC-containing particles and total aerosol are equal. While the latter condition is closely fulfilled if BC is internally mixed with substantial coatings, size-independent BC volume fractions are a priori not expected. Nevertheless, the scavenged fractions of total aerosol volume and BC mass are essentially equal on average. However, deviations of several data points in Fig. 8a from the 1:1 line are greater than the measurement uncertainty, indicating that even at remote locations the BC scavenged fraction can differ from the total aerosol volume scavenged fraction in individual cloud events. This is likely due to some size dependence of the contribution of BC to the aerosol volume and/or disagreement between the critical activation diameters of BC-free and BC-containing particles. For example, new particle formation events followed by growth to sizes remaining below the droplet activation cut-off diameter, e.g. as reported in Tröstl et al. (2016), are one possible mechanism that can result in the BC scavenged fraction becoming greater than that of the total aerosol volume.

The scavenged fractions of BC and the aerosol volume observed in fog events in Zurich by Motos et al. (2019) are also included in Fig. 8b. The peak supersaturation in fog is much lower than that of typical clouds at the Jungfraujoch. Nevertheless, one cloud during the CLACE2016 campaign had a peak supersaturation as low as the fog data (∼0.05 %). The scavenged fractions of BC and total aerosol volume are very low at such low peak supersaturations because the activation cut-off is in the upper tail of the size distributions. However, during the fog events, the scavenged fraction of BC was found to be consistently lower by a factor of ∼2 compared to that of the total aerosol volume. The presence of externally mixed fresh BC-containing particles at the urban location might explain this difference. Below we will show that the BC mixing state is indeed among the parameters controlling activation on the single-particle level. However, more comprehensive data sets would be required to confirm that differences in resulting bulk scavenged fractions, which also depend on size distribution and mean mixing state, are indeed systematic in urban fog.

Matsui (2016) used a mixing-state-resolved 3-D model to simulate the mixing state of BC-containing particles over East Asia and to estimate the critical supersaturation required for CCN activation of these particles. He concluded that almost all BC-containing particles activate to form droplets at 1.0 % supersaturation while 20 % to 50 % by number stay in the interstitial phase at 0.1 % supersaturation. He applied a theoretical approach equivalent to the one verified in the present study (see Sect. 4.4). These model results are in qualitative agreement with our observations. However, a direct, quantitative comparison of number-based activated fractions of BC over East Asia with mass-based scavenged fractions of BC at the Jungfraujoch is not justified because mass- and number-based activated fractions can differ for the same aerosol population and because the sources and levels of air pollution are different in central Europe and East Asia.

The SMPS measurements behind the interstitial and total inlets and Eq. (1) were used to infer the size-dependent activation of aerosol particles as discussed above in Sect. 4.1 and shown in Fig. 2. The SP2 measurements behind these inlets were used in an equivalent manner to specifically investigate the activation of BC-containing particles to cloud droplets. Figure 2 shows, on the basis of four example cloud events, that the SP2-based results for BC-free particles (blue and green lines) agree with the SMPS-based results for all particles (pink lines). This comparison is appropriate as the BC-free particles represent around 70 %–95 % of all particles by number (see Sect. 2.2.2 for our operational definition of “BC-free” particle). These independent measurements of activated fractions agree well because the optical diameters provided by the SP2 for BC-free particles are equal to the respective mobility diameters measured by the SMPS, which was tested by comparing corresponding size distributions from these two instruments (not shown). Such consistency in sizing is expected for spherical particles if appropriate calibration and data processing procedures are applied to the SP2 light-scattering signals. The optical sizing of BC-containing particles by the SP2 requires the more sophisticated LEO-fit technique (see Sect. 2.2.2), which was limited to optical diameters greater than 180 nm. The SP2-LEO-fit-derived size-dependent activated fractions of BC-free and BC-containing particles shown in Fig. 2 as green and black lines, respectively, are in agreement within experimental uncertainty. Such agreement indicates that the majority of the BC-containing particles with a diameter greater than 180 nm consist of small BC cores with substantial coating acquired through various processes during atmospheric transport to the remote Jungfraujoch site (through for example condensation of oxidized organic compounds, coagulation with particles or in-cloud processes). Such small insoluble cores hardly alter the hygroscopicity of the entire particle compared to a BC-free particle. Using single-particle mass spectrometry, Zhang et al. (2017) performed an equivalent comparison in southern China and also found that the activated fraction of BC-containing particles was similar or slightly lower compared to that of the total aerosol in the vacuum aerodynamic diameter range from about 200 to 1300 nm.

The scavenged fraction of BC mass can be more directly understood by analysing activated fractions as a function of BC core size rather than total particle diameter. The finding that the BC scavenged fraction is primarily controlled by cloud peak supersaturation, as shown in Fig. 8 and discussed in Sect. 4.2, is also clearly shown in Fig. 9a, which shows the BC activated fraction as a function of the rBC mass equivalent diameter for all stable liquid cloud periods: the activated fraction increases with increasing SSpeak at a given BC core diameter. The 2b August stable cloud period seems to be an outlier as the activated fraction is particularly high in relation to the corresponding SSpeak. However, the fact that the activation plateau was particularly high during this period explains this singularity (see Fig. S3b). A total of 50 % activation is reached at a BC core diameter of approximately 100 nm during the cloud periods with lowest supersaturations of around 0.2 %–0.25 %. By contrast, the activated fraction is ≥90 % all the way down to DrBC≈60 nm for the clouds with the highest peak supersaturations (> 0.7 %). This explains why the mass fractions of scavenged BC at the Jungfraujoch vary between roughly 60 % and 100 % for SSpeak ranging from 0.2 % to 1 % (Fig. 8) given the fact that the BC core mass size distribution typically peaks in the range 120 nm ≤DrBC≤170 nm (illustrated by the mode shown in Fig. 9b and Motos et al., 2019).

Mixed-phase or even completely glaciated clouds may occur at lower temperatures. Mixed-phase clouds may result in the conversion of particles from droplets (activated particles) to interstitial aerosol through the Wegener–Bergeron–Findeisen process (e.g. Cozic et al., 2007), thereby potentially obscuring the causal relationship between SSpeak and droplet activation. However, Verheggen et al. (2007) showed that Dhalfcloud remains well-defined and that only small differences in average Dhalfcloud exist between mixed-phase and liquid clouds. This suggests that the Wegener–Bergeron–Findeisen process does not affect the inferred SSpeak. The fact that the Wegener–Bergeron–Findeisen process evaporates some cloud droplets, whereby the droplet nuclei are released back to the interstitial aerosol, explains that the activated fraction was lower in most clouds at temperatures below -5 ∘C compared to that in warm clouds at comparable SSpeak (see the dashed lines in Fig. S3a). The 26–27b June stable cloud period is an exception in so far as the activated fraction of BC was comparable to warm cloud results despite low TJFJ. This cloud may have been a supercooled liquid cloud rather than a mixed-phase cloud. The fact that a supercooled liquid cloud was an exception at the Jungfraujoch for temperatures below -5 ∘C may indicate that cloud glaciation is only rarely limited by ice nuclei concentrations. No in situ measurements of cloud properties were performed to determine the phase of the clouds in order to test this hypothesis.

According to the Köhler theory (Sect. 3.3), the BC core diameter of an internally mixed BC-containing particle is not the decisive parameter for its critical supersaturation (even for a hypothetical spherical core–shell morphology). Instead, in the absence of surfactants, the overall particle diameter and the mean hygroscopicity are important: the acquisition of water-soluble coatings on BC cores is expected to decrease the critical supersaturation. In addition to the LEO-fit technique, we also applied the delay time method, described in Sect. 2.2.2, to investigate the influence of BC mixing state using SP2 data. This method makes it possible to split BC-containing particles with a certain core size into two distinct classes, one containing exclusively thickly coated BC particles and the other one containing BC particles with thin to moderate coatings, with a classification threshold at a BC volume fraction of ∼30 %. This binary mixing state analysis was applied to the BC data from three example stable cloud periods covering the range of SSpeak typically encountered at the Jungfraujoch. Figure 9c shows the number fractions of particles in these two classes as a function of BC core diameter: the majority of BC-containing particles are thinly or moderately coated. It is important to note that this is not necessarily in contradiction to the expectation that BC at the Jungfraujoch is mostly internally mixed because the threshold between these two classes represents BC volume fractions as low as ∼30 % (i.e. a coating thickness of 40–50 nm on a core with DrBC=185 nm). Figure 9d shows the BC activated fraction curves segregated into the two coating thickness classes for the three cloud periods shown in Fig. 9c. No coating effect on cloud droplet activation was found for the cloud with SSpeak of 0.86 % (yellow lines). This indicates that at high supersaturation, essentially all BC-containing particles within the core size range covered by the SP2 activated to cloud droplets, even without substantial coating. By contrast, a distinct coating effect was found at lower SSpeak when the activated fraction of smaller BC cores drops below the plateau values reached at larger cores. For the 5 July and 4 August periods, the activated fractions for the thickly coated class are always greater than or equal to the activated fractions for the thinly to moderately coated class. This clearly shows that acquisition of coating increases the ability of a BC-containing particle with a certain BC core size to form a cloud droplet. This result qualitatively confirms the expectation from the Köhler theory that coating acquisition reduces the critical supersaturation for droplet activation of BC-containing particles through the combined effects of particle hygroscopicity (Raoult's law) and size (Kelvin effect). The relative influence of each of these two effects can however not be distinguished here, because a particle classified as thickly coated is both larger and more hygroscopic than another classified as thinly to moderately coated, for a fixed BC core size. It needs to be noted that the observed effect on the integrated BC mass scavenged fraction is small for the BC properties and clouds encountered at the Jungfraujoch, because the core size range in which activation is sensitive to the BC mixing state is clearly below the peak of the BC core mass size distribution (Fig. 9a) in most cases.

The size-segregated activation of BC cores observed in a previous study during a fog event at an urban site in Zurich, Switzerland, is also shown in Fig. 9 (Motos et al., 2019). The peak supersaturations in this fog event were in the range 0.040 %–0.051 %, which is typical for mid-latitude fog (Hammer et al., 2014b) and almost an order of magnitude lower than the supersaturations in most of the clouds at the Jungfraujoch site. Accordingly, the activation onset diameter above which BC cores are activated to fog droplets is much greater, i.e. as large as ∼130 nm for thickly coated BC cores and above around 230 nm for thinly to moderately coated BC. This explains the low BC scavenged fraction at the low fog supersaturations shown in Fig. 8.

Ching et al. (2018) used the particle-resolved aerosol model PartMC-MOSAIC to simulate the aging of BC-containing particles in urban plumes. They modelled two-dimensional BC core size and mixing state distributions, and they then inferred size-segregated activation curves and integrated scavenged fractions for BC using the κ-Köhler theory. It is not possible to directly compare the results of their model simulations with our experimental observations because of potential differences in BC size distributions and mixing states between the different environments. Nevertheless, our results confirm several of their findings in a qualitative manner. First, the simulated and observed activated fractions as a function of BC core diameter (e.g. the curves shown in Fig. 9a) are of very similar shape and exhibit the same dependence on SSpeak. Second, our observation that SSpeak is the main parameter controlling the BC scavenged fraction and that the sensitivity to the BC mixing state increases with decreasing supersaturation was reproduced in their simulations.

The delay time method, which was applied to the SP2 data for the analyses presented above, only provides a binary mixing state classification. Quantitative mixing state information can be retrieved from the SP2 data using the LEO-fit approach described in Sect. 2.2.2, though at the expense of limiting the accessible size range. Coating thickness distributions for BC cores with mass equivalent diameters in the range 170 nm ≤DrBC≤200 nm are shown in Fig. 10a for unactivated particles (interstitial inlet), droplet residual particles (PCVI inlet) and all particles (total inlet) sampled for a short period during the 4 August stable cloud period. Results are only available for this short period due to problems with the PCVI inlet discussed in Sect. 3.7. Fortunately, supersaturations were low during this cloud period (0.20 %; Table 1), which meant some BC stayed in the interstitial aerosol (Fig. 8). Figure 10a shows that, on average, the droplet residual BC-containing particles were more thickly coated than the interstitial BC-containing particles. Corresponding activated fractions as a function of coating thickness are shown in Fig. 10b, segregated by the inlet pairs used to perform the calculation with either Eq. (1) or (2). A robust trend of gradually increasing activated fraction with increasing coating thickness was observed despite considerable uncertainty of these data points due to limited counting statistics and comparing measurements that were taken with minor difference (switching valves approach). This shows that acquisition of coatings facilitates activation, consistent with the delay time method results shown in Fig. 9d.

The results presented in the previous section demonstrate qualitatively that the acquisition of coatings by BC particles increases their ability to form cloud droplets. Here we go a step further by comparing calculated and observed droplet activation thresholds on a single BC-containing particle level. Combining the SP2 data with the CCN measurements makes it possible to predict the critical supersaturation of individual BC-containing particles as described in Sect. 3.6. This prediction can then be compared with the actual activation to cloud droplets, which is inferred from the SP2 measurements behind the total and interstitial inlets. Motos et al. (2019) performed such a closure study for the activation of BC in fog. Here we investigate activation of BC in clouds at the Jungfraujoch, which typically have much higher peak supersaturations than fog.

Results for two example cloud periods are shown in Fig. 11. The properties of individual BC-containing particles are shown in Fig. 11a1 and b1 for the samples taken behind the total inlet (grey data points) and the interstitial inlet (coloured by coating thickness). The cloud peak supersaturations are shown as light blue horizontal lines. In an ideal case, i.e. perfectly well defined and homogeneous peak supersaturation and aerosol composition, and negligible measurement noise and bias, one would expect that no interstitial particles show up below the light blue lines (i.e. activated fraction = 100 % since SScrit < SSpeak) and that the numbers of BC-containing particles behind the interstitial and total inlets are equal above the light blue lines (i.e. activated fraction = 0 %). A trend in this direction can be seen in Fig. 11a1 and b1. Aggregating the data and calculating activation curves as a function of predicted critical supersaturation (black lines in Fig. 11a2 and b2) reveal that, within experimental uncertainty, the supersaturation corresponding to the half-activation threshold for BC-containing particles indeed coincides with the peak supersaturation for both cloud events. This demonstrates that closure between predicted and observed activation of the BC-containing particles is achieved with the combination of the κ-Köhler theory, the ZSR mixing rule and SP2 measurements of particle properties.

An alternative but equivalent method of performing this closure exercise is to compare the observed activation spectrum of the BC-containing particles (black lines in Fig. 11a2 and b2) with that of the total aerosol based on SMPS measurements (green lines; inferred from the size-segregated activation spectra shown in Fig. 7). The activated fraction of the total aerosol reaches Dhalfcloud exactly at the cloud peak supersaturation, because this is nothing less than the approach used to infer the peak supersaturation. The activation curves of BC-containing particles closely follow those of the total aerosol, indicating successful closure. The simple combination of the spherical core–shell morphology assumption, κ-Köhler theory and the ZSR rule is a sufficiently detailed approach to predict how insoluble BC alters the droplet activation behaviour of BC-containing particles compared to that of BC-free particles.

The two stable cloud periods shown in Fig. 11 have an SSpeak at the low end of the range of typical supersaturations observed at the Jungfraujoch. They were chosen because the BC-containing particle size range accessible to the SP2 LEO-fit approach is limited and some fraction of analysable particles remaining in the interstitial aerosol was required to perform the analysis. The influence of BC mixing state on cloud droplet activation at different supersaturations was further assessed independently of particle size by calculating the activated fractions as a function of the coating thickness for BC-containing particles with a fixed overall optical diameter of Dopt=200 nm. Results for seven example cloud periods from both the CLACE2016 and CLACE2010 campaigns are shown in Fig. 12. In clouds with high SSpeak, the activated fraction of BC-containing particles (coloured solid lines) equals that of BC-free particles of the same size (triangles attached to horizontal dashed lines), regardless of whether or not the BC-containing particles are coated. This is in agreement with the theoretically expected behaviour: the threshold coating thickness, calculated with the κ-Köhler theory and the ZSR mixing rule and indicated with a cross at half-rise activated fraction for each cloud period in Fig. 12, is negligible at SSpeak≥∼0.5 % for BC-containing particles with an overall diameter of 200 nm. During the cloud periods with low to medium SSpeak in the range from 0.15 % to 0.3 %, the activation plateau at thick coatings is clearly less than 100 %. However, this is a result of temporal variations in SSpeak and not due to properties of the BC-containing particles, since the activated fractions of BC-free particles with a diameter of 200 nm agree with the activation plateaus of BC-containing particles with thick coatings. The BC cores with no or very thin coatings do not activate at these low to medium SSpeak values. Furthermore, the coating thickness at half-rise activated fraction (open circles in Fig. 12) agrees with the theoretically expected threshold coating thickness within measurement uncertainty. This successful closure between predicted and observed activation thresholds again confirms that, under the simplifying assumptions applied in this study (spherical core–shell morphology, surface tension of pure water), the combination of the κ-Köhler theory and the ZSR mixing rule is a suitable method of predicting the activation of BC-containing particles of known size and mixing state.

It has to be noted that, in the present study, we have tested the validity of the κ-Köhler theory and the ZSR mixing rule for only a small subset of large BC cores with very thin coatings at medium to high SSpeak, due to the limited size range of particles accessible to the SP2 LEO-fit analysis. Motos et al. (2019) used the same approach in fog and showed that this simplified theoretical approach is also valid at very low supersaturations and for a wider range of BC core sizes. Therefore, the method still remains to be examined against field observations of small to medium BC core sizes at medium to high SSpeak (e.g. SSpeak > 0.3 %). However, the scavenged fraction of BC in atmospheric clouds is only weakly sensitive to the exact behaviour of small to medium BC cores in this supersaturation range (e.g. Fig. 8), such that potential errors in the simplified theoretical model would be of little consequence. The closure achieved in this study for atmospheric BC is in line with a recent controlled laboratory study using a similar theoretical model and SP2 measurements of BC size and mixing state (Dalirian et al., 2018).