Aerosol activation characteristics and prediction at the central European ACTRIS research station of Melpitz, Germany

Understanding aerosol particle activation is essential for evaluating aerosol indirect effects (AIEs) on climate. Long-term measurements of aerosol particle activation help to understand the AIEs and narrow down the uncertainties of AIEs simulation. However, they are still scarce. In this study, more than 4 years of comprehensive aerosol measurements were utilized at the central European research station of Melpitz, Germany, to gain insight into the aerosol particle activation and provide recommendations on improving the prediction of number concentration of cloud condensation nuclei (CCN, N_CCN). (1) The overall CCN activation characteristics at Melpitz are provided. As supersaturation (SS) increases from 0.1 % to 0.7 %, the median N_CCN increases from 399 to 2144 cm⁻³, which represents 10 % to 48 % of the total particle number concentration with a diameter range of 10–800 nm, while the median hygroscopicity factor (κ) and critical diameter (D_c) decrease from 0.27 to 0.19 and from 176 to 54 nm, respectively. (2) Aerosol particle activation is highly variable across seasons, especially at low-SS conditions. At SS=0.1 %, the median N_CCN and activation ratio (AR) in winter are 1.6 and 2.3 times higher than the summer values, respectively. (3) Both κ and the mixing state are size-dependent. As the particle diameter (D_p) increases, κ increases at D_p of ∼40 to 100 nm and almost stays constant at D_p of 100 to 200 nm, whereas the degree of the external mixture keeps decreasing at D_p of ∼40 to 200 nm. The relationships of κ vs. D_p and degree of mixing vs. D_p were both fitted well by a power-law function. (4) Size-resolved κ improves the N_CCN prediction. We recommend applying the κ–D_p power-law fit for N_CCN prediction at Melpitz, which performs better than using the constant κ of 0.3 and the κ derived from particle chemical compositions and much better than using the N_CCN (AR) vs. SS relationships. The κ–D_p power-law fit measured at Melpitz could be applied to predict N_CCN for other rural regions. For the purpose of improving the prediction of N_CCN, long-term monodisperse CCN measurements are still needed to obtain the κ–D_p relationships for different regions and their seasonal variations.

1 Introduction

The specific subset of aerosol particles that serves as nuclei for the condensation of water vapor, forming cloud droplets at a given supersaturation (SS) condition, is known as cloud condensation nuclei (CCN). Aerosol particle activation affects the aerosol and cloud interactions (ACIs), thereby changing the cloud microstructure (Zhao et al., 2012; Jia et al., 2019; Wang et al., 2019), precipitation (Khain, 2009; Wang et al., 2011; Fan et al., 2012, 2018), radiation (Twomey, 1974, 1977; Albrecht, 1989; Zhao and Garrett, 2015), and by these effects the global climate (Ramanathan et al., 2001; Rosenfeld et al., 2019). The latest sixth assessment report from IPCC (2021) pointed out that aerosol indirect effects (AIEs) remain the most considerable uncertainty in assessing the anthropogenic contribution to present and future climate change.

The ambient SS and aerosol activation ability are both important for predicting the number concentration of cloud droplets. The classical Köhler theory (Köhler, 1936), combining the Raoult law with the Kelvin effect, illustrates that the aerosol particle activation depends on particle size, chemical composition, and the given SS. Petters and Kreidenweis (2007) parameterized the Raoult term with a single hygroscopicity factor κ to capture the water activity without needing to know anything about the dissolved compounds. Different perspectives have been presented on the influence of particle size and composition on the CCN activation. In terms of a single aerosol particle, the actual particle size plays a more important role than the chemical composition for activation because of the different range in which κ and particle diameter (D_p) vary and the reciprocal relationship between κ and the third power of the critical D_p ($D_{\mathrm{c}}^{\mathrm{3}}$) at a given SS. As for a population of aerosol particles, Dusek et al. (2006) concluded that particle number size distribution (PNSD) matters more than the chemical composition distribution, which has been supported by many experiments. Even sometimes, assuming a constant κ still predicted CCN number concentration (N_CCN) well (e.g., Sihto et al., 2011; Wang et al., 2018a). Andreae and Rosenfeld (2008) reviewed the previous studies on aerosol particle activation and recommended that for modeling purposes, the global κ values of 0.3±0.1 and 0.7±0.2 can be representative for continental and marine aerosol, respectively, which has been widely used to predict N_CCN. The regional variability should be emphasized because the mean κ measured in urban, rural, and forest exhibits significant differences. For instance, Sihto et al. (2011) suggested an average κ of 0.18 to predict the CCN activation well in boreal forest conditions in Hyytiälä, Finland. A fixed κ of 0.31 suffices to calculate the N_CCN in a suburban site located in the center of the North China Plain (Wang et al., 2018a). The mean κ is 0.5 in a near-coast background station (CESAR Tower) in the Netherlands (Schmale et al., 2018). The median κ ranges from 0.02 to 0.16 at SS=0.1–1.0 % in an urban background site in Budapest, Hungary (Salma et al., 2021). Therefore, the assumption of a constant κ=0.3 may not be appropriate when trying to predict N_CCN for different continental regions.

Additionally, some experiments, especially conducted on more diverse particulate sources, have indicated that chemistry does play an important role in N_CCN variability (e.g., Nenes et al., 2002; Petters and Kreidenweis, 2007; Rose et al., 2010). Not only the bulk chemical composition with a constant κ should be considered for N_CCN prediction, but the size-resolved chemical composition (Deng et al., 2011; Wu et al., 2016), and the mixing state should be applied (Su et al., 2010; Zhang et al., 2014). Information on the organic aerosol fraction improves N_CCN prediction considerably (Poulain et al., 2010; Zhang et al., 2016; Kuang et al., 2020). Freshly formed particles are about 1 nm in diameter (Kulmala et al., 2012), which must grow to tens of nanometers in diameter to serve as the effective CCN at a relatively high SS of ∼1 % (Dusek et al., 2006) and even larger than 200 nm to be efficient at SS less than 0.1 % (Deng et al., 2013). Aerosol chemical composition changes during the growing and aging processes. For instance, photochemical processes promote the formation of secondary inorganic species and increase the particle size, causing a positive correlation between κ and particle size (Massling et al., 2009; Zhang et al., 2017; Wang et al., 2018b). On the other hand, in sulfate-dominated new particle formation (NPF) events with subsequent particle growth by condensation of organic vapors, the κ of small particles may exceed the κ of the larger ones (Wang et al., 2018a). If the κ of organic aerosol increases from 0.05 to 0.15, the global average aerosol radiative forcing would decrease by ∼1 W m⁻², which is in the same order of magnitude as the overall climate forcing of anthropogenic aerosol during the industrialization period (Rastak et al., 2017).

To obtain the regional parameters of aerosol particle activation, extensive field campaigns have been conducted worldwide. Besides the significant spatial difference, also the temporal variations of aerosol activation characteristics are essential for N_CCN prediction (Andreae and Rosenfeld, 2008). Most of the observations lasted 1–2 months or even less, mainly focusing on the effects of short-term weather processes or pollution events on aerosol particle activation, such as the effects of the summer monsoon (Jayachandran et al., 2020), wet removal (Croft et al., 2009), NPF events (Dusek et al., 2010; Wu et al., 2015), biomass burning (Rose et al., 2010), and aerosol particle aging as well as oxidation processes (Zhang et al., 2016, 2017). The long-term CCN measurements (of at least 1 full year) are still rarely reported, resulting in insufficient knowledge concerning the seasonal and annual cycles of aerosol particle activation, which are also critical for model predictions and evaluations. Burkart et al. (2011) reported the particle activation in the urban background aerosol of Vienna, Austria, based on 11-month aerosol and CCN concentration measurements. Paramonov et al. (2015) reported a synthesis of CCN measurements within the EUCAARI network using the long-term data collected at 14 locations. Pöhlker et al. (2016) presented the climatology of CCN properties of a remote central Amazonian rain forest site using 1-year measurements. Che et al. (2017) provided the aerosol activation properties in the Yangtze River Delta, China, based on ∼1-year measurements. Using the long-term (of most >1 year) aerosol and CCN concentration measurements from 12 sites, Schmale et al. (2018) presented the spatial differences in aerosol particle activation for various regional backgrounds. However, systematic studies focusing on the seasonal cycle of size-resolved particle activation and respective CCN predictions are still scarce in the central European continent. Such a study would be of great help for understanding ACIs and narrowing down the regional uncertainties in climate predictions.

In this investigation, more than 4 years of comprehensive measurements of aerosol physical, chemical, and activation properties collected at the ACTRIS (Aerosol, Clouds and Trace Gases Research Infrastructure, http://www.actris.eu/, last access: 14 June 2022) site of Melpitz, Germany, are utilized. The major objective is to gain insight into the aerosol particle activation and provide recommendations on methods for N_CCN predictions. We present therefore the long-term observations and seasonal cycles of various particle activation variables such as N_CCN, activation ratio, critical diameter, size-resolved κ, and mixing state. Furthermore, we evaluated the accuracy of N_CCN calculated from five different activation schemes and finally provide recommendations on N_CCN predictions at Melpitz and for other rural regions.

2 Methodology

2.1 Experiment details

Atmospheric aerosol measurements were conducted at the Melpitz observatory (51.54^∘ N, 12.93^∘ E; 86 m a.s.l.), 50 km to the northeast of Leipzig, Germany. The aerosol particles observed at Melpitz can be regarded as representative for the central European rural background conditions (Birmili et al., 2009). The surroundings of the site are mostly pastures and forests without significant sources of anthropogenic emissions. More detailed descriptions of the Melpitz site can be found, for example, in Poulain et al. (2020).

Figure 1 Schematic diagram of the experimental setup. D-MPSS – dual-mobility particle size spectrometer; ACSM – aerosol chemical species monitor; MAAP – multi-angle absorption photometer; DMA – differential mobility analyzer; CPC – condensation particle counter; CCNC – cloud condensation nuclei counter.

This study focuses on the physicochemical properties and the activation ability of aerosol particles using the data collected at Melpitz from August 2012 to October 2016. Figure 1 depicts the experimental setup. All instruments were in the same container laboratory and utilized the same air inlet. Ambient aerosol particles were first pretreated through a PM₁₀ Anderson inlet, and an automatic aerosol diffusion dryer kept the relative humidity in sampling lines less than 40 % following the ACTRIS recommendations. Subsequently, the aerosol flow was divided into the different instruments using an isokinetic splitter. Particle number size distributions (PNSDs) were measured using a dual-mobility particle size spectrometer (D-MPSS, TROPOS-type; Birmili et al., 1999; Wiedensohler et al., 2012) with a diameter range of 5–800 nm. An aerosol chemical speciation monitor (ACSM, Aerodyne Inc; Ng et al., 2011) was used to measure the chemical compositions of the non-refractory submicron aerosol particulate matter (nitrate, sulfate, chloride, ammonium, and organics). A multi-angle absorption photometer (MAAP, model 5012, Thermo Scientific; Petzold and Schönlinner, 2004) was used to measure the particle light absorption coefficients and to estimate the equivalent black carbon (eBC) mass concentration. For simultaneous measurement of particle and CCN number size distributions, dried aerosol particles were passed through the bipolar charger to establish charge equilibrium (Wiedensohler, 1988) and then through a differential mobility analyzer (DMA) for selecting a monodisperse particle fraction. After the DMA, the flow was split to pass through a condensation particle counter (CPC, model 3010, TSI) to measure the total number concentration of the selected monodisperse condensation nuclei (N_CN) and through a cloud condensation nuclei counter (CCNC, model 100, Droplet Measurement Technologies; Roberts and Nenes, 2005) to measure the N_CCN. Thus, the size-dependent activated fraction (AF, N_CCN/N_CN) curve, i.e., the AF at a certain diameter (D_p) of dry particles, could be obtained. The losses in both instruments were checked, and it was corrected for in the inversion routine. The coupling between size selection and CCNC was programmed in a way that the size-resolved measurements started only after the temperature and thereby the SS of the CCNC were stabilized. As the diameter scan started after SS stabilization, the measurement itself was the same length at all SS conditions. At fully stabilized CCNC conditions we did one D_p scan at per SS setting. A total of five different SS conditions were set in the CCNC instrument (0.1 %, 0.2 %, 0.3 %, 0.5 %, and 0.7 %). A complete SS cycle lasted ∼2.5 h, and the slight variations in the 2.5 h total SS cycle were only due to the waiting time until the temperature of the CCNC was stabilized.

All the instrumentation was frequently calibrated within the framework of the European Center for Aerosol Calibration and Characterization (ECAC, https://www.actris-ecac.eu/, last access: 14 June 2022). The ACSM was regularly calibrated according to the manufacturer's recommendations with 350 nm monodispersed ammonium nitrate and ammonium sulfate particles (Freney et al., 2019). The D-MPSS was calibrated following the recommendations in Wiedensohler et al. (2018). Throughout the campaign, the CCNC was calibrated once a year following the procedures outlined in Rose et al. (2008) using the E-AIM model (Clegg et al. 1998). The measurement uncertainties of these instruments should be noted. The uncertainty in the MAAP is within 10 % (Müller et al., 2011), and those in the D-MPSS and CCNC are both on the order of 10 % (Wiedensohler et al., 2018; Rose et al., 2008). For the SS setting in CCNC, Gysel and Stratmann (2013) pointed out that an achievable accuracy in SS is 10 % (relative) at SS>0.2 % and less than 0.02  % (absolute) at the lower SS. For the ACSM data, the uncertainty in determining the total non-refractory mass is 9 %, while for the individual chemical components, the uncertainty is 15 % for nitrate, 28 % for sulfate, 36 % for ammonium, and 19 % for organic matter (Crenn et al., 2015).

Due to instrument failures and maintenance operations, missing measurements occurred during the campaign. Effective data coverage is shown in Fig. S1 in the Supplement. Overall, the CCNC, D-MPSS, and ACSM–MAAP captured 45 578 AF curves, 103 052 PNSDs, and 26 876 h aerosol chemical measurements, which covered 63 %, 92 %, and 77 % of the campaign time, respectively. For 42 % of the time, all these instruments measured together.

2.2 Methods

Each AF curve (N_CCN/N_CN vs. D_p) was first corrected for multiply charged particles. Multiply (mostly doubly) charged particles appear in the AF curve as a plateau or shoulder at small diameters because they have the same electrical mobility diameter as singly charged smaller particles (Rose et al., 2008; Henning et al., 2014). To correct for this, the fraction of multiply charged particles as determined from the D-MPSS measurements was subtracted from each value of N_CCN/N_CN in AF. The PNSDs from the D-MPSS measurements (5 to 800 nm) are needed as the DMA–CCNC size range does not cover the large particle fraction, which is essential for the correction. Subsequently, we obtained the corrected AF curves.

Each corrected AF curve was fitted with a sigmoid function,

$$\begin{array}{}\text{(1)}& \mathrm{AF}=a+b/\left(\mathrm{1}+\exp \left(-{\displaystyle \frac{D_{\mathrm{p}}-D_{\mathrm{c}}}{{\mathit{\sigma }}_{\mathrm{s}}}}\right)\right),\end{array}$$

where a is the offset from 0 in the y direction and b is the height of the upper plateau of the sigmoidal function, D_c is the critical diameter, and σ_s is a measure for the width of the sigmoid function. This AF fit was multiplied with the PNSD to gain the CCN number size distribution and by integrating the total number of CCN, i.e., N_CCN.

The critical diameter (D_c) of dry particles, κ, and mixing state at each SS condition can be derived from the AF fit results. Affected by aerosol mixing, the AF rises gradually from 0 to the max (∼1) rather than displaying an intermittent mutation. D_c is defined as the diameter of the dry particles from which 50 % of the particles are activated at the given SS.

The shape of the AF curve, i.e., the relative width of the AF, represents the degree of external mixture, which can be quantified by the ratio of $(D_{\mathrm{75}}-D_{\mathrm{25}})/D_{\mathrm{c}}$ (Jurányi et al., 2013). D₇₅ and D₂₅ are the diameters at which 75 % and 25 % of the particles are activated at the given SS. Internal mixture implies that all particles with any given dry size have equal κ with $(D_{\mathrm{75}}-D_{\mathrm{25}})/D_{\mathrm{c}}=\mathrm{0}$, whereas a distribution of different κ at a given particle size can be observed for externally mixed aerosol with higher $(D_{\mathrm{75}}-D_{\mathrm{25}})/D_{\mathrm{c}}$ values. Note that the particle composition varying at different sizes is not defined as external mixing in this study. Jurányi et al. (2013) confirmed the reliability of this approach by comparing the κ distributions derived from parallel monodisperse CCN measurements and hygroscopicity tandem differential mobility analyzer (HTDMA) measurements.

According to the derivation of κ-Köhler theory (Petters and Kreidenweis, 2007), the κ can be calculated from D_c at a given SS:

$$\begin{array}{}\text{(2a)}& \mathit{\kappa }={\displaystyle \frac{\mathrm{4}{A}^{\mathrm{3}}}{\mathrm{27}{D}_{\mathrm{c}}^{\mathrm{3}}{\ln }^{\mathrm{2}}\left(\mathrm{1}+\mathrm{SS}/\mathrm{100}\right)}},\end{array}$$

with

$$\begin{array}{}\text{(2b)}& A={\displaystyle \frac{\mathrm{4}{\mathit{\sigma }}_{s/a}{M}_{\mathrm{w}}}{\mathrm{RT}{\mathit{\rho }}_{\mathrm{w}}}},\end{array}$$

where ${\mathit{\sigma }}_{s/a}$ is the droplet surface tension (assumed to be that of pure water, 0.0728 nm⁻²), M_w is the molecular weight of water, R is the universal gas constant, T is the absolute temperature, ρ_w is the density of water, and A can be considered a function of T. Thus, the size-resolved κ (pair of κ and D_c) can be obtained at each SS cycle. Our monodisperse CCN measurements provide the size-resolved κ within D_p (D_c) of ∼40–200 nm, which depends largely on the SS setting of 0.1 % to 0.7 %. Note that Eq. (2a) is derived from an approximation of the κ-Köhler equation, and when κ is less than 0.2, it causes a slight bias in calculating κ (Petters and Kreidenweis, 2007). Additionally, the debate about the importance of ${\mathit{\sigma }}_{s/a}$ changes, and the connected bulk/surface partitioning on activation of aerosols is on ongoing (e.g., Ovadnevaite et al., 2017; Vepsäläinen et al., 2022), which is not focused on in this study.

Table 1 Densities (ρ) and hygroscopicity factor (κ) for each component.

Besides deriving it from the monodisperse CCN measurements, κ can be derived from the ACSM and MAAP chemical composition measurements (κ_chem) using the Zdanovskii–Stokes–Robinson (ZSR) mixing rule (Zdanovskii, 1948; Stokes and Robinson, 1966) combined with κ-Köhler theory:

$$\begin{array}{}\text{(3)}& {\mathit{\kappa }}_{\mathrm{chem}}=\sum _i{\mathit{\epsilon }}_i{\mathit{\kappa }}_i,\end{array}$$

where κ_i and ε_i mean the κ and volume fraction for each component, respectively, and i is the number of the component in the mixture. The ε_i was derived from its measured component i mass concentration and density (ρ_i). A simple ion-pairing scheme (Gysel et al., 2007) was used in this study with the κ_i and ρ_i values listed in Table 1 (Wu et al., 2015). A κ of 0.1 is used for particulate organics (Dusek et al., 2010; Gunthe et al., 2009, 2011). For black carbon, we use a κ of 0 (Rose et al., 2011; Schmale et al., 2018).

The CCN number size distribution is a part of the particle number size distribution (PNSD), which approximately corresponds to the part of PNSD with D_p>D_c when assuming particles to be internally mixed (Fig. S2 in the Supplement). The assumption of the internal mixing could be reasonable because the median values of the parameter b and $(D_{\mathrm{75}}-D_{\mathrm{25}})/D_{\mathrm{c}}$ are 1.0 and 0.18. Thus, D_c plays a critical role on diagnosing N_CCN in models, which can be derived from κ parameterization at a given SS. When κ is obtained, D_c(κ,SS) is calculated from Eq. (2a). And, assuming an internal mixture, the predicted N_CCN is the integration of the PNSD from D_c, that is,

$$\begin{array}{}\text{(4)}& \mathrm{Predicted}{N}_{\mathrm{CCN}}=\underset{D_{\mathrm{c}}}{\overset{\mathrm{800}}{\int }}\mathrm{PNSD}\left(D_{\mathrm{p}}\right)\mathrm{d}{D}_{\mathrm{p}}.\end{array}$$

Figure 2 Relationship between CCN number concentration (N_CCN) and supersaturation (SS) measured at Melpitz and other stations.

3 Results

3.1 Aerosol activation characteristics

As SS increases, the CCN number size distribution broadens towards smaller particle sizes (Fig. S3 in the Supplement), causing an increase in N_CCN and activation ratio (AR, i.e., ratio of N_CCN to total aerosol number concentration with a diameter range of 10 to 800 nm, N_aero). At Melpitz, the median N_CCN and AR increase from 399 to 2144 cm⁻³ and 0.10 to 0.48 when SS increases from 0.1 % to 0.7 %. As shown in Fig. 2, the N_CCN measured at Melpitz is slightly higher than that measured in more remote rural background stations, e.g., in Vavihill, Sweden (Fors et al., 2011); Hyytiälä, Finland (Paramonov et al., 2015); Southern Great Plains, USA (Liu and Li, 2014); and Mahabaleshwar, India (Singla et al., 2017). However, compared to the N_CCN measured in polluted regions (e.g., Rose et al., 2010; Deng et al., 2011; Kim et al., 2014; Varghese et al., 2016), the Melpitz N_CCN is much lower.

Figure 3 (a) Relationships between CCN number concentration (N_CCN) and supersaturation (SS), and relationship between activation ratios (AR) and SS for different seasons. (b) Seasonal trends of N_CCN and AR at SS=0.1 % and 0.7 %. Dots represent the median values of N_CCN and AR. Shaded areas represent the values in the range from the 25th to 75th percentile. Red lines are power-law fittings for N_CCN (and AR) vs. SS. Two parameters of the fitting results are shown in brackets.

Figure 3a presents the N_CCN vs. SS and AR vs. SS relationships at each season and all datasets at Melpitz. The two relationships are similar, and both can be fitted well with using a power-law function (Twomey, 1959). The fit was also performed with an error function (Pöhlker et al., 2018), and the fitted parameters are in the Supplement (Table S2). Over the whole period, the median values of the slope parameter and the coefficient in the N_CCN–SS power-law fit are 2851 cm⁻³ and 0.75, respectively, which are within the range of values for continental aerosol (slope parameter of 600–3500 cm⁻³ and coefficient of 0.4–0.9) reported in Seinfeld and Pandis (2016). The slope parameters in the power-law fitting represent the sensitivity of the N_CCN and AR to the variation in SS, which is highest in summer and lowest in winter. The seasonal variations of N_CCN and AR at SS=0.1 % and 0.7 % are shown in Fig. 3b. In summer, the median N_CCN and AR are both lowest at SS=0.1 %, which contributed to the largest sensitivity of N_CCN and AR to SS, i.e., the largest slope parameter in the power-law fitting among the four seasons. Additionally, the shape of the PNSD contributed to explain the sensitivity of N_CCN and AR to SS. The PNSD in summer was steepest in the 40–200 nm size range among the four seasons (Fig. S4 in the Supplement). Thus, in summer, a small shift in D_c will change the N_CCN and AR much more than those in winter where the PNSD looks broader, causing the strong sensitivity of N_CCN and AR to SS.

Figure 4 Seasonal variations of (a) aerosol particle number size distribution (dN_aero/dlogD_p vs. D_p, where D_p is particle diameter), (b) total aerosol number concentration with a D_p range of 10 to 800 nm (N_aero) and geometric mean diameter of the particles (GMD), and (c) mass concentration and ratio of each component in aerosol particle with D_p less than 1 µm and the hygroscopicity factor calculated from the chemical composition (κ_chem). Dots represent the median values. Shaded areas represent the values in the range from the 25th to 75th percentile.

To explain the seasonal variations in aerosol activation characteristics, we investigated the PNSD and chemical compositions as shown in Fig. 4. In summer, affected by the frequent NPF events (Ma et al., 2015; Wang et al., 2017), the Aitken-mode particles with D_p<100 nm accounted for the largest portion of the PNSD (Fig. S4 in the Supplement), resulting in the highest N_aero and the smallest geometric mean diameter $\left(\mathrm{GMD}=\exp \left(\frac{\sum _i{n}_i\times \ln D_i}{N_{\mathrm{aero}}}\right)\right)$ among the four seasons. Additionally, in summer, there was the lowest bulk κ_chem, with median value of 0.24 corresponding to the highest organic mass fraction (56 % of total mass), which could be related to the strong formation of the secondary organic aerosol (SOA). Therefore, the N_CCN and AR both kept relatively low values in summer, especially at low-SS conditions (e.g., at SS=0.1 %). On the contrary, in winter, the relatively low number concentration of Aitken-mode particles caused the lowest N_aero and the largest GMD among the four seasons, which could be owing to the rare NPF events. Meanwhile, in winter, low temperatures favored the particulate phase of nitrate (Poulain et al., 2011), causing the highest nitrate mass fraction (31 % of total mass) among the four seasons, which might explain the highest κ_chem (median value of 0.34). Taking all three together, the lowest N_aero, the largest GMD, and the highest κ_chem contribute to the highest AR value in winter at each SS condition. The relationships between κ_chem and each particle component and the correlations among seasonal median values of N_aero, GMD, and κ_chem are in the Supplement (Sect. S1, Figs. S5 and S6). Additionally, no significant yearly trends of the CCN activation characteristics are found during the 4-year measurements, and the results are provided in the Supplement (Sect. S2 and Fig. S7).

Figure 5 Monthly variations of (a) the hygroscopicity factor calculated from monodisperse CCN measurements (κ_CCN) at a supersaturation (SS) of 0.1 % and 0.7 % and the hygroscopicity factor calculated from particle chemical composition (κ_chem), (b) the critical diameter of dry particle for activation (D_c) at SS=0.1 % and 0.7 %, and (c) the degree of external mixture $\left(\right(D_{\mathrm{75}}-D_{\mathrm{25}})/D_{\mathrm{c}})$ at SS=0.1 % and 0.7 %. The definitions of D₇₅ and D₂₅ are the D_p at which 75 % and 25 % of the particles are activated at the given SS, respectively. Dots represent the median values. Shaded areas represent the values in the range from the 25th to 75th percentile.

Figure 6 (a) Relationship between the hygroscopicity factor calculated from monodisperse CCN measurements (κ_CCN) and particle diameter (D_p), and (b) degree of external mixture $\left(\right(D_{\mathrm{75}}-D_{\mathrm{25}})/D_{\mathrm{c}})$ vs. D_p at each season. The definitions of D₇₅ and D₂₅ are the D_p at which 75 % and 25 % of the particles are activated at the given SS, respectively. Red lines are power-law fits. Dots represent the median values. Shaded areas represent the values in the range from the 25th to 75th percentile.

Table 2 Seasonal median values of the hygroscopicity factor derived from the chemical composition (κ_chem), the hygroscopicity factor derived from monodisperse CCN measurements (κ_CCN), the critical diameter of dry particle for activation (D_c), and the degree of external mixture ((D₇₅ – D₂₅)/D_c) at each supersaturation (SS) condition. The unit of D_c is nanometers (nm).

3.2 Size-resolved particle hygroscopicity factor and mixing state

The hygroscopicity factor and the mixing state directly influence the D_c and the shape of the AF curve, thereby changing the N_CCN at a given SS condition. Affected by the variations of particle composition, these two parameters are not constant and both vary with particle size and season.

Figure 5a shows monthly median values of κ_chem and κ calculated from monodisperse CCN measurements (κ_CCN) at SS of 0.1 % and 0.7 %. Their seasonal median values are summarized in Table 2. At Melpitz, the median κ_CCN decreased from 0.27 to 0.19 as SS increased from 0.1 % to 0.7 %, which was less than the median bulk κ_chem of 0.3. The seasonal variation of κ_CCN at SS of 0.1 % is similar to that of κ_chem, whereas the seasonal trend in κ_CCN is much weaker at SS=0.7 %. Essentially, the relationship between κ_CCN and SS is determined by the κ_CCN vs. D_p relationship. The κ_CCN values at SS of 0.1 % and 0.7 % correspond to the median D_c (i.e., D_p) of 176 and 54 nm, respectively. As the ACSM is sensitive to particle mass rather than number concentration, the bulk composition is dominated by the contribution of the larger particles. In the median volume size distribution of particles, the peak diameter was ∼300 nm (Poulain et al., 2020). Thus, κ_chem may be representative for the larger particles rather than for the smaller particles. Owing to the positive correlation between κ and D_p (Fig. 6a), the κ_chem representing the larger particles could be greater than the κ_CCN for the smaller particles. Figure 5b depicts the monthly variation of D_c at SS of 0.1 % and 0.7 %, which shows the opposite trend to κ_CCN (SS) because of the negative correlation of $D_{\mathrm{c}}^{\mathrm{3}}$ (SS) vs. κ (SS) shown in Eq. (2a). Compared to the D_c at lower SS conditions (e.g., 0.1 %), D_c has a more significant seasonal trend at higher SS conditions (e.g., 0.7 %). At SS=0.7 %, the low κ_CCN caused the largeD_c in summer, whereas the high κ_CCN caused the small D_c in spring and winter.

The monthly trend of the external-mixing degree $\left(\right(D_{\mathrm{75}}-D_{\mathrm{25}})/D_{\mathrm{c}})$ is shown in Fig. 5c. Jurányi et al. (2013) pointed out that the $(D_{\mathrm{75}}-D_{\mathrm{25}})/D_{\mathrm{c}}$ ranged from 0.08 to 0.12 for ammonium sulfate calibration measurements at SS=0.1–1.0 %, which indicated an internal mixture within measurement accuracy. For our measurements, the median $(D_{\mathrm{75}}-D_{\mathrm{25}})/D_{\mathrm{c}}$ over all datasets ranges from 0.15 to 0.20 at SS=0.1–0.7 %. The median $(D_{\mathrm{75}}-D_{\mathrm{25}})/D_{\mathrm{c}}$ was low in summer and spring and high in winter and autumn. The results tend to indicate that the aerosol particles at Melpitz were more internally mixed in summer and spring, whereas they were less internally mixed in winter and autumn. In summer, the lower contribution from anthropogenic emissions and the faster aging process as well as SOA formation caused by atmospheric chemistry certainly contribute to making particles more internally mixed. Changes in organic aerosol (OA) composition can be found in Crippa et al. (2014), Poulain et al. (2014), and Chen et al. (2022). In cold seasons, the local pollution (100 km around) is dominated by liquid fuel, biomass, and coal combustions mostly for house heating (van Pinxteren et al., 2016). During winter, long-range transport from the eastern wind brings to the station continental air masses which are strongly influenced by anthropogenic emissions (in opposition to western marine air masses). These particles are a mixture of different anthropogenic sources emitted all along the transport as well as including some local and regional sources (most house heating). All of them at different aging states cause the overall particles to be more externally mixed.

As mentioned above, κ_CCN (and $(D_{\mathrm{75}}-D_{\mathrm{25}})/D_{\mathrm{c}})$ vs. D_p relationships determine the relationship between κ_CCN (and $(D_{\mathrm{75}}-D_{\mathrm{25}})/D_{\mathrm{c}})$ and SS. Monodisperse CCN measurements provide the size-resolved κ and $(D_{\mathrm{75}}-D_{\mathrm{25}})/D_{\mathrm{c}}$. At a given SS condition, κ_CCN represents the κ of particles at D_p=D_c, and the same is true for $(D_{\mathrm{75}}-D_{\mathrm{25}})/D_{\mathrm{c}}$. As shown in Fig. 6a, κ_CCN increases with D_p at the D_p range of ∼40 to 100 nm, whereas κ_CCN almost stays constant at D_p of 100 to 200 nm for all seasons. Additionally, the increase in κ_CCN with D_p varies with season. The κ_CCN vs. D_p relationship is fitted by a power-law function at each season. In summer, there is the lowest slope parameter in the κ_CCN vs. D_p power-law fit, meaning that the κ_CCN is least sensitive to D_p. Compared to the cold seasons, the anthropogenic emissions linked to house heating strongly reduce in summer, which affects the smaller particles, and the dominant small particles (D_p<100 nm) are associated with NPF and the SOA formation. NPF is a complex process which depends on the availability of condensing material (H₂SO₄ and organic), as well as pre-existing particles (coagulation and condensation sink parameters). Therefore, same condensing material on the gas phase can either condense on pre-existing particles (usually larger than 100 nm and then detected by ACSM) or lead to NPF formation. A direct consequence of it is a probable smaller effect of the size-dependent chemical composition of the particles. This might explain why κ_CCN values at SS of 0.1 % and 0.7  % are closer, i.e., the weaker sensitivity of κ_CCN to D_p in summer. Figure 6b presents the $(D_{\mathrm{75}}-D_{\mathrm{25}})/D_{\mathrm{c}}$ vs. D_p relationship. As particle size increases, $(D_{\mathrm{75}}-D_{\mathrm{25}})/D_{\mathrm{c}}$ decreases at D_p of ∼40 to 200 nm for all seasons, meaning that small particles are less internally mixed. The reason is that during the aerosol aging process, not only particle size increases but κ becomes more uniform. The ($D_{\mathrm{75}}-D_{\mathrm{25}})/D_{\mathrm{c}}$ vs. D_p relationship is also fitted well by a power-law function at each season. The lowest absolute value of the slope parameter was observed in summer, indicating that the degree of external mixture was least sensitive to D_p, which could be related to the less mixing between the local emissions and long-range transport particles in summer.

Table 3 Introduction of five activation schemes. The meaning of the abbreviations can be found in Appendix A.

Figure 7 Predicted vs. measured CCN number concentration (N_CCN) for different seasons. The predicted N_CCN is calculated from five different schemes with a detailed introduction shown in Table 3. Color bar represents the different supersaturation (SS) conditions. Black lines are the linear fits. The slope and R² of the linear regression and the median relative deviation (RD) between the predicted and measured N_CCN are shown in each panel. Each row represents the results using the same scheme in different seasons. Each column represents the results using different schemes in the same season.

3.3 N_CCN prediction at Melpitz

N_CCN plays an important role in modeling the formation and evolution of clouds. In this section, we evaluate the accuracy of N_CCN predicted from five schemes. Table 3 introduces the five schemes, which can be summarized into two categories. From polydisperse CCN measurements, the N_CCN (AR) and SS relationships can be obtained, and their fitting results can be used to predict N_CCN at the given SS conditions, which belongs to the first category, corresponding to the N1 and N2 schemes in Table 3, respectively. Compared to CCN measurements, it is generally more common and simpler to obtain the PNSD measurements. Thus, we usually predict N_CCN using the real-time PNSD combined with the parameterized κ (D_c), which belongs to the second category. The second category includes the last three schemes (K1, K2, and K3) in Table 3, but they vary in assuming κ. The K1 scheme used a fixed κ of 0.3 without temporal and size-dependent variations, as recommended for continental aerosol (Andreae and Rosenfeld, 2008), which is also the median value of κ_chem over all data settings at Melpitz. The K2 scheme used the bulk κ_chem calculated from aerosol chemical composition, which is also non-size-dependent but changes over time. The K3 scheme used the κ–D_p power-law fit results shown in Fig. 6a, which are size-dependent without temporal variations at each season. Applying the κ–D_p power-law equation into Eq. (2a), D_c can be derived as function of SS,

$$\begin{array}{}\text{(5)}& D_{\mathrm{c}}={\left({\displaystyle \frac{\mathrm{4}\times A^{\mathrm{3}}}{\mathrm{27}\times \mathrm{coef}\times {\ln }^{\mathrm{2}}\left(\mathrm{1}+\mathrm{SS}/\mathrm{100}\right)}}\right)}^{\frac{\mathrm{1}}{\mathrm{slope}+\mathrm{3}}},\end{array}$$

where the slope and coef represent the slope parameter and the coefficient in the κ–D_p power-law fit. Subsequently, the predicted N_CCN can be calculated through Eq. (4). The second category assumed that aerosol particles are internally mixed at a particular D_p, as used in many previous N_CCN prediction studies (e.g., Deng et al., 2013; Pöhlker et al., 2016; Wang et al., 2018a).

The prediction results are shown in Fig. 7. The linear equation (y=kx) is used to fit the relationship between the predicted N_CCN and the measured one, and its slope represents the mean ratio of the predicted N_CCN to the measured N_CCN. The relative deviation (RD) equals the ratio of the absolute difference between the predicted N_CCN and the measured one to the measured N_CCN,

$$\begin{array}{}\text{(6)}& \mathrm{RD}={\displaystyle \frac{\mathrm{|}\mathrm{predicted}{N}_{\mathrm{CCN}}-\mathrm{measured}{N}_{\mathrm{CCN}}\mathrm{|}}{\mathrm{measured}{N}_{\mathrm{CCN}}}}.\end{array}$$

The median RD was used to quantify the deviation between predictions and measurements of each scheme. The slope and median RD shown in Fig. 7 are both calculated from all five SS conditions for each season. As shown in Fig. 7, the N1 and N2 schemes only provide rough estimates of the N_CCN, which is reflected in the high median RD. The results for N1 and N2 schemes are similar in that they both predict the overall mean N_CCN well (slopes of approximately 1.0) but with large median RDs. Compared to the N1 scheme, the N2 scheme is better because of the lower median RD. Compared to the first category (the N1 and N2 schemes), the second category (the K1, K2, and K3 schemes) predicts N_CCN better because of the lower median RD. The results for K1 and K2 are similar in that they both overestimate N_CCN by approximately 10 % (slopes of approximately 1.1) with similar median RDs. The reason for the N_CCN overestimation is that the constant κ of 0.3 and the real-time bulk κ_chem are both greater than the κ_CCN at each season. In winter, the κ_CCN was highest and the difference between the κ_CCN and the parameterized κ in K1 and K2 scheme was lowest, causing the best prediction of N_CCN among the four seasons. Owing to the largest difference between the κ_CCN and the parameterized κ, the N_CCN prediction was worst in summer for the K1 scheme and in autumn for the K2 scheme. The K3 scheme appears to be the best one for N_CCN prediction among the five schemes, which is reflected in the lowest median RDs and the fit slope of ∼1.0 for different seasons. The evaluations of the five schemes for the N_CCN prediction at each SS condition and each season are provided in Fig. S8 in the Supplement.

Figure 8 Relationships between the particle hygroscopicity factor (κ) and diameter (D_p) observed at different stations. Lines are power-law fits of κ vs. D_p.

The K3 scheme provides an improved prediction of N_CCN, which is obvious when compared to N1 and N2 schemes. Compared to K1 and K2 schemes, the K3 scheme reduced the approximately 10 % overestimation of N_CCN because the fitting slope decreased ∼0.1 on average. We simply evaluate the effects of the 10 % overestimation in N_CCN on predictions of cloud radiative forcing and precipitation. The methods are in Sect. S3 in the Supplement and Wang et al. (2019). Essentially, an overestimation of N_CCN leads to an overestimate of the number concentration of cloud droplet (N_C) in models. Theoretically, it can reduce a 3.2 % overestimation of cloud optical thickness, corresponding to global average difference of 1.28 Wm⁻² when assuming the cloud shortwave cooling effect of 40 Wm⁻² (Lee et al., 1997), which amounts to approximately one-third of the direct radiative forcing from a doubling CO₂. Additionally, the overestimation in N_CCN (and N_C) leads to underestimate of the strength of the autoconversion process in cloud (Liu et al., 2006), thereby suppressing precipitation. Therefore, although ACSM measurements can derive κ_chem and thus predict N_CCN, the monodisperse CCN measurements are still important to obtain the κ–D_p relationship and thus improve the predictions of N_CCN (and N_C) and climate.

Figure 8 compared the κ–D_p relationship measured at different regions. The κ–D_p relationship measured at Melpitz is similar to that measured at other rural regions with similar κ–D_p power-law fitting results, e.g., the Vavihill station in Sweden (Fors et al., 2011) and the Xinken station in China (Eichler et al., 2008). Therefore, the κ–D_p power-law fit measured at Melpitz could be applied to predict N_CCN for these rural regions. We conducted a CCN closure test to support this conclusion. Due to lacking the data of PNSD and CCN measurements at Vavihill and Xinken stations, we applied the κ–D_p power-law fitting measured at the two rural stations (green and purple lines in Fig. 8) to predict the N_CCN at Melpitz. Good prediction results were obtained with mean deviations of ∼1 % (Fig. S9 in the Supplement). However, it may cause considerable deviations for different aerosol background regions, e.g., the suburb stations in Xingtai, China (Wang et al., 2018a), Xinzhou, China (Chen et al., 2022), and Paris, France (Mazoyer et al., 2019), the coast of Barbados (Kristensen et al., 2016), the Amazon rainforest (Pöhlker et al., 2016), and the urban stations in Budapest, Hungary (Salma et al., 2021), Guangzhou, China (Chen et al., 2022), and Shanghai, China (Ye et al., 2013), because their κ–D_p relationships are different from that measured at Melpitz.

4 Conclusions

Aerosol particle activation plays an important role in determining N_C, thereby affecting cloud microphysics, precipitation processes, radiation, and climate. To reduce the uncertainties and gain more confidence in the simulations on AIEs, long-term measurements of aerosol activation characteristics are essential. However, they are still rarely reported. Based on more than 4 years of comprehensive measurements conducted at the central European ACTRIS site of Melpitz, Germany, this study presents a systematic seasonal analysis of aerosol activation characteristics and N_CCN predictions.

Over the whole period at Melpitz, the median N_CCN and AR increased from 399 to 2144 cm⁻³ and 0.10 to 0.48, with SS increasing from 0.1 % to 0.7 %, respectively. Aerosol activation characteristics are highly variable across seasons, especially at relatively low SS conditions. For instance, at SS=0.1 %, the median N_CCN and AR in winter are 1.6 and 2.3 times higher than the summer values, respectively. Aerosol particle activation depends on its physical and chemical properties. In summer, the highest N_aero, smallest GMD, and lowest κ_chem all contribute to the lowest AR and N_CCN among the four seasons, and the reverse holds true in winter. Additionally, in summer, the steepest PNSD in the 40–200 nm size range and the lowest κ_chem cause the strongest sensitivity of N_CCN and AR to SS even though the spread in κ_CCN is narrowest.

Both κ and the mixing state are size-dependent, thereby varying with SS. The median κ_CCN decreases from 0.27 to 0.19 as SS increases from 0.1 % to 0.7 %, which was less than the median bulk κ_chem. The seasonal trend of κ_CCN was similar to that of κ_chem, especially at relatively low SS conditions. The lowest κ_CCN and κ_chem were observed in summer, which related to the highest organic mass fraction in particles. Aerosol particles were more internally mixed in summer and spring, whereas they were less internally mixed in winter and autumn. In cold seasons, the increasing anthropogenic emissions linked to house heating mixed with the aged particles from long-range transport, which could decrease the degree of external mixing of particles. As D_p increases, κ_CCN increases at the D_p range of ∼40 to 100 nm and almost stays constant at the D_p range of 100 to 200 nm, whereas the $(D_{\mathrm{75}}-D_{\mathrm{25}})/D_{\mathrm{c}}$ monotonically decreases. The relationships of $(D_{\mathrm{75}}-D_{\mathrm{25}})/D_{\mathrm{c}}$ vs. D_p and κ vs. D_p are both fitted well by a power-law function for each season.

Five activation schemes are evaluated on the N_CCN predictions. Compared to using the classic N_CCN–SS or AR–SS power-law fits to predict N_CCN, the prediction is better when using the real-time PNSD combined with the parameterized κ, including a constant κ of 0.3, the bulk κ_chem, and the κ–D_p power-law fit. However, assuming a constant κ of 0.3 recommended for continental aerosol (Andreae and Rosenfeld, 2008) or the bulk κ_chem calculated from aerosol chemical composition causes significant overestimations of the N_CCN with median values of approximately 10 % for all SS conditions, which theoretically causes 3.2 % overestimation of cloud optical thickness, amounting to approximately one-third of the direct radiative forcing from a doubling CO₂ (Lee et al., 1997). Moreover, the strength of the autoconversion process in cloud could be underestimated (Liu et al., 2006). Size-resolved κ improves the N_CCN prediction. We recommend applying the κ–D_p power-law fit for N_CCN prediction, which obtains the best prediction among the five schemes.

The κ–D_p power-law fit presented in this study could apply to other rural regions. However, it may cause considerable deviations for different aerosol background regions. For instance, using the κ–D_p power-law fit measured in urban Budapest (Salma et al., 2021) for predicting Melpitz N_CCN could cause underestimation of N_CCN with a median value of 39 % for all SS conditions. Additionally, the seasonal difference of the κ–D_p relationship needs to be considered carefully for N_CCN prediction. At Melpitz, if the κ–D_p power-law fit measured in summer was used for predicting N_CCN in winter, it could cause underestimation of N_CCN with a median value of 13 % for all SS conditions. Although the κ–D_p relationships are similarly measured in rural stations, when comparing the different urban stations (e.g., Shanghai vs. Budapest in Fig. 8), these relationships are clearly different, and the reasons for the difference are still unclear. Thus, long-term monodisperse CCN measurements are still needed not only to obtain the κ–D_p relationships for different regions and for different seasons, but also to further investigate the reasons for the difference of the κ–D_p relationships measured at same type of regions. Finally, for the purpose of predicting N_CCN, the measurements of monodisperse CCN and particle chemical compositions are more expected, compared to the polydisperse CCN measurements.

Appendix A: Notation list

A	comprehensive parameter for ${\mathit{\sigma }}_{s/a}$, Mw, R, T, and ρw in Eq. (2b)
a	lower limit for calculating critical diameters at the set-nominal supersaturations in Eq. (1)
ACIs	aerosol and cloud interactions
ACSM	aerosol chemical species monitor
ACTRIS	Aerosol, Clouds and Trace Gases Research Infrastructure
AF	activated fraction, i.e., NCCN/NCN
AIEs	aerosol indirect effects
AR	activation ratio, i.e., NCCN/Naero
b	upper limit for calculating critical diameters at the set-nominal supersaturations in Eq. (1)
BC	black carbon
CN	condensation nuclei
CCN	cloud condensation nuclei
CCNC	cloud condensation nuclei counter
coef	coefficient in κ–Dp power-law fit
CPC	condensation particle counter
Dp	diameter of the dry particle
Dc	critical diameter of the dry particle
DX	D at which X % of the particles are activated
$(D_{\mathrm{75}}-D_{\mathrm{25}})/D_{\mathrm{c}}$	degree of external mixture
D-MPSS	dual-mobility particle size spectrometer
DMA	differential mobility analyzer
eBC	equivalent black carbon
fBC	mass fraction of BC in submicron aerosol
fnitrate	mass fraction of nitrate in submicron aerosol
forg	mass fraction of organics in submicron aerosol
fsulfate	mass fraction of sulfate in submicron aerosol
GMD	geometric mean diameter of PNSD
Mw	molecular weight of water
Naero	number concentration of aerosol with a Dp range of 10 to 800 nm
NC	number concentration of cloud droplet
NCN	number concentration of CN
NCCN	number concentration of CCN
NPF	new particle formation
OA	organic aerosol
PM10	particulate matter with the Dp<10 µm
PNSD	particle number size distribution
R	universal gas constant
R2	coefficient of determination
RD	relative deviation between the predicted NCCN and the measured one
SS	supersaturation
SOA	secondary organic aerosol
T	temperature
σs	the shape of the sigmoid function
${\mathit{\sigma }}_{s/a}$	droplet surface tension
κ	hygroscopicity factor of aerosol particle
κi	κ of each component
κCCN	κ calculated from the monodisperse CCN measurements
κchem	κ calculated from the aerosol chemical measurements
εi	volume fraction of each component
ρw	density of the liquid water