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

Abstract

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, $N_{\mathrm{CCN}}$). (1) The overall CCN activation characteristics at Melpitz are provided. As supersaturation (SS) increases from 0.1 % to 0.7 %, the median $N_{\mathrm{CCN}}$ increases from 399 to 2144 cm${}^{-\mathrm{3}}$, which represents 10 % to 48 % of the total particle number concentration with a diameter range of 10–800 nm, while the median hygroscopicity factor ($\mathit{\kappa }$) and critical diameter ($D_{\mathrm{c}}$) 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 $\mathrm{SS}=\mathrm{0.1}$ %, the median $N_{\mathrm{CCN}}$ and activation ratio (AR) in winter are 1.6 and 2.3 times higher than the summer values, respectively. (3) Both$\mathit{\kappa }$ and the mixing state are size-dependent. As the particle diameter ($D_{\mathrm{p}}$) increases, $\mathit{\kappa }$ increases at $D_{\mathrm{p}}$ of $\sim \mathrm{40}$ to 100 nm and almost stays constant at $D_{\mathrm{p}}$ of 100 to 200 nm, whereas the degree of the external mixture keeps decreasing at $D_{\mathrm{p}}$ of $\sim \mathrm{40}$ to 200 nm. The relationships of $\mathit{\kappa }$ vs. $D_{\mathrm{p}}$ and degree of mixing vs. $D_{\mathrm{p}}$ were both fitted well by a power-law function. (4) Size-resolved$\mathit{\kappa }$ improves the $N_{\mathrm{CCN}}$ prediction. We recommend applying the$\mathit{\kappa }$–$D_{\mathrm{p}}$ power-law fit for $N_{\mathrm{CCN}}$ prediction at Melpitz, which performs better than using the constant $\mathit{\kappa }$ of 0.3 and the $\mathit{\kappa }$ derived from particle chemical compositions and much better than using the$N_{\mathrm{CCN}}$ (AR) vs. SS relationships. The $\mathit{\kappa }$–$D_{\mathrm{p}}$ power-law fit measured at Melpitz could be applied to predict $N_{\mathrm{CCN}}$ for other rural regions. For the purpose of improving the prediction of $N_{\mathrm{CCN}}$, long-term monodisperse CCN measurements are still needed to obtain the $\mathit{\kappa }$–$D_{\mathrm{p}}$ 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 $\mathit{\kappa }$ 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 $\mathit{\kappa }$ and particle diameter ($D_{\mathrm{p}}$) vary and the reciprocal relationship between $\mathit{\kappa }$ and the third power of the critical $D_{\mathrm{p}}$ ($D_{\mathrm{c}}^{\mathrm{3}}$) 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 $\mathit{\kappa }$ still predicted CCN number concentration ($N_{\mathrm{CCN}}$) 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 $\mathit{\kappa }$ values of $\mathrm{0.3}\pm \mathrm{0.1}$ and $\mathrm{0.7}\pm \mathrm{0.2}$ can be representative for continental and marine aerosol, respectively, which has been widely used to predict $N_{\mathrm{CCN}}$. The regional variability should be emphasized because the mean $\mathit{\kappa }$ measured in urban, rural, and forest exhibits significant differences. For instance, Sihto et al. (2011) suggested an average $\mathit{\kappa }$ of 0.18 to predict the CCN activation well in boreal forest conditions in Hyytiälä, Finland. A fixed $\mathit{\kappa }$ of 0.31 suffices to calculate the $N_{\mathrm{CCN}}$ in a suburban site located in the center of the North China Plain (Wang et al., 2018a). The mean $\mathit{\kappa }$ is 0.5 in a near-coast background station (CESAR Tower) in the Netherlands (Schmale et al., 2018). The median $\mathit{\kappa }$ ranges from 0.02 to 0.16 at $\mathrm{SS}=\mathrm{0.1}$–1.0 % in an urban background site in Budapest, Hungary (Salma et al., 2021). Therefore, the assumption of a constant $\mathit{\kappa }=\mathrm{0.3}$ may not be appropriate when trying to predict $N_{\mathrm{CCN}}$ for different continental regions.

Additionally, some experiments, especially conducted on more diverse particulate sources, have indicated that chemistry does play an important role in $N_{\mathrm{CCN}}$ variability (e.g., Nenes et al., 2002; Petters and Kreidenweis, 2007; Rose et al., 2010). Not only the bulk chemical composition with a constant $\mathit{\kappa }$ should be considered for $N_{\mathrm{CCN}}$ 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 $N_{\mathrm{CCN}}$ 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 $\sim \mathrm{1}$ % (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 $\mathit{\kappa }$ 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 $\mathit{\kappa }$ of small particles may exceed the $\mathit{\kappa }$ of the larger ones (Wang et al., 2018a). If the $\mathit{\kappa }$ of organic aerosol increases from 0.05 to 0.15, the global average aerosol radiative forcing would decrease by $\sim \mathrm{1}$ W m${}^{-\mathrm{2}}$, 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 $N_{\mathrm{CCN}}$ 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 $\sim \mathrm{1}$-year measurements. Using the long-term (of most $\mathit{>}\mathrm{1}$ 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 $N_{\mathrm{CCN}}$ predictions. We present therefore the long-term observations and seasonal cycles of various particle activation variables such as $N_{\mathrm{CCN}}$, activation ratio, critical diameter, size-resolved $\mathit{\kappa }$, and mixing state. Furthermore, we evaluated the accuracy of $N_{\mathrm{CCN}}$ calculated from five different activation schemes and finally provide recommendations on $N_{\mathrm{CCN}}$ 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${}^{\circ }$ N, 12.93${}^{\circ }$ 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.

[Figure omitted. See PDF]

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 PM${}_{\mathrm{10}}$ 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 ($N_{\mathrm{CN}}$) and through a cloud condensation nuclei counter (CCNC, model 100, Droplet Measurement Technologies; Roberts and Nenes, 2005) to measure the $N_{\mathrm{CCN}}$. Thus, the size-dependent activated fraction (AF, $N_{\mathrm{CCN}}$/$N_{\mathrm{CN}}$) curve, i.e., the AF at a certain diameter ($D_{\mathrm{p}}$) 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 $D_{\mathrm{p}}$ 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 $\sim \mathrm{2.5}$ 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 $\mathrm{SS}\mathit{>}\mathrm{0.2}$ % 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 ($N_{\mathrm{CCN}}$/$N_{\mathrm{CN}}$ vs. $D_{\mathrm{p}}$) 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 $N_{\mathrm{CCN}}$/$N_{\mathrm{CN}}$ 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,

1$$\mathrm{AF}=a+b/\left(\mathrm{1}+\exp \left(-{\displaystyle \frac{D_{\mathrm{p}}-D_{\mathrm{c}}}{{\mathit{\sigma }}_{\mathrm{s}}}}\right)\right),$$ where $a$ is the offset from 0 in the $y$ direction and $b$ is the height of the upper plateau of the sigmoidal function, $D_{\mathrm{c}}$ is the critical diameter, and ${\mathit{\sigma }}_{\mathrm{s}}$ 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., $N_{\mathrm{CCN}}$.

The critical diameter ($D_{\mathrm{c}}$) of dry particles, $\mathit{\kappa }$, 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 ($\sim \mathrm{1}$) rather than displaying an intermittent mutation. $D_{\mathrm{c}}$ 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). $D_{\mathrm{75}}$ and $D_{\mathrm{25}}$ 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 $\mathit{\kappa }$ with $(D_{\mathrm{75}}-D_{\mathrm{25}})/D_{\mathrm{c}}=\mathrm{0}$, whereas a distribution of different $\mathit{\kappa }$ 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 $\mathit{\kappa }$ distributions derived from parallel monodisperse CCN measurements and hygroscopicity tandem differential mobility analyzer (HTDMA) measurements.

According to the derivation of $\mathit{\kappa }$-Köhler theory (Petters and Kreidenweis, 2007), the $\mathit{\kappa }$ can be calculated from $D_{\mathrm{c}}$ at a given SS: 2a$$\mathit{\kappa }={\displaystyle \frac{\mathrm{4}{A}^{\mathrm{3}}}{\mathrm{27}{D}_{\mathrm{c}}^{\mathrm{3}}{\ln }^{\mathrm{2}}\left(\mathrm{1}+\mathrm{SS}/\mathrm{100}\right)}},$$ with 2b$$A={\displaystyle \frac{\mathrm{4}{\mathit{\sigma }}_{s/a}{M}_{\mathrm{w}}}{\mathrm{RT}{\mathit{\rho }}_{\mathrm{w}}}},$$ where ${\mathit{\sigma }}_{s/a}$ is the droplet surface tension (assumed to be that of pure water, 0.0728 nm${}^{-\mathrm{2}}$), $M_{\mathrm{w}}$ is the molecular weight of water, $R$ is the universal gas constant, $T$ is the absolute temperature, ${\mathit{\rho }}_{\mathrm{w}}$ is the density of water, and $A$ can be considered a function of $T$. Thus, the size-resolved $\mathit{\kappa }$ (pair of $\mathit{\kappa }$ and $D_{\mathrm{c}}$) can be obtained at each SS cycle. Our monodisperse CCN measurements provide the size-resolved $\mathit{\kappa }$ within $D_{\mathrm{p}}$ ($D_{\mathrm{c}}$) of $\sim \mathrm{40}$–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 $\mathit{\kappa }$-Köhler equation, and when $\mathit{\kappa }$ is less than 0.2, it causes a slight bias in calculating $\mathit{\kappa }$ (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 ($\mathit{\rho }$) and hygroscopicity factor ($\mathit{\kappa }$) for each component.

Species	NH${}_{\mathrm{4}}$NO${}_{\mathrm{3}}$	(NH${}_{\mathrm{4}}{)}_{\mathrm{2}}$SO${}_{\mathrm{4}}$	NH${}_{\mathrm{4}}$HSO${}_{\mathrm{4}}$	H${}_{\mathrm{2}}$SO${}_{\mathrm{4}}$	Organics	BC
$\mathit{\rho }$ (kg m${}^{-\mathrm{3}}$)	1720	1769	1780	1830	1400	1700
$\mathit{\kappa }$	0.67	0.61	0.61	0.92	0.1	0

Besides deriving it from the monodisperse CCN measurements, $\mathit{\kappa }$ can be derived from the ACSM and MAAP chemical composition measurements (${\mathit{\kappa }}_{\mathrm{chem}}$) using the Zdanovskii–Stokes–Robinson (ZSR) mixing rule (Zdanovskii, 1948; Stokes and Robinson, 1966) combined with $\mathit{\kappa }$-Köhler theory: 3$${\mathit{\kappa }}_{\mathrm{chem}}=\sum _i{\mathit{\epsilon }}_i{\mathit{\kappa }}_i,$$ where ${\mathit{\kappa }}_i$ and ${\mathit{\epsilon }}_i$ mean the $\mathit{\kappa }$ and volume fraction for each component, respectively, and $i$ is the number of the component in the mixture. The ${\mathit{\epsilon }}_i$ was derived from its measured component $i$ mass concentration and density (${\mathit{\rho }}_i$). A simple ion-pairing scheme (Gysel et al., 2007) was used in this study with the ${\mathit{\kappa }}_i$ and ${\mathit{\rho }}_i$ values listed in Table 1 (Wu et al., 2015). A $\mathit{\kappa }$ of 0.1 is used for particulate organics (Dusek et al., 2010; Gunthe et al., 2009, 2011). For black carbon, we use a $\mathit{\kappa }$ 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 $D_{\mathrm{p}}\mathit{>}{D}_{\mathrm{c}}$ 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, $D_{\mathrm{c}}$ plays a critical role on diagnosing $N_{\mathrm{CCN}}$ in models, which can be derived from $\mathit{\kappa }$ parameterization at a given SS. When $\mathit{\kappa }$ is obtained, $D_{\mathrm{c}}(\mathit{\kappa },\mathrm{SS})$ is calculated from Eq. (2a). And, assuming an internal mixture, the predicted $N_{\mathrm{CCN}}$ is the integration of the PNSD from $D_{\mathrm{c}}$, that is, 4$$\mathrm{Predicted}{N}_{\mathrm{CCN}}=\underset{D_{\mathrm{c}}}{\overset{\mathrm{800}}{\int }}\mathrm{PNSD}\left(D_{\mathrm{p}}\right)\mathrm{d}{D}_{\mathrm{p}}.$$

Figure 2

Relationship between CCN number concentration ($N_{\mathrm{CCN}}$) and supersaturation (SS) measured at Melpitz and other stations.

[Figure omitted. See PDF]

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 $N_{\mathrm{CCN}}$ and activation ratio (AR, i.e., ratio of $N_{\mathrm{CCN}}$ to total aerosol number concentration with a diameter range of 10 to 800 nm, $N_{\mathrm{aero}}$). At Melpitz, the median $N_{\mathrm{CCN}}$ and AR increase from 399 to 2144 cm${}^{-\mathrm{3}}$ and 0.10 to 0.48 when SS increases from 0.1 % to 0.7 %. As shown in Fig. 2, the $N_{\mathrm{CCN}}$ 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 $N_{\mathrm{CCN}}$ measured in polluted regions (e.g., Rose et al., 2010; Deng et al., 2011; Kim et al., 2014; Varghese et al., 2016), the Melpitz $N_{\mathrm{CCN}}$ is much lower.

Figure 3

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

[Figure omitted. See PDF]

Figure 3a presents the $N_{\mathrm{CCN}}$ 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 $N_{\mathrm{CCN}}$–SS power-law fit are 2851 cm${}^{-\mathrm{3}}$ and 0.75, respectively, which are within the range of values for continental aerosol (slope parameter of 600–3500 cm${}^{-\mathrm{3}}$ 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 $N_{\mathrm{CCN}}$ and AR to the variation in SS, which is highest in summer and lowest in winter. The seasonal variations of $N_{\mathrm{CCN}}$ and AR at $\mathrm{SS}=\mathrm{0.1}$ % and 0.7 % are shown in Fig. 3b. In summer, the median $N_{\mathrm{CCN}}$ and AR are both lowest at $\mathrm{SS}=\mathrm{0.1}$ %, which contributed to the largest sensitivity of $N_{\mathrm{CCN}}$ 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 $N_{\mathrm{CCN}}$ 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 $D_{\mathrm{c}}$ will change the $N_{\mathrm{CCN}}$ and AR much more than those in winter where the PNSD looks broader, causing the strong sensitivity of $N_{\mathrm{CCN}}$ and AR to SS.

Figure 4

Seasonal variations of (a) aerosol particle number size distribution (d$N_{\mathrm{aero}}$/dlog$D_{\mathrm{p}}$ vs. $D_{\mathrm{p}}$, where $D_{\mathrm{p}}$ is particle diameter), (b) total aerosol number concentration with a $D_{\mathrm{p}}$ range of 10 to 800 nm ($N_{\mathrm{aero}}$) and geometric mean diameter of the particles (GMD), and (c) mass concentration and ratio of each component in aerosol particle with $D_{\mathrm{p}}$ less than 1 $\mathrm{\mu }$m and the hygroscopicity factor calculated from the chemical composition (${\mathit{\kappa }}_{\mathrm{chem}}$). Dots represent the median values. Shaded areas represent the values in the range from the 25th to 75th percentile.

[Figure omitted. See PDF]

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 $D_{\mathrm{p}}\mathit{<}\mathrm{100}$ nm accounted for the largest portion of the PNSD (Fig. S4 in the Supplement), resulting in the highest $N_{\mathrm{aero}}$ 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 ${\mathit{\kappa }}_{\mathrm{chem}}$, 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 $N_{\mathrm{CCN}}$ and AR both kept relatively low values in summer, especially at low-SS conditions (e.g., at $\mathrm{SS}=\mathrm{0.1}$ %). On the contrary, in winter, the relatively low number concentration of Aitken-mode particles caused the lowest $N_{\mathrm{aero}}$ 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 ${\mathit{\kappa }}_{\mathrm{chem}}$ (median value of 0.34). Taking all three together, the lowest $N_{\mathrm{aero}}$, the largest GMD, and the highest ${\mathit{\kappa }}_{\mathrm{chem}}$ contribute to the highest AR value in winter at each SS condition. The relationships between ${\mathit{\kappa }}_{\mathrm{chem}}$ and each particle component and the correlations among seasonal median values of $N_{\mathrm{aero}}$, GMD, and ${\mathit{\kappa }}_{\mathrm{chem}}$ 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 (${\mathit{\kappa }}_{\mathrm{CCN}}$) at a supersaturation (SS) of 0.1 % and 0.7 % and the hygroscopicity factor calculated from particle chemical composition (${\mathit{\kappa }}_{\mathrm{chem}}$), (b) the critical diameter of dry particle for activation ($D_{\mathrm{c}}$) at $\mathrm{SS}=\mathrm{0.1}$ % and 0.7 %, and (c) the degree of external mixture $\left(\right(D_{\mathrm{75}}-D_{\mathrm{25}})/D_{\mathrm{c}})$ at $SS=\mathrm{0.1}$ % and 0.7 %. The definitions of $D_{\mathrm{75}}$ and $D_{\mathrm{25}}$ are the $D_{\mathrm{p}}$ 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 omitted. See PDF]

Figure 6

(a) Relationship between the hygroscopicity factor calculated from monodisperse CCN measurements (${\mathit{\kappa }}_{\mathrm{CCN}}$) and particle diameter ($D_{\mathrm{p}}$), and (b) degree of external mixture $\left(\right(D_{\mathrm{75}}-D_{\mathrm{25}})/D_{\mathrm{c}})$ vs. $D_{\mathrm{p}}$ at each season. The definitions of $D_{\mathrm{75}}$ and $D_{\mathrm{25}}$ are the $D_{\mathrm{p}}$ 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.

[Figure omitted. See PDF]

Table 2

Seasonal median values of the hygroscopicity factor derived from the chemical composition (${\mathit{\kappa }}_{\mathrm{chem}}$), the hygroscopicity factor derived from monodisperse CCN measurements (${\mathit{\kappa }}_{\mathrm{CCN}}$), the critical diameter of dry particle for activation ($D_{\mathrm{c}}$), and the degree of external mixture (($D_{\mathrm{75}}$ – $D_{\mathrm{25}}$)/$D_{\mathrm{c}}$) at each supersaturation (SS) condition. The unit of $D_{\mathrm{c}}$ is nanometers (nm).

Parameters	SS (%)	All datasets	Spring	Summer	Autumn	Winter
${\mathit{\kappa }}_{\mathrm{chem}}$	–	0.30	0.32	0.24	0.31	0.34
${\mathit{\kappa }}_{\mathrm{CCN}}$	0.1	0.27	0.31	0.22	0.26	0.29
	0.2	0.27	0.32	0.23	0.24	0.30
	0.3	0.23	0.26	0.20	0.21	0.27
	0.5	0.19	0.22	0.18	0.18	0.22
	0.7	0.19	0.20	0.18	0.17	0.20
$D_{\mathrm{c}}$	0.1	176	167	187	177	170
	0.2	111	104	116	114	106
	0.3	89	85	93	92	84
	0.5	67	64	69	69	64
	0.7	54	53	55	55	53
$(D_{\mathrm{75}}-D_{\mathrm{25}})/D_{\mathrm{c}}$	0.1	0.15	0.13	0.12	0.18	0.19
	0.2	0.18	0.15	0.14	0.22	0.23
	0.3	0.19	0.15	0.14	0.24	0.23
	0.5	0.20	0.15	0.14	0.25	0.25
	0.7	0.20	0.17	0.15	0.27	0.27

3.2 Size-resolved particle hygroscopicity factor and mixing state

The hygroscopicity factor and the mixing state directly influence the $D_{\mathrm{c}}$ and the shape of the AF curve, thereby changing the $N_{\mathrm{CCN}}$ 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 ${\mathit{\kappa }}_{\mathrm{chem}}$ and $\mathit{\kappa }$ calculated from monodisperse CCN measurements (${\mathit{\kappa }}_{\mathrm{CCN}}$) at SS of 0.1 % and 0.7 %. Their seasonal median values are summarized in Table 2. At Melpitz, the median ${\mathit{\kappa }}_{\mathrm{CCN}}$ decreased from 0.27 to 0.19 as SS increased from 0.1 % to 0.7 %, which was less than the median bulk ${\mathit{\kappa }}_{\mathrm{chem}}$ of 0.3. The seasonal variation of ${\mathit{\kappa }}_{\mathrm{CCN}}$ at SS of 0.1 % is similar to that of ${\mathit{\kappa }}_{\mathrm{chem}}$, whereas the seasonal trend in ${\mathit{\kappa }}_{\mathrm{CCN}}$ is much weaker at $\mathrm{SS}=\mathrm{0.7}$ %. Essentially, the relationship between ${\mathit{\kappa }}_{\mathrm{CCN}}$ and SS is determined by the ${\mathit{\kappa }}_{\mathrm{CCN}}$ vs. $D_{\mathrm{p}}$ relationship. The ${\mathit{\kappa }}_{\mathrm{CCN}}$ values at SS of 0.1 % and 0.7 % correspond to the median $D_{\mathrm{c}}$ (i.e., $D_{\mathrm{p}}$) 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 $\sim \mathrm{300}$ nm (Poulain et al., 2020). Thus, ${\mathit{\kappa }}_{\mathrm{chem}}$ may be representative for the larger particles rather than for the smaller particles. Owing to the positive correlation between $\mathit{\kappa }$ and $D_{\mathrm{p}}$ (Fig. 6a), the ${\mathit{\kappa }}_{\mathrm{chem}}$ representing the larger particles could be greater than the ${\mathit{\kappa }}_{\mathrm{CCN}}$ for the smaller particles. Figure 5b depicts the monthly variation of $D_{\mathrm{c}}$ at SS of 0.1 % and 0.7 %, which shows the opposite trend to ${\mathit{\kappa }}_{\mathrm{CCN}}$ (SS) because of the negative correlation of $D_{\mathrm{c}}^{\mathrm{3}}$ (SS) vs. $\mathit{\kappa }$ (SS) shown in Eq. (2a). Compared to the $D_{\mathrm{c}}$ at lower SS conditions (e.g., 0.1 %), $D_{\mathrm{c}}$ has a more significant seasonal trend at higher SS conditions (e.g., 0.7 %). At $\mathrm{SS}=\mathrm{0.7}$ %, the low ${\mathit{\kappa }}_{\mathrm{CCN}}$ caused the large$D_{\mathrm{c}}$ in summer, whereas the high ${\mathit{\kappa }}_{\mathrm{CCN}}$ caused the small $D_{\mathrm{c}}$ 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 $\mathrm{SS}=\mathrm{0.1}$–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 $\mathrm{SS}=\mathrm{0.1}$–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, ${\mathit{\kappa }}_{\mathrm{CCN}}$ (and $(D_{\mathrm{75}}-D_{\mathrm{25}})/D_{\mathrm{c}})$ vs. $D_{\mathrm{p}}$ relationships determine the relationship between ${\mathit{\kappa }}_{\mathrm{CCN}}$ (and $(D_{\mathrm{75}}-D_{\mathrm{25}})/D_{\mathrm{c}})$ and SS. Monodisperse CCN measurements provide the size-resolved $\mathit{\kappa }$ and $(D_{\mathrm{75}}-D_{\mathrm{25}})/D_{\mathrm{c}}$. At a given SS condition, ${\mathit{\kappa }}_{\mathrm{CCN}}$ represents the $\mathit{\kappa }$ of particles at $D_{\mathrm{p}}=D_{\mathrm{c}}$, and the same is true for $(D_{\mathrm{75}}-D_{\mathrm{25}})/D_{\mathrm{c}}$. As shown in Fig. 6a, ${\mathit{\kappa }}_{\mathrm{CCN}}$ increases with $D_{\mathrm{p}}$ at the $D_{\mathrm{p}}$ range of $\sim \mathrm{40}$ to 100 nm, whereas ${\mathit{\kappa }}_{\mathrm{CCN}}$ almost stays constant at $D_{\mathrm{p}}$ of 100 to 200 nm for all seasons. Additionally, the increase in ${\mathit{\kappa }}_{\mathrm{CCN}}$ with $D_{\mathrm{p}}$ varies with season. The ${\mathit{\kappa }}_{\mathrm{CCN}}$ vs. $D_{\mathrm{p}}$ relationship is fitted by a power-law function at each season. In summer, there is the lowest slope parameter in the ${\mathit{\kappa }}_{\mathrm{CCN}}$ vs. $D_{\mathrm{p}}$ power-law fit, meaning that the ${\mathit{\kappa }}_{\mathrm{CCN}}$ is least sensitive to $D_{\mathrm{p}}$. 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 ($D_{\mathrm{p}}\mathit{<}\mathrm{100}$ nm) are associated with NPF and the SOA formation. NPF is a complex process which depends on the availability of condensing material (H${}_{\mathrm{2}}$SO${}_{\mathrm{4}}$ 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 ${\mathit{\kappa }}_{\mathrm{CCN}}$ values at SS of 0.1 % and 0.7 % are closer, i.e., the weaker sensitivity of ${\mathit{\kappa }}_{\mathrm{CCN}}$ to $D_{\mathrm{p}}$ in summer. Figure 6b presents the $(D_{\mathrm{75}}-D_{\mathrm{25}})/D_{\mathrm{c}}$ vs. $D_{\mathrm{p}}$ relationship. As particle size increases, $(D_{\mathrm{75}}-D_{\mathrm{25}})/D_{\mathrm{c}}$ decreases at $D_{\mathrm{p}}$ of $\sim \mathrm{40}$ 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 $\mathit{\kappa }$ becomes more uniform. The ($D_{\mathrm{75}}-D_{\mathrm{25}})/D_{\mathrm{c}}$ vs. $D_{\mathrm{p}}$ 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 $D_{\mathrm{p}}$, 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.

Category	Scheme	Introduction
First category: $N_{\mathrm{CCN}}$–SS or AR–SS empirical fit	N1	$N_{\mathrm{CCN}}$–SS power-law fits shown in Table 3
	N2	Real-time $N_{\mathrm{aero}}$ combined with AR–SS power-law fits shown in Table 3
Second category: real-time PNSD combined with the parameterized $\mathit{\kappa }$	K1	Real-time PNSD combined with a constant $\mathit{\kappa }$ of 0.3
	K2	Real-time PNSD combined with the real-time bulk ${\mathit{\kappa }}_{\mathrm{chem}}$
	K3	Real-time PNSD combined with $\mathit{\kappa }$–$D_{\mathrm{p}}$ power-law fits shown in Fig. 6a

Figure 7

Predicted vs. measured CCN number concentration ($N_{\mathrm{CCN}}$) for different seasons. The predicted $N_{\mathrm{CCN}}$ 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 R${}^{\mathrm{2}}$ of the linear regression and the median relative deviation (RD) between the predicted and measured $N_{\mathrm{CCN}}$ 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.

[Figure omitted. See PDF]

3.3

$N_{\mathrm{CCN}}$ prediction at Melpitz

$N_{\mathrm{CCN}}$ plays an important role in modeling the formation and evolution of clouds. In this section, we evaluate the accuracy of $N_{\mathrm{CCN}}$ predicted from five schemes. Table 3 introduces the five schemes, which can be summarized into two categories. From polydisperse CCN measurements, the $N_{\mathrm{CCN}}$ (AR) and SS relationships can be obtained, and their fitting results can be used to predict $N_{\mathrm{CCN}}$ 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 $N_{\mathrm{CCN}}$ using the real-time PNSD combined with the parameterized $\mathit{\kappa }$ ($D_{\mathrm{c}}$), 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 $\mathit{\kappa }$. The K1 scheme used a fixed $\mathit{\kappa }$ 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 ${\mathit{\kappa }}_{\mathrm{chem}}$ over all data settings at Melpitz. The K2 scheme used the bulk ${\mathit{\kappa }}_{\mathrm{chem}}$ calculated from aerosol chemical composition, which is also non-size-dependent but changes over time. The K3 scheme used the $\mathit{\kappa }$–$D_{\mathrm{p}}$ power-law fit results shown in Fig. 6a, which are size-dependent without temporal variations at each season. Applying the $\mathit{\kappa }$–$D_{\mathrm{p}}$ power-law equation into Eq. (2a), $D_{\mathrm{c}}$ can be derived as function of SS, 5$$D_{\mathrm{c}}={\left({\displaystyle \frac{\mathrm{4}\times A^{\mathrm{3}}}{\mathrm{27}\times \mathrm{coef}\times {\ln }^{\mathrm{2}}\left(\mathrm{1}+\mathrm{SS}/\mathrm{100}\right)}}\right)}^{\frac{\mathrm{1}}{\mathrm{slope}+\mathrm{3}}},$$ where the slope and coef represent the slope parameter and the coefficient in the $\mathit{\kappa }$–$D_{\mathrm{p}}$ power-law fit. Subsequently, the predicted $N_{\mathrm{CCN}}$ can be calculated through Eq. (4). The second category assumed that aerosol particles are internally mixed at a particular $D_{\mathrm{p}}$, as used in many previous $N_{\mathrm{CCN}}$ 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 $N_{\mathrm{CCN}}$ and the measured one, and its slope represents the mean ratio of the predicted $N_{\mathrm{CCN}}$ to the measured $N_{\mathrm{CCN}}$. The relative deviation (RD) equals the ratio of the absolute difference between the predicted $N_{\mathrm{CCN}}$ and the measured one to the measured $N_{\mathrm{CCN}}$, 6$$\mathrm{RD}={\displaystyle \frac{\mathrm{|}\mathrm{predicted}{N}_{\mathrm{CCN}}-\mathrm{measured}{N}_{\mathrm{CCN}}\mathrm{|}}{\mathrm{measured}{N}_{\mathrm{CCN}}}}.$$ 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 $N_{\mathrm{CCN}}$, 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 $N_{\mathrm{CCN}}$ 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 $N_{\mathrm{CCN}}$ better because of the lower median RD. The results for K1 and K2 are similar in that they both overestimate $N_{\mathrm{CCN}}$ by approximately 10 % (slopes of approximately 1.1) with similar median RDs. The reason for the $N_{\mathrm{CCN}}$ overestimation is that the constant $\mathit{\kappa }$ of 0.3 and the real-time bulk ${\mathit{\kappa }}_{\mathrm{chem}}$ are both greater than the ${\mathit{\kappa }}_{\mathrm{CCN}}$ at each season. In winter, the ${\mathit{\kappa }}_{\mathrm{CCN}}$ was highest and the difference between the ${\mathit{\kappa }}_{\mathrm{CCN}}$ and the parameterized $\mathit{\kappa }$ in K1 and K2 scheme was lowest, causing the best prediction of $N_{\mathrm{CCN}}$ among the four seasons. Owing to the largest difference between the ${\mathit{\kappa }}_{\mathrm{CCN}}$ and the parameterized $\mathit{\kappa }$, the $N_{\mathrm{CCN}}$ 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 $N_{\mathrm{CCN}}$ prediction among the five schemes, which is reflected in the lowest median RDs and the fit slope of $\sim \mathrm{1.0}$ for different seasons. The evaluations of the five schemes for the $N_{\mathrm{CCN}}$ prediction at each SS condition and each season are provided in Fig. S8 in the Supplement.

Figure 8

Relationships between the particle hygroscopicity factor ($\mathit{\kappa })$ and diameter ($D_{\mathrm{p}}$) observed at different stations. Lines are power-law fits of $\mathit{\kappa }$ vs. $D_{\mathrm{p}}$.

[Figure omitted. See PDF]

The K3 scheme provides an improved prediction of $N_{\mathrm{CCN}}$, 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 $N_{\mathrm{CCN}}$ because the fitting slope decreased $\sim \mathrm{0.1}$ on average. We simply evaluate the effects of the 10 % overestimation in $N_{\mathrm{CCN}}$ 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 $N_{\mathrm{CCN}}$ leads to an overestimate of the number concentration of cloud droplet ($N_{\mathrm{C}}$) in models. Theoretically, it can reduce a 3.2 % overestimation of cloud optical thickness, corresponding to global average difference of 1.28 Wm${}^{-\mathrm{2}}$ when assuming the cloud shortwave cooling effect of 40 Wm${}^{-\mathrm{2}}$ (Lee et al., 1997), which amounts to approximately one-third of the direct radiative forcing from a doubling CO${}_{\mathrm{2}}$. Additionally, the overestimation in $N_{\mathrm{CCN}}$ (and $N_{\mathrm{C}}$) 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 ${\mathit{\kappa }}_{\mathrm{chem}}$ and thus predict $N_{\mathrm{CCN}}$, the monodisperse CCN measurements are still important to obtain the $\mathit{\kappa }$–$D_{\mathrm{p}}$ relationship and thus improve the predictions of $N_{\mathrm{CCN}}$ (and $N_{\mathrm{C}}$) and climate.

Figure 8 compared the $\mathit{\kappa }$–$D_{\mathrm{p}}$ relationship measured at different regions. The $\mathit{\kappa }$–$D_{\mathrm{p}}$ relationship measured at Melpitz is similar to that measured at other rural regions with similar $\mathit{\kappa }$–$D_{\mathrm{p}}$ 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 $\mathit{\kappa }$–$D_{\mathrm{p}}$ power-law fit measured at Melpitz could be applied to predict $N_{\mathrm{CCN}}$ 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 $\mathit{\kappa }$–$D_{\mathrm{p}}$ power-law fitting measured at the two rural stations (green and purple lines in Fig. 8) to predict the $N_{\mathrm{CCN}}$ at Melpitz. Good prediction results were obtained with mean deviations of $\sim \mathrm{1}$ % (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 $\mathit{\kappa }$–$D_{\mathrm{p}}$ relationships are different from that measured at Melpitz.

4 Conclusions

Aerosol particle activation plays an important role in determining $N_{\mathrm{C}}$, 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 $N_{\mathrm{CCN}}$ predictions.

Over the whole period at Melpitz, the median $N_{\mathrm{CCN}}$ and AR increased from 399 to 2144 cm${}^{-\mathrm{3}}$ 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 $\mathrm{SS}=\mathrm{0.1}$ %, the median $N_{\mathrm{CCN}}$ 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 $N_{\mathrm{aero}}$, smallest GMD, and lowest ${\mathit{\kappa }}_{\mathrm{chem}}$ all contribute to the lowest AR and $N_{\mathrm{CCN}}$ 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 ${\mathit{\kappa }}_{\mathrm{chem}}$ cause the strongest sensitivity of $N_{\mathrm{CCN}}$ and AR to SS even though the spread in ${\mathit{\kappa }}_{\mathrm{CCN}}$ is narrowest.

Both $\mathit{\kappa }$ and the mixing state are size-dependent, thereby varying with SS. The median ${\mathit{\kappa }}_{\mathrm{CCN}}$ decreases from 0.27 to 0.19 as SS increases from 0.1 % to 0.7 %, which was less than the median bulk ${\mathit{\kappa }}_{\mathrm{chem}}$. The seasonal trend of ${\mathit{\kappa }}_{\mathrm{CCN}}$ was similar to that of ${\mathit{\kappa }}_{\mathrm{chem}}$, especially at relatively low SS conditions. The lowest ${\mathit{\kappa }}_{\mathrm{CCN}}$ and ${\mathit{\kappa }}_{\mathrm{chem}}$ 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 $D_{\mathrm{p}}$ increases, ${\mathit{\kappa }}_{\mathrm{CCN}}$ increases at the $D_{\mathrm{p}}$ range of $\sim \mathrm{40}$ to 100 nm and almost stays constant at the $D_{\mathrm{p}}$ 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. $D_{\mathrm{p}}$ and $\mathit{\kappa }$ vs. $D_{\mathrm{p}}$ are both fitted well by a power-law function for each season.

Five activation schemes are evaluated on the $N_{\mathrm{CCN}}$ predictions. Compared to using the classic $N_{\mathrm{CCN}}$–SS or AR–SS power-law fits to predict $N_{\mathrm{CCN}}$, the prediction is better when using the real-time PNSD combined with the parameterized $\mathit{\kappa }$, including a constant $\mathit{\kappa }$ of 0.3, the bulk ${\mathit{\kappa }}_{\mathrm{chem}}$, and the $\mathit{\kappa }$–$D_{\mathrm{p}}$ power-law fit. However, assuming a constant $\mathit{\kappa }$ of 0.3 recommended for continental aerosol (Andreae and Rosenfeld, 2008) or the bulk ${\mathit{\kappa }}_{\mathrm{chem}}$ calculated from aerosol chemical composition causes significant overestimations of the $N_{\mathrm{CCN}}$ 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 CO${}_{\mathrm{2}}$ (Lee et al., 1997). Moreover, the strength of the autoconversion process in cloud could be underestimated (Liu et al., 2006). Size-resolved $\mathit{\kappa }$ improves the $N_{\mathrm{CCN}}$ prediction. We recommend applying the $\mathit{\kappa }$–$D_{\mathrm{p}}$ power-law fit for $N_{\mathrm{CCN}}$ prediction, which obtains the best prediction among the five schemes.

The $\mathit{\kappa }$–$D_{\mathrm{p}}$ 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 $\mathit{\kappa }$–$D_{\mathrm{p}}$ power-law fit measured in urban Budapest (Salma et al., 2021) for predicting Melpitz $N_{\mathrm{CCN}}$ could cause underestimation of $N_{\mathrm{CCN}}$ with a median value of 39 % for all SS conditions. Additionally, the seasonal difference of the $\mathit{\kappa }$–$D_{\mathrm{p}}$ relationship needs to be considered carefully for $N_{\mathrm{CCN}}$ prediction. At Melpitz, if the $\mathit{\kappa }$–$D_{\mathrm{p}}$ power-law fit measured in summer was used for predicting $N_{\mathrm{CCN}}$ in winter, it could cause underestimation of $N_{\mathrm{CCN}}$ with a median value of 13 % for all SS conditions. Although the $\mathit{\kappa }$–$D_{\mathrm{p}}$ 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 $\mathit{\kappa }$–$D_{\mathrm{p}}$ relationships for different regions and for different seasons, but also to further investigate the reasons for the difference of the $\mathit{\kappa }$–$D_{\mathrm{p}}$ relationships measured at same type of regions. Finally, for the purpose of predicting $N_{\mathrm{CCN}}$, 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 ${\mathit{\sigma }}_{s/a}$, $M_{\mathrm{w}}$, $R$, $T$, and ${\mathit{\rho }}_{\mathrm{w}}$ 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., $N_{\mathrm{CCN}}$/$N_{\mathrm{CN}}$
AIEs	aerosol indirect effects
AR	activation ratio, i.e., $N_{\mathrm{CCN}}$/$N_{\mathrm{aero}}$
$b$	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 $\mathit{\kappa }$–$D_{\mathrm{p}}$ power-law fit
CPC	condensation particle counter
$D_{\mathrm{p}}$	diameter of the dry particle
$D_{\mathrm{c}}$	critical diameter of the dry particle
$D_X$	$D$ 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
$f_{\mathrm{BC}}$	mass fraction of BC in submicron aerosol
$f_{\mathrm{nitrate}}$	mass fraction of nitrate in submicron aerosol
$f_{\mathrm{org}}$	mass fraction of organics in submicron aerosol
$f_{\mathrm{sulfate}}$	mass fraction of sulfate in submicron aerosol
GMD	geometric mean diameter of PNSD
$M_{\mathrm{w}}$	molecular weight of water
$N_{\mathrm{aero}}$	number concentration of aerosol with a $D_{\mathrm{p}}$ range of 10 to 800 nm
$N_{\mathrm{C}}$	number concentration of cloud droplet
$N_{\mathrm{CN}}$	number concentration of CN
$N_{\mathrm{CCN}}$	number concentration of CCN
NPF	new particle formation
OA	organic aerosol
PM${}_{\mathrm{10}}$	particulate matter with the $D_{\mathrm{p}}\mathit{<}\mathrm{10}\mathrm{\mu }$m
PNSD	particle number size distribution
$R$	universal gas constant
$R^{\mathrm{2}}$	coefficient of determination
RD	relative deviation between the predicted $N_{\mathrm{CCN}}$ and the measured one
SS	supersaturation
SOA	secondary organic aerosol
$T$	temperature
${\mathit{\sigma }}_{\mathrm{s}}$	the shape of the sigmoid function
${\mathit{\sigma }}_{s/a}$	droplet surface tension
$\mathit{\kappa }$	hygroscopicity factor of aerosol particle
${\mathit{\kappa }}_i$	$\mathit{\kappa }$ of each component
${\mathit{\kappa }}_{\mathrm{CCN}}$	$\mathit{\kappa }$ calculated from the monodisperse CCN measurements
${\mathit{\kappa }}_{\mathrm{chem}}$	$\mathit{\kappa }$ calculated from the aerosol chemical measurements
${\mathit{\epsilon }}_i$	volume fraction of each component
${\mathit{\rho }}_{\mathrm{w}}$	density of the liquid water

Data availability

The data used in this study are available from Silvia Henning ([email protected]) upon request and 10.1594/PANGAEA.938215 (Wang et al., 2021).

The supplement related to this article is available online at: https://doi.org/10.5194/acp-22-15943-2022-supplement.

Author contributions

AW, SH, and LP designed the research. SH and LP collected the data at Melpitz. YW performed the data analysis and prepared the paper. All co-authors contributed to the interpretation of the results as well as paper review and editing.

Competing interests

The contact author has declared that none of the authors has any competing interests.

Disclaimer

Publisher’s note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Acknowledgements

We thank Achim Grüner and René Rabe for the careful maintenance of the measurements on site. We also thank Angela Buchholz and another anonymous reviewer for their helpful comments and suggestions on improving the paper.

Financial support

This research has been supported by the H2020 Research Infrastructures (ACTRIS grant no. 262254 and ACTRIS-2 grant no. 654109); the European Cooperation in Science and Technology (COLOSSAL grant no. CA16109); the Deutsches Forschungszentrum für Gesundheit und Umwelt, Helmholtz Zentrum München (F&E grant nos. 370343200 and 371143232); the Deutsche Forschungsgemeinschaft (HE grant no. 6770/2); the National Natural Science Foundation of China (grant nos. 42205072, 42075066, 42075063, 42175099, and 42005067); and the China Scholarship Council (grant no. 202008320513).

Review statement

This paper was edited by James Allan and reviewed by Angela Buchholz and one anonymous referee.