The size-resolved cloud condensation nuclei (CCN) activity and its prediction based on aerosol hygroscopicity and composition in the Pearl Delta River (PRD) region during wintertime 2014

A hygroscopic tandem differential mobility analyzer (HTDMA), a scanning mobility cloud condensation nuclei (CCN) analyzer (SMCA), and an Aerodyne high-resolution time-of-flight aerosol mass spectrometer (HR-ToF-AMS) were used to, respectively, measure the hygroscopicity, condensation nuclei activation, and chemical composition of aerosol particles at the Panyu site in the Pearl River Delta region during wintertime 2014. The distribution of the size-resolved CCN at four supersaturations (SSs of 0.1 %, 0.2 %, 0.4 %, and 0.7 %) and the aerosol particle size distribution were obtained by the SMCA. The hygroscopicity parameter κ (κ_CCN, κ_HTDMA, and κ_AMS) was, respectively, calculated based upon the SMCA, HTDMA, and AMS measurements. The results showed that the κ_HTDMA value was slightly smaller than the κ_CCN one at all diameters and for particles larger than 100 nm, and the κ_AMS value was significantly smaller than the others (κ_CCN and κ_HTDMA), which could be attributed to the underestimated hygroscopicity of the organics (κ_org). The activation ratio (AR) calculated from the growth factor – probability density function (Gf-PDF) without surface tension correction was found to be lower than that from the CCN measurements, due most likely to the uncorrected surface tension (σ_s∕a) that did not consider the surfactant effects of the organic compounds. We demonstrated that better agreement between the calculated and measured ARs could be obtained by adjusting σ_s∕a. Various schemes were proposed to predict the CCN number concentration (N_CCN) based on the HTDMA and AMS measurements. In general, the predicted N_CCN agreed reasonably well with the corresponding measured ones using different schemes. For the HTDMA measurements, the N_CCN value predicted from the real-time AR measurements was slightly smaller (∼6.8 %) than that from the activation diameter (D₅₀) method due to the assumed internal mixing in the D₅₀ prediction. The N_CCN values predicted from bulk chemical composition of PM₁ were higher (∼11.5 %) than those from size-resolved composition measured by the AMS because a significant fraction of PM₁ was composed of inorganic matter. The N_CCN values calculated from AMS measurement were underpredicted at 0.1 % and 0.2 % supersaturations, which could be due to underestimation of κ_org and overestimation of σ_s∕a. For SS values of 0.4 % and 0.7 %, slight overpredicted N_CCN values were found because of the internal mixing assumption. Our results highlight the need for accurately evaluating the effects of organics on both the hygroscopic parameter κ and the surface tension σ in order to accurately predict CCN activity.

1 Introduction

Aerosol particles can directly impact global climate by scattering and absorbing solar radiation (Stocker, 2013), while they can influence cloud formation, lifetime, and optical properties by acting as cloud condensation nuclei (CCN), indirectly exerting climatic forcing on the Earth's atmosphere. In general, aerosol particles increase the CCN concentration and hence cause cooling effects on the global radiation balance. However, to what extent aerosol particles contribute to the radiation forcing is still highly uncertain (Stocker, 2013). It is hence important to measure chemical composition and properties of aerosol particles in order to assess their abilities of acting as CCN and contribution to cloud formation, further facilitating our understanding of the impacts of atmospheric aerosols on regional and global climate.

The extent to which aerosol particles can affect cloud formation is dependent on their fraction that can be activated to become CCN. This fraction of activation is termed as CCN activity that is determined by the chemical composition, sizes, and the water saturation ratio of the particles (Farmer et al., 2015). The size-dependent saturation ratio (S) can be calculated from the Köhler equation (Köhler, 1936):

$$\begin{array}{}\text{(1)}& S=a_{\mathrm{w}}\exp \left({\displaystyle \frac{\mathrm{4}{\mathit{\sigma }}_{\mathrm{s}/\mathrm{a}}{M}_{\mathrm{w}}}{\mathrm{R}T{\mathit{\rho }}_{\mathrm{w}}D}}\right),\end{array}$$

where a_w is the water activity in solution, σ_s∕a is surface tension of the solution/air interface, M_w is the mole weight of water, R is the universal gas constant, T is temperature in Kelvin, and D is the diameter of the droplet. The a_w represents the Raoult effect, which means that the activation potential increases with the concentration of the solution. The term $\exp \left(\frac{\mathrm{4}{\mathit{\sigma }}_{\mathrm{s}/\mathrm{a}}{M}_{\mathrm{w}}}{\mathrm{R}T{\mathit{\rho }}_{\mathrm{w}}D}\right)$ represents Kelvin effect, which relates the surface curvature to the saturation vapor pressure of the droplet. The activation potential increases with increase of the droplet diameter or decrease of surface tension σ_s∕a, and the σ_s∕a value is sensitive to the organic surfactant effect. The two important parameters, the water activity (α_w) and surface tension (σ_s∕a), are dependent on the composition of the aerosol particles, assuming those particles have the same properties as their corresponding bulk solutions. The effects of organics on the CCN activity have been extensively investigated; however, many outstanding questions still remain. Sorjamaa et al. (2004) suggested that the partitioning of surfactants had to be considered when evaluating the Kelvin effect and the Raoult effect. According to their experimental results, the surfactant partitioning could alter the Raoult effect and the change is large enough to depress CCN activity. However, another experiment conducted by Engelhart et al. (2008) revealed that the organics in aged monoterpene aerosols could depress surface tension by about 0.01 N m⁻¹ and hence increase CCN activity. Ovadnevaite et al. (2017) also presented observational and theoretical evidence that the decrease of surface tension could prevail over the Raoult effect, which led to the increase of CCN activity. Salma et al. (2006) isolated humic-like substances (HULIS) from PM_2.5 fraction aerosol samples and investigated the surface tension properties of the HULIS pure solutions. The results show that thermodynamic equilibrium on surface could only be reached after several hours. Because the depression of surface tension was controlled by diffusion of surfactants from the bulk of the droplet to its surface, the extent of the actual decrease of surface tension was hence kinetically limited. A hybrid model proposed by Petters and Kreidenweis (2013) was used to predict the effects of surfactants on the CCN activity. The model predicted strong effects of the surfactants on ternary systems where common ions were present. However, due to the limited measurement techniques, the available laboratory data were still not sufficient to support this prediction and more solid data were needed to validate the surfactant effects on the CCN activity.

The CCN activity can be characterized by the hygroscopicity parameter κ that was initially proposed by Petters and Kreidenweis (2007). Aerosol hygroscopicity represents the ability of the particles to grow by absorbing water vapor from the atmosphere and the extent to which the particles are hygroscopic can be evaluated by the κ values, which can be determined from the HTDMA or cloud condensation nuclei counter (CCNc) measurements. The κ values were measured worldwide extensively either in field measurements or in laboratory experiments and depending on the organic content of the particles, a wide range of κ values was reported in the literature. Cerully et al. (2011) showed that the κ values measured in 2007 by a continuous-flow streamwise thermal gradient CCN (CFSTGC) chamber ranged mostly between 0.1 and 0.4 in a forest environment in Finland. Hong et al. (2014) obtained the average κ values of 0.15 (110 nm) and 0.28 (102 nm) measured by the HTDMA at the same site in 2010. Chang et al. (2010) used an AMS to measure aerosol chemical composition and a mole ratio of atomic oxygen to atomic carbon (O∕C) at a rural site in Canada. They reported a relationship between the κ values of organics and the O∕C ratio as ${\mathit{\kappa }}_{\mathrm{org}}=(\mathrm{0.29}\pm \mathrm{0.05})\cdot \left(\mathrm{O}/\mathrm{C}\right)$. Tritscher et al. (2011) conducted smog chamber experiments for measurements of the κ values of aging secondary organic aerosols and they found that the κ was a sensitive indicator of the secondary organic aerosol (SOA) properties.

Although the κ values were reported under different environments in many locations, only a few studies were conducted to measure κ in the Pearl River Delta (PRD) region (Cheung et al., 2015; Schurman et al., 2017). Jiang et al. (2016) compared the κ values between wintertime (0.18–0.22) and summertime (0.17–0.21) in Guangzhou. Cai et al. (2017) reported the κ values of about 0.4–0.6 and 0.2–0.3 measured by the HTDMA, respectively, in Cape Hedo (Japan) and Guangzhou (China). Alternatively, the average κ values can be predicted by the Zdanovskii–Stokes–Robinson (ZSR) mixing rule (Zdanovskii, 1948; Stokes and Robinson, 1966) which is based on the chemical composition of the aerosol particles from the AMS measurements. Liu et al. (2014) reported the κ values of 0.22 to 0.32 using the ZSR mixing rule, consistent with the values (0.25 to 0.34) based on the HTDMA measurements.

Once the κ values were determined, they could then be employed to predict the CCN activity that was characterized by two important parameters: activation diameter (D₅₀) and activation ratio (AR). Until now, the CCN activity (thus the above three parameters) can be determined using the following three methods:

1. The combination of CCNc and scanning mobility particle sizer (SMPS). The CCN number was measured by the CCNc at different supersaturation (SS, typically 0.05 %–1 %) ratios. Meanwhile, the D₅₀ and size-resolved activation ratios could be measured by combining the CCNc with a differential mobility analyzer (DMA) and a condensation particle counter (CPC) (Moore et al., 2011; Deng et al., 2011), referred to as scanning mobility CCN analysis (SMCA) based on measurements from a SMPS (DMA plus CPC) and a CCNc. This method can measure the size-resolved CCN distributions at a high time resolution (Moore et al., 2010) and has been applied in lab experiments (Asa-Awuku et al., 2009) and field campaigns (Moore et al., 2008) to measure CCN activity.

2. The ZSR method based on chemical composition measurements. The CCN concentrations were inverted from the chemical composition and the size distribution of the aerosol particles measured, respectively, from the aerosol mass spectrometer (AMS) and SMPS (Moore et al., 2012; Meng et al., 2014). The κ was then calculated from the ZSR mixing rule. In general, the particles were assumed to be internally mixed, which might lead to a large uncertainty (up to 80 %) in predicting N_CCN in some cases (Wang et al., 2010).

3. The HTDMA method. The size-resolved CCN distribution and activation ratios could be determined from hygroscopicity and size distribution measured using the HTDMA (Good et al., 2010; Wu et al., 2013). The HTDMA measured the distribution of hygroscopic growth factor (Gf) at a fixed relative humidity for a selected diameter of aerosol particles. Väisänen et al. (2016) reported that the measured N_CCN with the HTDMA agreed well with that from in-cloud prediction, where the sample was collected from a tower approximately 224 m above the surrounding lake level. On the other hand, Chan et al. (2008) attributed differences in κ from HTDMA and CCN measurements to sparingly soluble organics that did not easily deliquesce in the previous measurements.

The PRD region is one of the most economically invigorating regions in China. This region is subjected to severe air pollution due to intensive human activities and insufficient pollution control measures. High particle loading leads to both visibility degradation and large cooling effects due to decrease of solar radiation. During wintertime, high concentrations of fine particles also cause severe haze events that pose health risks for people at the regional scale. It is hence an ideal location to investigate the influence of local anthropogenic emissions on the particles properties. However, there is still lack of understanding on the relationship between the CCN activity and its controlling factors (e.g., chemical composition and hygroscopicity of aerosol particles), hindering policy makers to propose effective measures for climate-related policy making.

In this study, we used the SMCA, HTDMA, and HR-ToF-AMS to, respectively, measure CCN activity, hygroscopicity, and chemical composition. We reported the relationship between CCN activity and hygroscopicity/chemical composition of aerosol particles in the PRD region, where only a few studies on such a relationship were available in the literature. The measurements were performed during wintertime 2014 (November and December). The CCN properties were predicted based on the combined SMCA, HTDMA, and HR-ToF-AMS measurements. The methods employed to predict the CCN concentrations were evaluated and the impact of organics on CCN concentrations was discussed.

2 Experiments and data analysis

2.1 Measurement site

The field measurements were conducted at the Chinese Meteorological Administration (CMA) Atmospheric Watch Network (CAWNET) station in Panyu, Guangzhou, China, during wintertime 2014 (November and December). The Panyu station is located at the center of the PRD region and at the top of the Dazhengang mountain ($\mathrm{23}{}^{\circ }{\mathrm{00}}^{\prime }$ N, $\mathrm{113}{}^{\circ }{\mathrm{21}}^{\prime }$ E) with an altitude of about 150 m. No significant local emission sources were around the site. Detailed description of the measurement site and instruments (i.e., the HTDMA and the AMS) can be found elsewhere (Cai et al., 2017; Qin et al., 2017).

2.2 Instrumentation

2.2.1 Aerosol hygroscopicity measurements

Size-resolved aerosol hygroscopicity and particle number size distribution (PNSD) were measured by a HTDMA which was developed by Tan et al. (2013a). The hygroscopicity data were only available in November due to the failure of the HTDMA during December. An aerosol sampling port equipped with a PM₁ impactor inlet was used during the measurement period. Ambient sampling flow first passed through a Nafion dryer (model PD-70T-24ss, Perma Pure Inc., USA) to achieve a relative humidity (RH) of <10 %. We considered the particles to be dry when the RH values were less than 10 %. The particles were subsequently charged by a neutralizer (Kr85, TSI Inc.) and size selected by a differential mobility analyzer (DMA1, model 3081L, TSI Inc.). The monodisperse particles with a specific diameter (D₀) were then introduced into a Nafion humidifier (model PD-70T-24ss, Perma Pure Inc., USA) under a fixed RH of (90±0.44) %. Another differential mobility analyzer (DMA2, model 3081L, TSI Inc.) and a condensation particle counter (CPC, model 3772, TSI Inc.) were used to measure the number size distribution of the humidified particles (D_p). Thus, Gf of the particles can be calculated:

$$\begin{array}{}\text{(2)}& \mathrm{Gf}={\displaystyle \frac{{\mathrm{D}}_{\mathrm{p}}}{D_{\mathrm{0}}}}.\end{array}$$

During the campaign, we selected five dry mobility diameters (40, 80, 110, 150, and 200 nm) for the HTDMA measurements. The measurements were performed continuously except for regular calibration of the instrument. We used standard polystyrene latex spheres and ammonium sulfate to perform the DMA calibration to ensure the instrument functioned normally.

2.2.2 Size-resolved CCN activity measurements

Size-resolved CCN spectra and activation ratios were measured with the SMCA initially proposed by Moore et al. (2010). In this work, the SMCA consisted of a CCNc-100 (DMT Inc.), a differential mobility analyzer (DMA, model 3081L, TSI Inc.), and a condensation particle counter (CPC, model 3787, TSI Inc.). In the SMCA system, the combined DMA and CPC were used as a SMPS during the measurements. The dry particles after the Nafion dryer were neutralized by the Kr85 neutralizer and were subsequently classified by the DMA. The monodisperse particles were split into two streams: one to the CPC for measurement of total particle number concentration (N_CN) and another to the CCNc-100 for measurements of the CCN number concentration. The aerosol and CPC flow rates were both 1.0 L min⁻¹ for the DMA and the CPC (0.5 L min⁻¹ makeup flow and 0.5 L min⁻¹ sample flow), respectively. The CCNc-100 drew another aerosol flow rate of 0.5 L min⁻¹. The SMCA was protocolled to measure particles at a mobility diameter range of 10–400 nm. The supersaturation in the CCNc-100 was set to be 0.1 %, 0.2 %, 0.4 %, and 0.7 %, respectively, for each measurement cycle. The CCNc-100 was regularly calibrated with ammonium sulfate particles at the four SSs (0.1 %, 0.2 %, 0.4 %, and 0.7 %). Previous studies showed that different parameterizations in the Köhler theory can retrieve different critical supersaturations (Rose et al., 2008; Wang et al., 2017). When performing the CCNc calibration, we assumed the density and molecular weight of ammonium sulfate to be 1770 kg m⁻³ and 0.132141 kg mol⁻¹, respectively. In the CCNc calibration, the water activity (a_w) was approximated according to Rose et al. (2008):

$$\begin{array}{}\text{(3)}& a_{\mathrm{w}}=\exp (-i_{\mathrm{s}}{\mathit{\mu }}_{\mathrm{s}}{M}_{\mathrm{w}}),\end{array}$$

where i_s, μ_s, and M_w are the van 't Hoff factor, molality of solute, and the molar mass of water (0.01802 kg mol⁻¹), respectively. The van 't Hoff factor i_s is calculated from a polynomial fit to Pitzer model output data (Moore et al., 2010). In this study, we adopted the simplest parameterization of the surface tension of the solution (Rose et al., 2008); that is, it was simply approximated by the surface tension of pure water (0.072 N m⁻¹) according to Seinfeld and Pandis (2006).

We also set the temperature and the pressure to 298.15 K and 1026 hPa, respectively. A temperature gradient ΔT of about 3–8 K in the CCNc column was also used in the calibrations. Similarly, the DMA was calibrated with standard polystyrene latex spheres before and after the campaign for quality assurance and control.

2.2.3 Aerosol chemical composition measurements

An Aerodyne high-resolution time-of-flight aerosol mass spectrometer (HR-ToF-AMS) was employed in the campaign to measure non-refractory PM₁ chemical composition (bulk and size-resolved) including sulfate, nitrate, ammonium, chloride, and organics. The refractory components such as black carbon, sea salts, and crustal species cannot be measured by this instrument. Detailed description of the HR-ToF-AMS can be found elsewhere (DeCarlo et al., 2006; Jimenez et al., 2003). Here, only a brief description relevant to the measurements is given. The instrument was operated in three modes (pToF, V, and W modes). Particle size distribution could be obtained based on the time of flight of the particles in pToF mode. In V and W modes, the resolving power of the mass spectrometer was approximately 2000 and 4000, respectively. The instrument collected alternatively 5 min average mass spectra for the V plus pToF modes and the W mode. The monodisperse pure ammonium nitrate (NH₄NO₃) particles selected by a DMA (400 nm) were used weekly in the ionization efficiency (IE) calibration. Background signals were obtained daily for about 30 min by introducing filtered ambient air with a high-efficiency particulate air (HEPA) filter in the sample flow. Before and after the measurement, the sampling flow rate was calibration with a Gilian gilibrator. We also generated polystyrene latex (PSL) (Duke Scientific) and ammonium nitrate particles in a size range of 178–800 nm to calibrate the pToF size. Note that the mass concentrations were too low for particle diameters smaller than 65 nm and data for those particles were hence discarded in this study. A more detailed description of the AMS performance during the measurements can be found in Qin et al. (2017) and Cai et al. (2017).

The AMS measured size-resolved chemical composition of particles in a vacuum aerodynamic diameter (D_va). It is hence necessary to convert aerodynamic diameter to mobility diameter in order to compare the AMS data and the SMCA data. We adopted the equation derived by DeCarlo et al. (2004) to do the conversion. Here, we assume a density of 1700 kg m⁻³ for particles measured by the AMS (DeCarlo et al., 2004).

2.3 Data processing and methodology

2.3.1 Hygroscopicity

Due to the effects of diffusing transfer function, the measured distribution function (MDF) given by the HTDMA is only a skewed and smoothed integral transform of the actual growth factor – probability density function (Gf-PDF) of the particles (Gysel et al., 2009). Here, the TDMAfit algorithm (Stolzenburg and McMurry, 2008) was applied to narrow the uncertainties caused by the diffusion broadening. The TMDAfit algorithm describes the Gf-PDF as a combination of several (usually smaller than three) lognormal distribution functions, in which the parameters of each mode are considered as mean Gf, standard deviation, and number fraction. The detailed data inversion process of the HTDMA instrument can be found in Tan et al. (2013b). Note that we include multiply charged correction for the SMCA, SMPS, and HTDMA data when the data were inverted so that the contributions of the multiply charged particles were accounted for all the measured particle data.

As mentioned in the introduction, the CCN activity can be represented by a widely used hygroscopicity parameter κ (Petters and Kreidenweis, 2007). According to the κ-Köhler theory, for a known temperature, κ and Gf can be related via Eq. (4) (Petters and Kreidenweis, 2007):

$$\begin{array}{}\text{(4)}& \mathit{\kappa }=({\mathrm{Gf}}^{\mathrm{3}}-\mathrm{1})\left[{\displaystyle \frac{\mathrm{1}}{\mathrm{RH}}}\exp ({\displaystyle \frac{\mathrm{4}{\mathit{\sigma }}_{\mathrm{s}/\mathrm{a}}{M}_{\mathrm{w}}}{\mathrm{R}T{\mathit{\rho }}_{\mathrm{w}}D}}-\mathrm{1})\right],\end{array}$$

where ρ_w is the density of water (about 997.04 kg m⁻³ at 298.15 K), M_w is the molecular weight of water (0.018 kg mol⁻¹), σ_s∕a is the surface tension of the solution/air interface and here pure water is tentatively assumed for the solution (${\mathit{\sigma }}_{\mathrm{s}/\mathrm{a}}=\mathrm{0.0728}$ N m⁻¹ at 298.15 K), R is the universal gas constant (about 8.31 J mol⁻¹ K⁻¹), T is thermodynamic temperature in Kelvin (298.15 K), and D is the particle diameter (in meter).

2.3.2 CCN activation

The N_CN and N_CCN data were, respectively, measured by the SMPS and the CCNc-100 and they were used to calculate the size-resolved CCN ARs which was defined as the ratio of N_CCN to N_CN at each particle size. The activation ratio can be obtained by fitting the ratio with the sigmoidal function with respect to D_p:

$$\begin{array}{}\text{(5)}& {\displaystyle \frac{N_{\mathrm{CCN}}}{N_{\mathrm{CN}}}}={\displaystyle \frac{B}{\mathrm{1}+(\frac{D_{\mathrm{p}}}{D_{\mathrm{50}}}{)}^C}},\end{array}$$

where D_p is the particle dry diameter, B, C and D₅₀ are fitting coefficients that represent the asymptote, the slope, and the inflection point of the sigmoid, respectively (Moore et al., 2010). Note that the parameter C (in Eq. 5) is a fitting coefficient with no specific physical meaning. However, a small C value indicates a steep activation curve. D₅₀ is also called the critical diameter or the activation diameter, that is, the diameter at which 50 % of the particles are activated at a specific SS.

Alternatively, the hygroscopicity parameter κ can be calculated from the critical saturation ratio (Sc) and D₅₀ from the following equation (Petters and Kreidenweis, 2007):

$$\begin{array}{}\text{(6)}& \mathit{\kappa }={\displaystyle \frac{\mathrm{4}{A}^{\mathrm{3}}}{\mathrm{27}{D}_{\mathrm{50}}^{\mathrm{3}}(\ln \mathrm{Sc}{)}^{\mathrm{2}}}},A={\displaystyle \frac{\mathrm{4}{\mathit{\sigma }}_{\mathrm{s}/\mathrm{a}}{M}_{\mathrm{w}}}{\mathrm{R}T{\mathit{\rho }}_{\mathrm{w}}}}.\end{array}$$

2.3.3 CCN prediction based on HTDMA and AMS measurements

The N_CCN can be predicted based on either the aerosol hygroscopicity data (measured by the HTDMA) or the AMS data. Figure 1 is the schematic diagram of the four approaches we followed to predict N_CCN based on the above two measured datasets. In the first approach (I in Fig. 1), the mixing state and size dependence were taken into account. We assumed the critical hygroscopicity parameter κ_critical to be a function of the particle diameter and the supersaturation ratio (denoted as κ_critical(D_p, SS)). The κ_critical was hence defined as the point at which all the particles were activated at a specific diameter and a specific SS. Here, we measured hygroscopicity using the HTDMA at five dry diameters and the CCN concentrations at four SSs. We calculated the κ_critical(D_p, SS) using Eq. (6) for a known diameter and SS. A particle with a κ value higher than κ_critical(D_p, SS) was considered to be activated as CCN (Fig. 1a) and the shadow area represented the particles which can be activated as CCN for a known diameter and SS. The activation ratio for a specific diameter at a specific SS was obtained by integrating the κ-PDF for κ>κ_critical(D_p, SS).

Figure 1 A schematic representation of N_CCN prediction based on the HTDMA and the AMS measurements. The N_CCN can be predicted based on the fitted activation ratio (approach I) and the D₅₀ (approach II), both obtained from the HTDMA measurement, the size-resolved composition (approach III), and the bulk PM₁ composition (approach IV), both obtained from the AMS measurements. Panel (a) shows the representation of calculating the activation ratio for a specific diameter and SS, and the shadow area represents the particles which can be activated as CCN; panels (b) and (c) show the representations of the κ values obtained, respectively, from size-resolved chemical composition and bulk chemical composition; panel (d) shows the representation of fitting the activation ratio to the particle diameter D_p (red dot); panels (e), (f), (g), and (h) show the representations of predicting the N_CCN using the four approaches, respectively, and the shadow area represents the particles which can be activated as CCN.

This approach is similar to the one employed in Kammermann et al. (2010); however, we used the size-resolved activation ratio (AR_SR) to calculate the N_CCN. The AR_SR was determined by fitting the AR(D_p,SS) to the diameter D_p using Eq. (5) for the five measured diameters (Fig. 1d). Thus, the calculated N_CCN using the activation ratio can be expressed as (Fig. 1e)

$$\begin{array}{}\text{(7)}& N_{\mathrm{CCN}}\left(\mathrm{SS}\right)=\underset{\mathrm{0}}{\overset{\mathrm{\infty }}{\int }}{\mathrm{AR}}_{\mathrm{SR}}(D_{\mathrm{p}},\mathrm{SS})N_{\mathrm{CN}}\left(D_{\mathrm{p}}\right)\mathrm{d}{D}_{\mathrm{p}}.\end{array}$$

In the second approach (II in Fig. 1), the particles were assumed to be internally mixed. The D₅₀ was determined by fitting the AR(D_p,SS) to the diameter D_p (Fig. 1d). The N_CCN was obtained by integrating the cloud nuclei concentration for particles larger than D₅₀ based on the particle size distribution (Fig. 1f), according to the following equation (Eq. 8):

$$\begin{array}{}\text{(8)}& N_{\mathrm{CCN}}\left(\mathrm{SS}\right)=\underset{D_{\mathrm{50}}}{\overset{\mathrm{\infty }}{\int }}{N}_{\mathrm{CN}}\left(D_{\mathrm{p}}\right)\mathrm{d}{D}_{\mathrm{p}}.\end{array}$$

In the third and fourth approaches (III and IV in Fig. 1), the particles were also assumed to be internally mixed. We then calculated the κ value according to the ZSR rule (Eq. 9) based on the AMS measurements.

$$\begin{array}{}\text{(9)}& \mathit{\kappa }=\sum _i{\mathit{\epsilon }}_i{\mathit{\kappa }}_i,\end{array}$$

where ε_i is the volume fraction of each component in the particles; κ_i is the κ value of each component.

The AMS only provided the ion concentrations during the measurements, while the ZSR rule required the volume fraction and hygroscopicity of each component. A simplified ion pairing scheme developed by Gysel et al. (2007) was used to reconstruct the ${\mathrm{NH}}_{\mathrm{4}}^{+}$, ${\mathrm{SO}}_{\mathrm{4}}^{\mathrm{2}-}$, and ${\mathrm{NO}}_{\mathrm{3}}^{-}$ measured by the AMS:

$$\begin{array}{}\text{(10)}& {\displaystyle }& {\displaystyle }{n}_{{\mathrm{NH}}_{\mathrm{4}}{\mathrm{NO}}_{\mathrm{3}}}=n_{{\mathrm{NO}}_{\mathrm{3}}^{-}}\text{(11)}& {\displaystyle }& {\displaystyle }{n}_{{\mathrm{H}}_{\mathrm{2}}{\mathrm{SO}}_{\mathrm{4}}}=max(\mathrm{0},N_{{\mathrm{SO}}_{\mathrm{4}}^{\mathrm{2}-}}-n_{{\mathrm{NH}}_{\mathrm{4}}^{+}}+n_{{\mathrm{NO}}_{\mathrm{3}}^{-}})\text{(12)}& {\displaystyle }& {\displaystyle }{n}_{{\mathrm{NH}}_{\mathrm{4}}{\mathrm{HSO}}_{\mathrm{4}}}=min\left(\mathrm{2}{n}_{{\mathrm{SO}}_{\mathrm{4}}^{\mathrm{2}-}}-n_{{\mathrm{NH}}_{\mathrm{4}}^{+}}+n_{{\mathrm{NO}}_{\mathrm{3}}^{-}},n_{{\mathrm{NH}}_{\mathrm{4}}^{+}}-n_{{\mathrm{NO}}_{\mathrm{3}}^{-}}\right)\text{(13)}& {\displaystyle }& {\displaystyle }{n}_{({\mathrm{NH}}_{\mathrm{4}}{)}_{\mathrm{2}}{\mathrm{SO}}_{\mathrm{4}}}=max\left(n_{{\mathrm{NH}}_{\mathrm{4}}^{+}}-n_{{\mathrm{NO}}_{\mathrm{3}}^{-}}-n_{{\mathrm{SO}}_{\mathrm{4}}^{\mathrm{2}-}},\mathrm{0}\right)\text{(14)}& {\displaystyle }& {\displaystyle }{n}_{{\mathrm{HNO}}_{\mathrm{3}}}=\mathrm{0},\end{array}$$

where n denotes the number of moles of each component (i.e., ${\mathrm{NH}}_{\mathrm{4}}^{+}$, ${\mathrm{SO}}_{\mathrm{4}}^{\mathrm{2}-}$, and ${\mathrm{NO}}_{\mathrm{3}}^{-}$). Here, we used the uncoupled diameter-dependent thermodynamic equilibrium model (ADDEM) proposed by Topping et al. (2005) to calculate the κ values of the inorganic species and those of the organics were tentatively assumed to be 0.1 (Meng et al., 2014). Table 1 lists the κ values of the relevant species used in the study based on the calculations and the above assumption.

Table 1 The κ values of the related species in the study.

^a κ of inorganic compounds is derived from ADDEM (Topping et al., 2005). ^b κ of organics is from Meng et al. (2014).

Here, instead of being determined from fitting of AR_SR to D_p used in the second approach, the D₅₀ was calculated from the above κ values using Eq. (6). In the third approach, the κ values were size resolved because the chemical composition of the particles was size dependent (Fig. 1b). In the fourth approach, the particles were assumed to have the same chemical composition and hygroscopicity as those in PM₁ (Fig. 1c). The N_CCN was then predicted using Eq. (8) (Fig. 1g and h).

3 Results and discussion

3.1 Overview

Table 2 summarizes the observed CCN activity during the campaign. Overall, the average N_CCN at 0.1 %, 0.2 %, 0.4 %, and 0.7 % SS were about 3100, 5100, 6500, and 7900 cm⁻³, respectively. The average ARs at the above four SSs were 0.26, 0.41, 0.53, and 0.64, respectively. The average D₅₀ values at the above four SSs were 156, 107, 78, and 58 nm, respectively. The N_CCN at 0.7 % SS was, respectively, lower than those of the previous measurements (10 731 cm⁻³ at 0.67 % SS) in July 2006 in Guangzhou (Rose et al., 2010) but much higher than those measured (2085 cm⁻³ at 0.7 % SS) in May 2011 in Hong Kong (Meng et al., 2014), while the $N_{\mathrm{CCN}}/N_{\mathrm{CN},\mathrm{tot}}$ was lower than that from the previous measurements (at 0.67 % SS) in Guangzhou (0.59; Rose et al., 2010) and similar to that from the measurements (at 0.7 % SS) in Hong Kong (0.64; Meng et al., 2014). The D₅₀ was larger than that in the previous measurements in Guangzhou (49 nm) and in Hong Kong (47 nm), due to the lower particle hygroscopicity in Guangzhou. The differences of the κ_CCN values between the two measurements (0.21 in this winter campaign vs. 0.28 during the summer season in Guangzhou both at 0.7 % SS) suggested that the particles in the summer were in general more hygroscopic and hence were more readily activated than those in the winter, implying different chemical composition of the particles between the two distinct seasons. Mochida et al. (2010) measured the size-resolved CCN activity in Cape Hedo, a remote marine site rarely affected by anthropogenic emissions. The results showed that the D₅₀ at 0.1 % SS in Cape Hedo was about 130 nm, much smaller than that in Guangzhou, leading to higher hygroscopicity of atmospheric particles in Cape Hedo than that in Guangzhou.

Figure 2 The mass fraction of the bulk NR-PM₁ composition (a) and the mass fraction of the size-resolved composition (b).

Table 2 Summary of the measured CCN concentration, activation ratio, and D₅₀ at the four supersaturations during the campaign.

Figure 2 shows the average mass fraction of NR-PM₁ bulk composition and size-resolved (64–731 nm) composition. The organics were dominant in the bulk NR-PM₁ (50 %), followed by sulfate (26 %) and nitrate (12 %) (Fig. 2a). The mass fraction of the organics decreased with the size (Fig. 2b) from 73 % at 64 nm to 42 % at 397 nm. The mass fraction of organics at 397 nm was close to that of NR-PM₁ bulk, due to the fact that the PM₁ mass is dominated by particles in a diameter range of 200–500 nm (Tan et al., 2016). In comparison, the dominant NR-PM₁ species observed in Hong Kong were sulfate (51.0 %) and organics (28.2 %) (Lee et al., 2013), which is significantly different from our measurements, due probably to different origins of the dominant air masses between the two seasons. The measurement site in Guangzhou was impacted predominantly by the air mass from the north, where straw burning contributes to a high mass fraction of organic matter (Cao et al., 2008).

Figure 3 The median and interquartile PNSD, κ obtained from HTDMA, AMS, and CCN measurements during the campaign. The κ was pointed against their corresponding median D₅₀ (SMCA and AMS) or measured diameter (HTDMA). Dots represent the median value and the bars represent the interquartile range. The blue, red, and green colors represent κ_CCN, κ_AMS, and κ_HTDMA, respectively.

Figure 3 shows the κ values based, respectively, on the CCN (κ_CCN), AMS (κ_AMS), and HTDMA (κ_HTDMA) measurements, along with the measured PNSD (10–400 nm) during the campaign. The shadow area represents the interquartile range of the PNSD. A distinct peak at around 90 nm was observed from the PNSD (Fig. 3). The κ_AMS was calculated based on the size-resolved chemical composition, assuming the particles are internally mixed. At 0.7 % SS, the D₅₀ was about 58 nm. Hence, no κ_AMS was reported at this SS since we only measured particle composition above 63 nm using the AMS in this study. The κ values were shown in the interquartile range, with the largest variation from the CCN measurements (Fig. 3). As shown in Fig. 3, the difference between κ_CCN and κ_HTDMA is statistically insignificant at all employed diameters, while the one between κ_AMS and κ_CCN became statistically significant at larger sizes of the particles. The p value between the κ_AMS and the κ_ccn was close to 0, indicating that the correlation between them is significant. The κ_HTDMA values were lower than those of the corresponding κ_CCN at most of the particle sizes, consistent with the previous observation (Pajunoja et al., 2015). This was probably due to the fact that particles contain a certain fraction of low-solubility composition, such as SOA, contributing differently to hygroscopic growth and CCN activation. The available AMS data (Fig. 3) show that the κ_AMS values were lower than the corresponding κ_CCN and κ_HTDMA values at all size ranges, and the differences become larger with increasing particle sizes. This was probably due to underestimated hygroscopicity in the organic composition when using the AMS data, since we assumed a κ value of 0.1 for all organics at all particle sizes. The hygroscopicity increased with particle diameters due to aerosol aging which increased the hygroscopic organic contents. Previous studies showed that the κ_org values of larger particles are lower than those for smaller particles (Lance et al., 2013; Zhao et al., 2015), and hygroscopicity of organics is often found to be related to its chemical composition (f₄₄ or O∕C) in both field and laboratory studies (Chang et al., 2010; Massoli et al., 2010; Lambe et al., 2011; Mei et al., 2013, and other references therein). We showed that the f₄₄ increased with the particle size from the AMS data (Fig. S1 in the Supplement). Note that the f₄₄ for particle diameters smaller than 100 nm was discarded due to the data quality. The results indicate that the degree of oxidation of the organics was higher for larger size particles and the hygroscopicity for larger particles is higher (Chang et al., 2010). The measured κ_mean values fall in a range of 0.22–0.30 for the particle sizes of 40–200 nm measured by the HTDMA in this study. The other aerosol hygroscopicity measurement in PRD (Jiang et al., 2016) reported the κ_mean values ranging from 0.18 to 0.22 in the 2012 winter season and 0.17 to 0.21 in the 2013 summer season, suggesting an increase of the aerosol hygroscopicity, which might result from an increasing mass fraction of nitrate in recent years (Zhang et al., 2015; Itahashi et al., 2018), although the fraction decrease of less hygroscopic compounds is not as significant as the fraction increase of the nitrate. However, the fraction of the non-hydroscopic compounds (i.e., EC) decreases more rapidly than the organic compounds.

Figure 4 The size-resolved activation ratios measured by the SMCA at four different supersaturations. Note that the curves were fitted according to the SMCA measurements.

Figure 4 shows the ARs measured by SMCA at four supersaturation ratios (0.1 %, 0.2 %, 0.4 %, 0.7 %) for particles below 300 nm. The activation curves obtained in this study were segmented into three sections: a steady rise at low ARs, a middle sharp increase, and a plateau at almost 100 % AR. We defined the steepness as the rate at which the AR increased with the particle sizes. Figure 4 shows the steepness increased with the SS, indicating that the curves became steeper with the SS and a larger variation of the D₅₀ was expected. In addition, the CCN activity was more sensitive to particle diameters at higher SS, which can be seen from partial derivative of κ_critical by ∂D₅₀ (Eq. 15):

$$\begin{array}{}\text{(15)}& {\displaystyle \frac{\partial {\mathit{\kappa }}_{\mathrm{critical}}}{\partial D_{\mathrm{50}}}}=-{\displaystyle \frac{\mathrm{4}{A}^{\mathrm{3}}}{\mathrm{9}{D}_{\mathrm{50}}^{\mathrm{4}}\left(\mathrm{lnSc}\right){}^{\mathrm{2}}}}.\end{array}$$

For a certain SS, the κ_critical value became more sensitive to D₅₀ with decrease of the D₅₀. Meanwhile, a high SS usually led to a low D₅₀. Therefore, the AR would vary with D_p more readily at higher SS and the curve would become steeper. A higher SS allowed a smaller particle to be activated and the activation curve became steeper, and vice versa for a lower SS.

The steepness of activation curve was also associated with the heterogeneity of aerosol chemical composition; that is, a steeper activation curve meant that aerosol particles had higher similarity in hygroscopicity. A bimodal distribution (peaks at about 1–1.1 and 1.5–1.7 Gf) of the Gf-PDFs was observed along the Gf coordinate at all five sizes of the particles measured by the HTDMA in this study (Fig. 5), corresponding, respectively, to the less- and more-hygroscopic modes. Larger size particles contain higher fractions of more-hygroscopic inorganic matter which leads to the increase of Gf of the more-hygroscopic mode. The less-hygroscopic mode usually represents externally mixed black carbon or fresh organics. Thus, the less-hygroscopic mode for larger size particles more likely represents the external mixing non-hygroscopic black carbon with a Gf value of 0.8–1.1, indicating that the Gf of the less-hygroscopic mode decreased and that of the more-hygroscopic mode increased with the particle diameter (Fig. 5). Since less-hygroscopic particles were usually associated with externally mixed black carbon (BC) or fresh organics and more-hygroscopic particles usually represent the inorganic matter or BC coated with inorganic matter (internally mixed). The decrease of peak area of less-hygroscopic mode and the increase of more-hygroscopic mode indicate that the number fraction of less-hygroscopic particles decreased while the more-hygroscopic particles fraction increased. Thus, the particles became more internally mixed. Here, a parameter σ is introduced to illustrate the deviation of Gf-PDF (Gysel et al., 2009):

$$\begin{array}{}\text{(16)}& {\displaystyle }& {\displaystyle }{\mathrm{Gf}}_{\mathrm{mean}}=\underset{\mathrm{0}}{\overset{\mathrm{\infty }}{\int }}\mathrm{Gf}c\left(\mathrm{Gf}\right)\mathrm{dGf}\text{(17)}& {\displaystyle }& {\displaystyle }\mathit{\sigma }=\left(\underset{\mathrm{0}}{\overset{\mathrm{\infty }}{\int }}\right(\mathrm{Gf}-{\mathrm{Gf}}_{\mathrm{mean}}{)}^{\mathrm{2}}c\left(\mathrm{Gf}\right)\mathrm{dGf}{)}^{\frac{\mathrm{1}}{\mathrm{2}}},\end{array}$$

where the c(Gf) denotes Gf-PDF and Gf_mean denotes number weighted mean Gf. The σ was employed as a measure of the spread of Gf-PDF which represents the heterogeneity of aerosol chemical composition (Sjogren et al., 2008; Liu et al., 2011). A small σ indicated that the heterogeneity of aerosol chemical composition was low and aerosol particles had higher similarity in hygroscopicity. The parameter C (in Eq. 5) determined the shape of the activation curve which was segmented into steep and smooth parts. A small C value means a steep activation curve, and vice versa. Here, an activation curve was assumed to be steep when the C values were lower than the lower quartile of all the C values, while the activation curve was considered to be smooth when the C values were higher than the upper quartile of all the C values. Table 3 summarizes the σ values of Gf-PDF for the corresponding steep and smooth activation curve at the four supersaturations. In general, the σ increased with the diameter, indicating that larger particles had higher heterogeneity of aerosol chemical composition. Meanwhile, the σ values for smooth curve were generally higher than the σ values for steep curve. The results implied that the shapes of activation curves were related to the heterogeneity of aerosol chemical composition. Cai et al. (2017) compared the Gf-PDF between Guangzhou and Cape Hedo and the results showed that only more-hygroscopic particles were observed in Cape Hedo, indicating that atmospheric particles tend to be more internally mixed in Cape Hedo than in Guangzhou. Meanwhile, atmospheric particles in Guangzhou have a higher degree of external mixing affected by more anthropogenic emissions, which in turn affect the CCN activity.

Table 3 The average of σ values of Gf-PDF measured by the HTDMA for five diameters for the steep and smooth activation ratio at four supersaturations.

Figure 5 The Gf-PDF as a function of Gf measured by the HTDMA for the five diameters.

3.2 Impact of organics on CCN activity

Figure 6 shows the relationship between the D₅₀ obtained from the SMCA measurements and the size-resolved mass fractions of organics (f_org) at three supersaturation ratios (0.1 %, 0.2 %, and 0.4 % SS). In general, the D₅₀ increased with f_org at the three SSs, with slopes of 127, 66, and 21, and fitting coefficients (R²) of 0.47, 0.31, and 0.1 at 0.1 %, 0.2 %, and 0.4 % SS, respectively. The particles usually became less hygroscopic with increase of the organic fractions (f_org), which then required larger particles to be activated. At lower SS, better correlations were found between the f_org and the D₅₀ because the D₅₀ was more sensitive to hygroscopicity (the activation ratios increase slower with particle sizes at lower SS as shown in Fig. 4). It was hence more obvious at lower SS that the modification of the particle hygroscopicity caused by the change of the mass fraction of organic matter could greatly modify the D₅₀ which might further affect the CCN activity. At higher SS, according to Eq. (6), particles were more easily activated as CCN and the change of particle hygroscopicity would not significantly alter the CCN activity.

Figure 6 The relationship between size-resolved mass fraction of organics and D₅₀ at three supersaturations. The red, blue, and green dots and line represent 0.1 %, 0.2 %, and 0.4 % SSs, respectively.

Organics can affect the CCN activity via two opposite ways: they can decrease the CCN activity by increasing the less hygroscopic organic fraction of the particles and thus increase the D₅₀ as shown in Fig. 6; they can also increase the CCN activity by decreasing the surface tension of the particles. The latter effect has been demonstrated experimentally. For example, an increase of CCN activity was observed when organics were added to sulfate ammonium (Engelhart et al., 2008). In this study, we investigated the impacts of organics on CCN activity through adjusting the value of surface tension until the calculated AR values based on HTDMA measurements agreed with those obtained from SMCA measurements (measured AR). The calculated AR values were systematically lower than the corresponding measured ones because here the surface tension of bulk pure water (0.072 N m⁻¹) was assumed when calculating the AR from the HTDMA measurements (Fig. 7). Note that the surface tension is not the only factor that determines the AR and other factors such as the sparingly soluble compounds in the particles may contribute to the AR, although they are currently not understood. Previous studies found that the hygroscopicity of the particles measured by the HTDMA could be lower than that measured by the CCNc (Chan et al., 2008; Pajunoja et al., 2015; Petters et al., 2009; Hansen et al., 2015; Hong et al., 2014) which might be attributed to low soluble compounds in the particles. The deviation of the calculated AR from the measured AR is probably dependent on the degree of dissolution of particles and the oxidative state of the organics in the particles.

Figure 7 The predicted activation ratio based on HTDMA measurement vs. the measured activation ratio at 0.1 %, 0.2 %, 0.4 %, and 0.7 % SS for 40, 80, 110, 150, and 200 nm particles.

The surface tension of a nanoparticle was substantially different from that of its bulk solution due to the curvature effect (Ahn et al., 1975; Bogdan, 1997). The effects of size and composition on the surface tension were currently not well understood. Here, we proposed an approach to evaluate the impact of organics on the surface tension (σ_s∕a) based on the fraction change of the calculated AR to the measured AR. We defined this fraction change (δ_AR) as a function of surface tension, diameter, and supersaturation:

$$\begin{array}{ll}{\displaystyle }& {\displaystyle }{\mathit{\delta }}_{\mathrm{AR}}\left({\mathit{\sigma }}_{\mathrm{s}/\mathrm{a}},D_{\mathrm{p}},\mathrm{SS}\right)={\displaystyle \frac{{\mathrm{AR}}_{\mathrm{m}}\left(D_{\mathrm{p}},\mathrm{SS}\right)-{\mathrm{AR}}_{\mathrm{c}}\left({\mathit{\sigma }}_{\mathrm{s}/\mathrm{a}},D_{\mathrm{p}},\mathrm{SS}\right)}{{\mathrm{AR}}_{\mathrm{m}}(D_{\mathrm{p}},\mathrm{SS})}}\\ \text{(18)}& {\displaystyle }& {\displaystyle }\times \mathrm{100}\mathit{\%},\end{array}$$

where AR_m(D_p,SS) is the measured AR for a certain diameter and SS, and ${\mathrm{AR}}_{\mathrm{c}}({\mathit{\sigma }}_{\mathrm{s}/\mathrm{a}},D_{\mathrm{p}},\mathrm{SS})$ is the calculated AR for a certain diameter, SS, and σ_s∕a. We excluded particles at the size of 200 nm because they were easily activated even at 0.1 % SS and the δ_AR was expected to be independent of σ_s∕a. Here, the σ_s∕a value varied between 0.03 and 0.072 N m⁻¹ (surface tension of pure water). Figure 8 shows the δ_AR as a function of σ_s∕a for the four particle diameters (40, 80, 110, 150 nm). The δ_AR decreased with increase of the σ_s∕a for all given particle sizes, changing more rapidly for smaller particles (i.e., from 200 % to −100 % for 40 nm) than bigger particles (i.e., from 20 % to −10 % for 150 nm). The R² values between measured AR and predicted AR for a certain diameter and four supersaturations at ${\mathit{\sigma }}_{\mathrm{s}/\mathrm{a}}=\mathrm{0.072}$ N m⁻¹ were 0.35, 0.93, 0.95, and 0.91, respectively. The δ_AR values reached zero when the σ_s∕a was set to be about 0.054 N m⁻¹ for 40, 80, and 110 nm particles, and 0.062 N m⁻¹ for 150 nm particles, with a R² of 0.88, 0.94, 0.94, and 0.88, respectively. As a compromise, here we adopt a σ_s∕a value of 0.058 N m⁻¹ (denoted as ${\mathit{\sigma }}_{\mathrm{s}/\mathrm{a}}^{\ast }$) to predict AR. This ${\mathit{\sigma }}_{\mathrm{s}/\mathrm{a}}^{\ast }$ value significantly increased the R² compared to that based on the pure water assumption (0.072 N m⁻¹) for 40 nm particles, while it was reasonably well for other sizes of particles (80, 110, 150 nm). The AR was then recalculated using the ${\mathit{\sigma }}_{\mathrm{s}/\mathrm{a}}^{\ast }$ value and the prediction was significantly improved (Fig. 9). We calculated the p value between the measured and predicted AR and the results showed that the p value is close to 0, indicating a significant correlation between the two variables. The results demonstrated that partitioning of organics into aerosol particles would decrease their surface tension. Therefore, the pure water assumption for surface tension would lead to high uncertainties when it was applied to predict the activation ratios of the aerosol particles at a certain size. Note that we did not consider the effects of individual organics due to the limited data from the chemical composition measurements. How chemical composition affects the surface tension of the particles is yet to be investigated.

Figure 8 The relative deviation between predicted AR and measured AR at different assumed σ_s∕a; the color code represents R² between calculated AR and measured AR.

Figure 9 The predicted activation ratio using the new surface tension assumption (${\mathit{\sigma }}_{\mathrm{s}/\mathrm{a}}^{\ast }$) based on HTDMA measurement vs. the measured activation ratio at 0.1 %, 0.2 %, 0.4 %, and 0.7 % SS for 40, 80, 110, 150, and 200 nm particles.

3.3 The N_CCN prediction

3.3.1 The N_CCN prediction based on the HTDMA measurements

In this study, we used several approaches to predict the N_CCN based on the HTDMA measurements, from either the activation curve or the D₅₀. Table 4 summarizes the methods that were used to predict the N_CCN, along with the slope and R² between the predicted and the measured values. The mixing state of the aerosol particles is an important parameter in determining the N_CCN. The prediction of N_CCN using the activation curve means the N_CCN was calculated based on Eq. (7). Meanwhile, the prediction of N_CCN using the D₅₀ means that the N_CCN was calculated based on Eq. (8) and the D₅₀ was determined from fitting the size-resolved activation ratio by Eq. (5). The activation curve represented actual mixing state, while the D₅₀ approach assumed that all particles were internally mixed. Scheme 5 in Table 4 was the method based on the activation curve with the new ${\mathit{\sigma }}_{\mathrm{s}/\mathrm{a}}^{\ast }$ (0.058 N m⁻¹). Equations (7) and (8) were, respectively, used to calculate the N_CCN following schemes 1, 2, 5, and the rest of the schemes. Scheme 5 (real-time activation curve using ${\mathit{\sigma }}_{\mathrm{s}/\mathrm{a}}^{\ast }$) provided the best N_CCN predicted value (closest to the measured one), followed by scheme 3 (real-time D₅₀) > scheme 4 (average D₅₀) > scheme 1 (real-time activation curve) > scheme 2 (average activation curve). The R² values for all the approaches were in general high (around 0.93). The CCN prediction based on scheme 2 led to the largest underestimation over the measured values. In general, the real-time data (schemes 1 and 3) gave better predicted N_CCN than the corresponding average data (schemes 2 and 4).

Table 4 The overview of different schemes used in the N_CCN prediction based on HTDMA measurements.

Figure 10 shows the correlation between the measured N_CCN and the predicted N_CCN from schemes 1–5 at the four SSs. For schemes 1–4, the predicted N_CCN values were found to be the largest deviation from the corresponding measured ones at 0.1 % SS among all the approaches, probably due to the pure water assumption for surface tension (${\mathit{\sigma }}_{\mathrm{s}/\mathrm{a}}=\mathrm{0.072}$ N m⁻¹). Meanwhile, because the CCN activity was sensitive to hygroscopicity of the particles at low SS, the uncertainties of hygroscopicity data would lead to large errors in the prediction of CCN. As discussed in the previous section, the D₅₀ was more sensitive to the σ_s∕a at lower supersaturations, leading to a large deviation of the N_CCN from the measured value. The best agreement between the calculated AR and the measured AR was seen using scheme 5, as the slopes at the four SSs were close to 1 (Fig. 10q–t).

Figure 10 The relationship between measured N_CCN and predicted N_CCN based on schemes 1, 2, 3, 4, and 5. The black lines represent 1:1 lines.

3.3.2 The N_CCN prediction based on AMS measurements

We proposed five approaches based on HTDMA measurements to predict the N_CCN in the previous section. Alternatively, we can calculate the N_CCN based on AMS measurements. Here, we proposed four methods based on either size-resolved chemical composition or bulk PM₁ chemical composition from the AMS measurements (Table 5). Here, we assumed that the particles were internally mixed and the median κ_AMS obtained from bulk composition was 0.28, higher than those from size-resolved composition (0.24–0.26 in Fig. 3), probably due to a higher mass fraction of inorganic matter in bulk NR-PM₁ (Fig. 2). We excluded the size-resolved data at 0.7 % SS due to their poor quality. Note that the impact on the calculated κ_AMS values and the predicted N_CCN was minor using the κ value (0.53) of ammonium sulfate from Petters and Kreidenweis (2007). For example, the κ_AMS values slightly increased from 0.27 to 0.28 at 0.1 % SS; the slopes for schemes 6, 8, and 9 in Table 5 slightly increased from 0.9859 to 0.9898, 0.9721 to 0.9834, and 0.9742 to 0.9973, respectively, while the one for scheme 7 did not change. Figure 11 shows the correlation between the measured and predicted N_CCN from schemes 6–9. The N_CCN was underpredicted at 0.1 % SS and was overpredicted at 0.7 % SS. We proposed three potential factors that might impact N_CCN prediction based on AMS measurements. (1) The assumed κ_org values were probably underestimated for particles larger than 100 nm, leading to the underestimated N_CCN at low SS. As shown in Fig. 3, the predicted κ shows a larger deviation from the measured value for a larger particle. The D₅₀ values were more sensitive to particle hygroscopicity at lower SS, as discussed in the previous section. (2) Pure water was assumed for surface tension. As we have shown in the previous section, the σ_s∕a values for the aerosol particles were found to be much smaller than the σ_s∕a for pure water (0.072 N m⁻¹). As a result, the pure water assumption for surface tension led to the N_CCN underestimation. In addition, again the D₅₀ was more sensitive to σ_s∕a at the low SS. (3) Black carbon (BC) particles were not included and the particles were assumed to be internally mixed. The BC particles were known to be non-hygroscopic and had a low CCN activity. During the campaign period, the average BC concentration was about 5.91 µg m⁻³, which accounts for 7 % in PM_2.5. The assumption of no BC particles would lead to the overestimation of N_CCN. Here, the particles were assumed to be internally mixed in the AMS measurements. This would lead to an overestimation of the N_CCN when the ambient particles tend to be externally mixed (Wang et al., 2010; Sánchez Gácita et al., 2017). However, the internal mixing assumption seems to play a minor role in predicting the N_CCN at 0.1 % SS since the particles at about 140–180 nm tend to be internally mixed, as shown in Fig. 5. In this case, the κ_org assumption and the pure water assumption played more important roles than the mixing state assumption at low SS (i.e., 0.1 % SS). Figure 11 shows significant underestimation of N_CCN at 0.1 % SS (Fig. 11a, e, i, m), while more or less comparable to the measured N_CCN at higher SS (i.e., 0.2 %, 0.4 %, 0.7 %). The difference between the κ_AMS and κ_CCN became smaller and the corresponding D₅₀ value decreased with the increase of the SS so that the impacts of the κ_org assumption and the pure water assumption became minor with the increase of the SS. Instead, the internal mixing state assumption would play a more important role in the prediction (Meng et al., 2014). As shown in Fig. 5, the peak height and area of the less-hygroscopic mode became larger for the smaller size particles (i.e., 40 nm particles), implying that small particles were likely to be externally mixed; that is, the non-hygroscopic or less hygroscopic species including BC and insoluble organics were less likely coated with inorganic salts. Hence, the internal mixing assumption could lead to an overestimated N_CCN.

Table 5 The overview of methods used in the N_CCN prediction based on AMS measurements.

Figure 11 The relationship between measured N_CCN and predicted N_CCN based on schemes 6, 7, 8, and 9. The black lines represent 1:1 lines.

As discussed above, the two important parameters (κ_org and σ_s∕a) had significant impacts on the N_CCN prediction. We denoted ${\mathit{\kappa }}_{\mathrm{org}}^{\ast }$ and ${\mathit{\sigma }}_{\mathrm{s}/\mathrm{a}}^{\ast }$ as important representations, respectively, for hygroscopicity and surface tension contributed from organics. We also pointed out that the κ_org was dependent on the particle size, and hence here we further assumed the ${\mathit{\kappa }}_{\mathrm{org}}^{\ast }$ values to be 0.15 and 0.1, respectively, for particles larger and smaller than 100 nm. Note that we previously assumed the κ_org to be 0.1 for all particle sizes. Here, we gave an example of the improvements at 0.1 % SS when the κ_org and σ_s∕a values were, respectively, replaced with the ${\mathit{\kappa }}_{\mathrm{org}}^{\ast }$ and ${\mathit{\sigma }}_{\mathrm{s}/\mathrm{a}}^{\ast }$ ones (Fig. 12). The κ_AMS value calculated at 0.1 % SS based on ${\mathit{\kappa }}_{\mathrm{org}}^{\ast }$ was 0.288, very close to the corresponding κ_CCN value (0.30), indicating that an improvement was made for the N_CCN prediction when including the ${\mathit{\kappa }}_{\mathrm{org}}^{\ast }$ value. The N_CCN prediction could be greatly improved when including both ${\mathit{\sigma }}_{\mathrm{s}/\mathrm{a}}^{\ast }$ and ${\mathit{\kappa }}_{\mathrm{org}}^{\ast }$ in the calculation. For example, the underestimate of N_CCN decreased from 44 % (Fig. 11a) to 4 % (Fig. 12b). In addition, we also investigated the effects of the σ_s∕a values in a range of 0.054 to 0.062 N m⁻¹ as discussed in Sect. 3.2. The shadow area in Fig. 12b represents the variation of linear fit between the measured and predicted N_CCN. An under- and overestimated value of 16 % ( slope of 0.84) and 8 % (slope of 1.08) was obtained for the predicted N_CCN to the measured N_CCN using a σ_s∕a value of 0.054 and 0.062 N m⁻¹, respectively, indicating that the predicted N_CCN agreed reasonably with the measured ones when the σ_s∕a values between 0.054 and 0.062 N m⁻¹ were used in this study. We conclude that the predicted N_CCN can agree better with the measured one when including both ${\mathit{\sigma }}_{\mathrm{s}/\mathrm{a}}^{\ast }$ and ${\mathit{\kappa }}_{\mathrm{org}}^{\ast }$ in the calculation at low SS.

Figure 12 The relationship between measured N_CCN and predicted N_CCN at SS 0.1 % based on size-resolved chemical composition using ${\mathit{\kappa }}_{\mathrm{org}}^{\ast }$ (a) and ${\mathit{\kappa }}_{\mathrm{org}}^{\ast }$ and ${\mathit{\sigma }}_{\mathrm{s}/\mathrm{a}}^{\ast }$ (b). The shadow area represents the variation of the linear fit using the σ_s∕a values from 0.054 to 0.062 N m⁻¹.

4 Summary and conclusions

The CCN activity is an important parameter that determines the extent to which atmospheric particles can influence cloud formation. It is hence essential to predict CCN activity so that a quantitative assessment of atmospheric particles on cloud formation can be made. While numerous studies were performed to investigate the CCN activity under different atmospheric conditions around the world, only a few of them were made in the PRD region in China. In this study, several advanced instruments (i.e., the SMCA, AMS, and HTDMA) were used to, respectively, measure CCN activity, chemical composition, and hygroscopicity in PRD during wintertime 2014. A variety of schemes was proposed to determine the CCN activity based on the measurements. Here, two important properties were considered when evaluating the CCN activity: the hygroscopic parameter κ and the surface tension of the particles. Three methods (i.e., the SMCA, the AMS plus ZSR, and the HTDMA) were employed to calculate the κ values based on our measurements. The results show that the deviation between κ_AMS and κ_CCN became larger at low supersaturation ratios, indicating that the organic components in larger size particles were more aged and hygroscopic. The activation curve became smoother at the low SS, which could be partly attributed to the higher heterogeneity of chemical composition for larger particles. In general, the Gf-PDF measured by the HTDMA exhibited a bimodal distribution with a less-hygroscopic mode and a more-hygroscopic mode. The less-hygroscopic mode was more significant at smaller diameters, indicating a more external mixing for smaller particles, while the more-hygroscopic mode increased with diameter and became broader, implying higher hygroscopicity and more complex chemical composition for larger particles. The shapes of activation curve were related to the σ values of the Gf-PDF. The higher σ values suggest the higher heterogeneity of chemical composition and smooth activation curve. A κ value of 0.22–0.30 measured by the HTDMA was obtained for 40–200 nm particles in this study during the measurement period, larger than those previously measured in the PRD region, indicating an increasing mass fraction of nitrate in recent years.

Organic compounds could influence CCN activity through modifying the hygroscopicity and surface tension of the particles. The impacts of organics on CCN activity were also investigated in this study. The increase of organic mass fraction in the particles could lead to the decrease of the aerosol hygroscopicity and hence increase the D₅₀, especially at low supersaturation. In addition, organics could decrease the surface tension σ_s∕a. This could lead to the underestimated CCN activity if the pure water solution is assumed when inverting the HTDMA data. We evaluated the impact of the surface tension on the activation ratios over a wide range of σ_s∕a values (0.03–0.07 N m⁻¹) for several measured size particles (40, 80, 110, and 150 nm) and found that a σ_s∕a value of 0.058 N m⁻¹ was the best fit between predicted AR and measured AR, which could then be used to predict the CCN activity in the PRD region. Based on the hygroscopicity and chemical composition measured in this study, we proposed several schemes to predict the CCN activity. Overall, the predicted N_CCN agreed well with the measure one. The slope and R² of N_CCN predicted from average data were similar to the N_CCN predicted from real-time data. The N_CCN obtained from HTDMA measurement was underpredicted if the pure water assumption was used, and better agreement with the measured values can be achieved by using the adjusted σ_s∕a (i.e., ${\mathit{\sigma }}_{\mathrm{s}/\mathrm{a}}^{\ast }=\mathrm{0.058}$ N m⁻¹). Similarly, the N_CCN predicted from AMS measurement was underestimated at low supersaturations and overestimated at high supersaturations, due to an assumption of fixed 0.1 for κ_org and the external mixing state. Better predicted CCN concentrations can be obtained by using ${\mathit{\sigma }}_{\mathrm{s}/\mathrm{a}}^{\ast }$ and ${\mathit{\kappa }}_{\mathrm{org}}^{\ast }$ in the calculation, especially at low supersaturations. For high supersaturations, the effect of internal mixing assumption should be taken into consideration. We concluded that better agreement between predicted and measured CCN concentrations could be achieved by taking the effects of organics into account on the hygroscopicity, surface tension, and the mixing state of the particles. More work on the roles of organics in the CCN activity is obviously needed in order to better understand the impacts of atmospheric particles on cloud formation and hence climate.