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:

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):

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).

2.3.1 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):

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:

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):

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 1A 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.

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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)

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):

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.

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:

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 1The 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).

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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).

3.3.1 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 4The overview of different schemes used in the N_CCN prediction based on HTDMA measurements.

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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 10The 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.

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

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

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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 12The 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.

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