A new method for calculating number concentrations of cloud condensation nuclei based on measurements of a three-wavelength humidified nephelometer system

The number concentration of cloud condensation nuclei (CCN) plays a fundamental role in cloud physics. Instrumentations of direct measurements of CCN number concentration (NCCN) based on chamber technology are complex and costly; thus a simple way for measuring NCCN is needed. In this study, a new method for NCCN calculation based on measurements of a three-wavelength humidified nephelometer system is proposed. A three-wavelength humidified nephelometer system can measure the aerosol lightscattering coefficient (σsp) at three wavelengths and the lightscattering enhancement factor (fRH). The Ångström exponent (Å) inferred from σsp at three wavelengths provides information on mean predominate aerosol size, and hygroscopicity parameter (κ) can be calculated from the combination of fRH and Å. Given this, a lookup table that includes σsp, κ and Å is established to predict NCCN. Due to the precondition for the application, this new method is not suitable for externally mixed particles, large particles (e.g., dust and sea salt) or fresh aerosol particles. This method is validated with direct measurements of NCCN using a CCN counter on the North China Plain. Results show that relative deviations between calculatedNCCN and measuredNCCN are within 30 % and confirm the robustness of this method. This method enables simplerNCCN measurements because the humidified nephelometer system is easily operated and stable. Compared with the method using a CCN counter, another advantage of this newly proposed method is that it can obtain NCCN at lower supersaturations in the ambient atmosphere.

nuclei (CCN) plays a fundamental role in cloud physics.Instrumentations of direct measurements of CCN number concentration (N CCN ) based on chamber technology are complex and costly; thus a simple way for measuring N CCN is needed.In this study, a new method for N CCN calculation based on measurements of a three-wavelength humidified nephelometer system is proposed.A three-wavelength humidified nephelometer system can measure the aerosol lightscattering coefficient (σ sp ) at three wavelengths and the lightscattering enhancement factor (f RH).The Ångström exponent (Å) inferred from σ sp at three wavelengths provides information on mean predominate aerosol size, and hygroscopicity parameter (κ) can be calculated from the combination of f RH and Å.Given this, a lookup table that includes σ sp , κ and Å is established to predict N CCN .Due to the precondition for the application, this new method is not suitable for externally mixed particles, large particles (e.g., dust and sea salt) or fresh aerosol particles.This method is validated with direct measurements of N CCN using a CCN counter on the North China Plain.Results show that relative deviations between calculated N CCN and measured N CCN are within 30 % and confirm the robustness of this method.This method enables simplerN CCN measurements because the humidified nephelometer system is easily operated and stable.Compared with the method using a CCN counter, another advantage of this newly proposed method is that it can obtain N CCN at lower supersaturations in the ambient atmosphere.

Introduction
Cloud condensation nuclei (CCN) are the aerosol particles that form cloud droplets by hygroscopic growth.CCN number concentration (N CCN ) plays a fundamental role in cloud microphysics and aerosol indirect radiative effect.In general, the direct measurement of N CCN is achieved in a chamber under supersaturated conditions (Hudson, 1989;Nenes et al., 2001;Rose et al., 2008).Due to the requirement of high accuracies of working conditions like temperatures, vapors and flow rates in chambers, the direct measurement of N CCN is complex and costly (Rose et al., 2008;Lathem and Nenes, 2011).Thus, developments of simplified measurements of N CCN are required.In recent years, attention has been focused on measurements of aerosol optical properties (Jefferson, 2010;Ervens et al., 2007;Gasso and Hegg, 2003), which are simple and well developed (Covert et al., 1972;Titos et al., 2016).For aerosol population free of sea salt or dust, the accumulation mode aerosol not only dominates aerosol scattering ability but also contributes most to N CCN .Thus, the calculation of N CCN based on measurements of aerosol optical properties is feasible and can facilitate N CCN measurement.
There are methods for calculating N CCN based on measurements of aerosol optical properties.For the first, N CCN as well as the hygroscopicity parameter (κ) can be calculated based on measurements of a humidified nephelometer system in combination with aerosol particle number size distribution (PNSD; Ervens et al., 2007;Chen et al., 2014).Thus addi-Published by Copernicus Publications on behalf of the European Geosciences Union.N CCN predicted at SS > 0.3 % with a 0.9 R2 .

Ervens et al. (2007)
HaChi 2 on the North China Plain Aged continental air mass PNSD and f RH Similar to Ervens et al. (2007).N CCN calculated with the hygroscopicity parameter constrained by f (RH) and PNSD.
Slopes around 1 and R 2 around 0.9.N CCN profile retrieved from backscatter (or extinction) vertical profile assuming their ratios are the same as the ratio at surface, which can be calculated by backscatter (or extinction) and N CCN measured at the surface.
N CCN predicted on most days for 0.1 % SS and on 20-40 % of the days at 1 % SS.

Ghan and
Collins ( 2004) ARM5 Climate Research Facility central site at

Continental air mass
Backscatter (or extinction) and RH profile.
CCN variance explained for 25-63 % of Ghan et al. (2006) the Southern Great Plains N CCN predicted based on empirical relationship between AOT and N CCN as a power law.
N CCN predicted at SS > 0.3 % with a 0.88 R 2 , but with a factor-of-4 range of N CCN at a given AOT.

Andreae (2009)
Four ARM sites Polluted air mass SSA, backscatter fraction and σ sp N CCN estimated from fitting parameters for the N CCN activity spectra, which can be calculated based on their empirical relationships with aerosol optical properties.
N CCN predicted with slopes around 0.9 and R 2 around 0.6.Shinozuka et al. (2015) tional measurements of PNSD are needed.For the second, N CCN is calculated based on statistical relationships between N CCN and aerosol optical properties, such as scattering coefficient (σ sp ), Ångström exponent (Å) and single-scattering albedo (SSA; Jefferson, 2010;Shinozuka et al., 2015).Å is the exponent commonly used to describe the dependence of σ sp on wavelength as the formula shows: where β is the aerosol number concentration.The coefficient of determination (R 2 ) between measured and calculated N CCN using the first method is about 0.9.For the second method, R 2 is generally lower than 0.9, although the instruments are cheaper and easier in operation.Applications similar to the second method are widely used in remote sensing.
As shown in Table 1, earlier studies found that the aerosol volume or aerosol PNSD retrieved from remote sensing measurements can be used to calculate N CCN (Gasso and Hegg, 2003;Kapustin et al., 2006).Recently, either aerosol optical depth (AOD) or aerosol vertical profile has been used to predict N CCN directly (Ghan and Collins, 2004;Ghan et al., 2006;Andreae, 2009;Liu and Li, 2014).
In the statistical relationship between N CCN and aerosol optical properties, σ sp or AOD is mainly the proxy of aerosol absolute concentration, while Å or SSA can be used to reveal the variations of aerosol CCN activity, as shown in Table 1.Based on Köhler theory (Köhler, 1936;Petters and Kreidenweis, 2007), aerosol CCN activity is determined by aerosol size and aerosol chemical composition, and aerosol chemical composition can be defined as aerosol hygroscopicity.Information about aerosol size and aerosol hygroscopicity is critical to N CCN prediction, and their absence can lead to a deviation by a factor of 4 (Andreae, 2009).Compared with aerosol hygroscopicity, aerosol size is more important in determining CCN activity (Dusek et al., 2006).The value of Å can provide information on mean predominate aerosol size (Brock et al., 2016;Kuang et al., 2017a).As a result, N CCN calculation from Å and the extinction coefficient is found to be accurate to some extent (Shinozuka et al., 2015).As proxies for aerosol hygroscopicity, SSA or aerosol light-scattering enhancement factor (f RH) is commonly used, albeit not so effective (Jefferson, 2010;Liu and Li, 2014).f RH is defined as where σ sp (RH) is the humidified σ sp at a given relative humidity (RH).SSA is determined by the ratio between the light-absorbing carbonaceous and less-absorbing components.Black carbon dominates the absorption of solar radiation and is a main hydrophobic component as well.Lessabsorbing components consist of inorganic salts and acids, as well as most organic compounds, which are generally hygroscopic components.SSA correlates positively with aerosol hygroscopicity (Rose et al., 2010) but deviates significantly due to the diversity of hygroscopicity of less-absorbing components.Thus N CCN calculation combining SSA, backscatter fraction and σ sp still leads to significant deviations, with R 2 = 0.6 (Jefferson, 2010).As for f RH, there was a study that applied aerosol optical quantities (σ sp or aerosol optical thickness) with f RH or SSA to calculateN CCN (Liu and Li, 2014).In their study, compared with the combination of SSA and aerosol optical quantities, the combination of f RH and aerosol optical quantities is found to be less accurate in estimating N CCN , even though f RH is directly connected with aerosol hygroscopicity (Liu and Li, 2014).This may result from the significant dependence of f RH on aerosol size (Chen et al., 2014;Kreidenweis and Asa-Awuku, 2014;Kuang et al., 2017a).As mentioned before, PNSD is needed for better calculation of κ and N CCN from f RH in previous studies (Ervens et al., 2007;Chen et al., 2014).A new method to estimate κ from f RH and Å was proposed recently (Kuang et al., 2017a;Brock et al., 2016).Based on this method, f RH can be used to calculate N CCN without measurements of PNSD and can be expected to improve the N CCN prediction just based on measurements of aerosol optical properties.
In this study, the relationship between N CCN and aerosol optical properties measured by a humidified nephelometer system is studied and a new method forN CCN prediction is proposed.This new method is validated based on data observed in the Gucheng campaign on the North China Plain and can be expected to improve measurements of N CCN due to advantages of applying nephelometers.

Data
Data in this study are mainly measured at Gucheng (39.15 • N, 115.74 • E) during autumn in 2016 on the North China Plain.Gucheng is 100 km southwest from Beijing and 40 km northeast from Baoding and has background pollution conditions on the North China Plain.The observation site was surrounded by farmland and about 3 km away from the town of Gucheng.This campaign started on 20 October and lasted for nearly 1 month.
Instruments used in the Gucheng campaign were located in a measurement container under temperature maintained at 25 • C. Ambient aerosol was sampled and dried to RH lower than 30 % by an inlet system consisting of a PM10 inlet, inline Nafion dryers, and a RH and temperature sensor (Vaisala HMP110).Then the sample aerosol was separated by a splitter and directed into various instruments.During this campaign, σ sp , f RH, particle-size-resolved activation ratio (AR) and PNSD were obtained.
f RH and σ sp at three wavelengths were measured by a humidified nephelometer system consisting of two nephelometers (Aurora 3000, Ecotech Inc.) and a humidifier.In addition, Å can be calculated directly from σ sp measured by a nephelometer.The humidifier with a Gore-Tex tube humidified the sample air up to 90 % RH.A whole cycle of humidification from 50 to 90 % RH lasted about 45 min.Dried σ sp was obtained directly from dried sample aerosol measured by one nephelometer, and humidified σ sp was obtained from humidified aerosol measured by another nephelometer.f RH can be calculated by dividing humidified σ sp by dried σ sp .Detailed description of the humidified nephelometer system was illustrated in Kuang et al. (2017a).
The particle-size-resolved AR, defined as the ratio of N CCN to total particles at a specific particle size, was measured by a system mainly consisting of a differential mobility analyzer (DMA, model 3081) and a continuous-flow CCN counter (model CCN200, Droplet Measurement Technologies, USA; Roberts and Nenes, 2005;Lance et al., 2006).The system selected mono-disperse particles with the DMA coupled with an electrostatic classifier (model 3080; TSI, Inc., Shoreview, MN USA) and measured AR of the monodisperse particles by a condensation particle counter (CPC model 3776; TSI, Inc.) and CCN counter.Ranges of particle size and supersaturation (SS) were 10-300 nm and 0.07-0.80%, respectively.Measurements at five supersaturations (0.07, 0.10, 0.20, 0.40 and 0.80 %) were conducted sequentially with each cycle lasting for 1 h, and N CCN at 0.07 % supersaturation was used in this study.Due to non-idealities of the CCN counter at supersaturations lower than 0.10 %, CCN measurement at 0.07 % supersaturation was found to be the most uncertain (Rose et al., 2008) and can lead to deviations of measured N CCN in this study.Before and after the campaign, supersaturations set in this system were calibrated using ammonium sulfate (Rose et al., 2008).More information about the system is available in Deng et al. (2011) and Ma et al. (2016).
PNSD with a particle diameter from 9 nm to 10 µm was measured by a mobility particle size spectrometer (SMPS, TSI Inc., model 3996) and an aerodynamic particle sizer (APS, TSI Inc., model 3321).SMPS consisted of a DMA, an electrostatic classifier and a CPC (model 3776; TSI, Inc., Shoreview, MN USA) and measured PNSD with a diameter lower than 700 nm.
In addition, PNSD and σ sp from 2011 to 2014 during four campaigns (Wuqing in 2011, Xianghe in 2012 and 2013, and Wangdu in 2014) in the North China Plain were used in this study.PNSD in these campaigns was measured by a twin differential mobility particle sizer (TDMPS, Leibniz Institute for Tropospheric Research (IfT), Germany) and an APS (TSI Inc., model 3321).A TSI 3563 nephelometer was used to obtain σ sp at three wavelengths.Details about the four campaigns can be found in Ma et al. (2011Ma et al. ( , 2016) ) and Kuang et al. (2016Kuang et al. ( , 2017a)).

Theories
Hygroscopic growth of particles at a certain relative humidity can be described by κ-Köhler theory (Petters and Kreidenweis, 2007): where g(RH) is the geometric diameter growth factor; κ is the hygroscopicity parameter; RH is the relative humidity; ρ W is the density of water; M W is the molecular weight of water; σ s/a is the surface tension of the solution-air interface, which is assumed to be equal to the surface tension of the pure water-air interface; R is the universal gas constant; and T is the temperature.When accounting for the impact of Å, κ f can be derived directly from f RH (Brock et al., 2016;Kuang et al., 2017a).A single-parameter parameterization scheme proposed by Brock et al. (2016) connects f RH and κ by the approximately proportional relationship between total aerosol volume and σ sp : where κ sca is a parameter for fitting f RH curves and can be used to predict κ f in combination with Å as in recent studies (Brock et al., 2016;Kuang et al., 2017a).This method of calculating κ f based on κ sca and Å was confirmed by good agreement with κ f calculated from f RH and PNSD.
N CCN can be calculated from size-resolved AR at a certain SS and PNSD (referred to as n(log D P )) as follows: (5) In general, size-resolved AR curves are complicated and always replaced by a critical diameter (D c ) to simplify calculation (Deng et al., 2013).The critical diameter is defined as where D P,max is the maximum diameter of the measured PNSD.In other words, the integral of PNSD larger than D c equals the measured N CCN .And a critical κ (κ c ) can be calculated by Eq. ( 3) and indicates CCN activity and hygroscopicity of particles.

Calculation of N CCN based on measurements of a humidified nephelometer system
Free of sea salt aerosol and dust aerosol, accumulation mode aerosol dominates both the optical scattering ability at short wavelengths and the CCN activity at low supersaturations, and thus a reasonable relationship between σ sp and N CCN can be achieved.Figure 1 shows the size distribution of cumulative contributions of σ sp at 450nm and N CCN at 0.07 % with various Å and κ c , and corresponding normalized PNSDs based on data measured during the four campaigns on the North China Plain.During the four campaigns, no sea salt aerosol or dust aerosol was observed (Ma et al., 2011(Ma et al., , 2016;;Kuang et al., 2016Kuang et al., , 2017a)).For continental aerosol without sea salt or dust, Å varies from 0.5 to 1.8, and κ c varies from 0.1 to 0.5 (Cheng et al., 2008;Ma et al., 2011;Liu et al., 2014;Kuang et al., 2017b).As mentioned before, Å can be used as a proxy of the overall size distribution of aerosol populations, with smaller Å indicating more larger particles.In Fig. 1, comparisons for Å are made between 0.5 and 1.9 and for κ c are made between 0.1 and 0.5.As larger particles contribute more to light scattering and CCN activation, cumulative contributions of both σ sp and N CCN increase significantly at the diameter range of accumulation mode particles.
Because more hygroscopic particles are able to activate at smaller diameters, the cumulative contribution of N CCN with higher κ c increases at smaller diameters.In general, major contributions of both σ sp and N CCN are made by particles from 200 to 500 nm for various Å and κ c .This implies the feasibility of inferring N CCN from aerosol optical properties.Because particles smaller than 200 nm can activate at supersaturations higher than 0.07 % while scattering less light at wavelengths longer than 450 nm, which are shown as the light-color lines in Fig. 1, it is obvious that significant differences will exist between cumulative contributions of σ sp and N CCN .This means σ sp and N CCN are dominated by different particles, and poor correlation between σ sp and N CCN can be expected.Thus the method of inferring N CCN from aerosol optical properties is applicable for shorter wavelengths and lower supersaturations.
Furthermore, PNSD with higher Å indicates more Aitken mode particles and fewer accumulation mode particles.Thus large particles contribute less for both σ sp and N CCN when Å are higher, characterizing an increase of cumulative contribution curves at smaller diameters.In detail, cumulative contribution curves of σ sp at 1.9 Å are about 0.3 higher than these curves at 0.5 Å in the size range of 200 to 700 nm, while cumulative contribution curves of N CCN at 1.9 Å are 0.2 no higher than these curves at 0.5 Å. Changes of cumulative contributions of N CCN and σ sp with various Å reveal that the shape of PNSD can influence the correlation between N CCN and σ sp .This is confirmed by previous studies in which Å is found to play an important role in calculating N CCN from σ sp (Shinozuka et al., 2015;Liu and Li, 2014).
The relationship between σ sp and N CCN dependent on Å and κ c is evaluated by calculating σ sp and N CCN with different PNSDs (classified by Å) and different κ c .In detail, ratios of N CCN to σ sp , referred to as AR sp , are calculated to eliminate the effect of variations of particle concentrations consistent at all diameters.Results at a supersaturation of 0.07 % are shown in Fig. 2, and AR sp is higher than 0 and lower than 10.In general, AR sp are higher for more hygroscopic particles or smaller particles.As particles become more hygroscopic, more CCN can be expected when σ sp is fixed.As aerosol populations consist of more smaller CCN-active particles, the increase of σ sp is weaker than that of N CCN .For example, particles with diameters slightly larger than D c contribute less to σ sp than particles with diameters much larger than D c .
In detail, the sensitivity of AR sp to Å also changes with Å and κ c .When Å are higher than 1.4 and κ c is lower than 0.2, AR sp is insensitive to Å; while when Å are lower than 1 and κ c are higher than about 0.3, AR sp is more sensitive to Å than κ c .This higher sensitivity of AR sp to Å reveals that, if the mean predominate size of particles is smaller, the increase of N CCN due to the increase of Å mentioned in the previous paragraph can be larger as a result.This is the consequence of the sensitivity of AR sp to Å resulting from the variation of small CCN-active particles, as mentioned before.Based on the lookup table illustrated in Fig. 2, N CCN at a supersaturation of 0.07 % can be calculated simply from Å, κ f and σ sp , which can be obtained from measurements of a three-wavelength humidified nephelometer system.The description of this simple method is shown in Fig. 3.A new lookup table needs to be made for N CCN estimation at other supersaturations, which should ideally be less than 0.07 % as mentioned in the caption of Fig. 1.
One critical issue about the method is the conversion of the κ f obtained from the humidified nephelometer system to the κ c under supersaturated conditions.There are two main factors making this conversion necessary.First, closure studies of aerosol hygroscopicity found significant deviations between hygroscopicity at sub-saturated conditions and supersaturated conditions (Wex et al., 2009;Irwin et al., 2010;Good et al., 2010;Renbaum-Wolff et al., 2016).Their difference can be expected to be about 0.1 for accumulation mode aerosol (Wu et al., 2013;Whitehead et al., 2014;Ma et al., 2016).Second, κ f indicates the hygroscopicity of total particles and can be quite different from aerosol hygroscopicity at a specific diameter due to variations of size-dependent particle hygroscopicity.Kuang et al. (2017a) found a difference around 0.1 between κ f and κ inferred from g(RH) measurements for accumulation mode particles whose κ f is no larger than 0.2.In this study, a simple conversion wherein κ c is 0.2 higher than κ f is used to calculate N CCN , while for κ f larger than 0.2, a smaller difference of 0.1 between κ c and κ f should be used (Kuang et al., 2017a).This simplified relationship between κ c and κ f is a rough estimate regardless of the complexity of differences of aerosol hygroscopicity measured by different instruments, but it is still used in this study for two reasons.First, the accurate conversion cannot be achieved without detailed information of the particle hygroscopicity, which is difficult and complicated to measure.Second, a deviation of κ c less than 0.1 generally leads to a deviation of N CCN less than 20 % (Ma et al., 2016), which is comparable with the deviation of CCN measurements.As a result, for a simple method of N CCN calculation, this simple conversion is applicable.In addition, it is important to note that the value of the difference between κ c and κ f is also a rough estimate regardless of the complexity of aerosol hygroscopicity under different conditions, and the influence of κ deviation on N CCN calculation needs to be further examined based on field observation.For fresh aerosol, the actual κ can be too large (about 4 times the κ values for some organic components; Wex et al., 2009;Renbaum-Wolff et al., 2016) or too small (nearly zero for inorganic components and black carbon) and thus is not suitable for the application of this method.
Besides aerosol size and hygroscopicity, the aerosol mixing state can also affect aerosol CCN activity.When primary aerosol emissions are strong, aerosol populations are likely to be externally mixed and a realistic treatment of aerosol mixing state is critical for N CCN calculation (Cubison et al., 2008;Wex et al., 2010).But for regions away from strong aerosol primary emissions, the influence of mixing state on aerosol CCN activity is small and the assumption of internal mixing state is effective for the estimation of N CCN (Dusek et al., 2006;Deng et al., 2013;Ervens et al., 2010).For regions above the boundary layer where clouds form and measurements of N CCN are important, aerosol generally tends to be internally mixed when there is no strong vertical transport (McMeeking et al., 2011;Ferrero et al., 2014) and there are no plumes (Moteki and Kondo, 2007;McMeeking et al., 2011).In addition, it should be noted that influences of aerosol hygroscopicity and aerosol size on aerosol CCN ac-Figure 4. Overview of measurements in Gucheng in 2016.Upper plot: time series of N CCN at a supersaturation of 0.07 % (red dots); σ sp at the wavelength of 50 nm (green dots); and their ratios (black dots), referred to as AR sp .Lower plot: time series of κ f (red dots) and Å (green dots).The grey bars are periods when the sensitivity of AR sp to κ c is notable.tivity are more significant than the aerosol mixing state and the deviation of N CCN calculation due to the assumption that the aerosol mixing state is smaller than the deviation due to aerosol size and aerosol hygroscopicity.In the new method of this paper, using Å and κ c to indicate the influence of aerosol size and aerosol hygroscopicity on aerosol CCN activity will increase the deviation of N CCN calculation, which is much larger than the deviation due to the assumption of aerosol mixing state.As a result, the improvement ofN CCN calculation by introducing a more detailed mixing state than internal mixing is limited, and aerosol populations are assumed to be internally mixed for simplification.Thus this method might not be applicable for regions or air masses greatly affected by strong primary aerosol emissions.Furthermore, this new method cannot be applied for regions where sea salt or dust prevails, as mentioned before.In summary, this method can be used to calculate N CCN for air mass tending to be domi-nated by aged aerosol particles, like continental regions and cloud-forming heights.

Validation based on N CCN measurement
The method for calculating N CCN based on measurements of the humidified nephelometer system, including the conversion of κ c and the lookup table, is examined using data measured in Gucheng.
An overview of the data from Gucheng is shown in Fig. 4. From polluted periods to clean periods, significant variations of N CCN and σ sp can be found, but AR sp of N CCN to σ sp stays around 5. On 23 an 29 October, N CCN and σ sp are lower than 2000 # cm −3 and 500 Mm −1 , respectively; while on 20, 26 October and 3 November, N CCN and σ sp are higher than 2000 # cm −3 and 500 Mm −1 , respectively.These variations of N CCN and σ sp are mainly due to the variation of the www.atmos-meas-tech.net/11/895/2018/particle number concentration rather than the shape of particle size distribution and aerosol hygroscopicity.Variations of AR sp result from the variations of Å and κ c , which indicate the variations of aerosol microphysical properties and chemical compositions.
In general, AR sp is more sensitive to variations of Å than κ c .As mentioned before, the sensitivity of AR sp to Å is determined by both Å and κ f .In detail, Å during the campaign mainly ranges from 0.5 to 1.5, and κ f ranges mainly from 0.05 to 0.2, which means that κ c ranges from 0.25 to 0.4.These values of Å and κ f correspond to a significant sensitivity of AR sp to Å, as the lookup table shows in Fig. 2. The sensitivity of AR sp to κ c is much smaller and only notable during some short periods (grey bars in Fig. 4).For example, from 5 to 7 November, variations of κ f and Å are opposite and result in nearly constant AR sp ; from 30 October to 2 November, consistent variations of Å and κ f lead to greater variations of AR sp than other periods.This weak sensitivity of AR sp to κ f may be due to the uncertainty of κ c calculated from κ f based on the simplified conversion.
Based on the lookup table of κ c and Å, AR sp is calculated and applied to calculate N CCN with σ sp .The calculated AR sp and N CCN are compared with the measured AR sp and N CCN , shown as the green dots in Fig. 5.In general, good agreements between calculations and measurements are achieved, and relative deviations are within 30 %.For the comparison of AR sp , the system relative deviation is less than 10 %.For the comparison of N CCN , the slope and the correlation coefficient of the regression are 1.03 and 0.966, respectively.
In addition, the variation of κ and its influence on AR sp and N CCN calculation are studied.As shown in Fig. 6, κ is around 0.2 and independent from Å and κ c , and over 80 % of κ ranges from 0.1 to 0.3.A notable deviation of κ can only be found when Å is higher than 1.5.High values of Å represent existences of small particles, which tend to be freshly emitted and experience inefficient aging processes.In this case, this simplified conversion of κ c may not be applicable.Furthermore, κ with different values are applied in the new method to calculate N CCN .In the first way, κ of the κ c conversion is set to be 0.05 higher or lower than 0.2, which means κ of 0.25 or 0.15.The corresponding results are presented as the red dots and blue dots in Fig. 5.In the second way, a constant κ c of 0.34, which is the average of the κ c values in the Gucheng campaign, is used to calculate AR sp and N CCN ; it is shown as the grey dots in Fig. 5.In general, differences among calculations using various κ c conversions are quite small.The κ difference of 0.05 in κ c conversion only leads to a difference of 10 % for the system relative deviation of calculated N CCN .The correlation coefficient of the calculation using a constant κ c is just a little lower than correlation coefficients of calculations using a κ c conversion.As a result, for data measured in the Gucheng campaign, the method of calculating N CCN is insensitive to the uncertainty of the κ c conversion, and a κ of 0.2 is applicable in this new method.In this study, the insensitivity of calculated N CCN -to-κ c conversion is partly due to the small variation of κ f during the campaign.However, the variation of κ c can be quite large and cause unignorable deviations of calculated N CCN .As previous studies of N CCN measurement have shown, the variation of κ c is often small, and a constant κ c can be used to calculate N CCN accurately (Andreae and Rosenfeld, 2008;Gunthe et al., 2009;Rose et al., 2010;Deng et al., 2013).Results in this study are similar to these previous studies.But large variations of κ c are also found in some other studies.In the North China Plain, fluctuations of aerosol hygroscopicity during new-particle-formation events and soot emissions lead to significant deviations of calculated N CCN from average aerosol hygroscopicity (Ma et al., 2016).Furthermore, the influence of κ c cannot be ignored because the value of the average hygroscopicity is different in various regions during various periods.In summer of the North China Plain, measured κ f at sub-saturated conditions can reach up to 0.45 when inorganic components dominate in particles (Kuang et al., 2016).In this case, calculated N CCN ignoring κ c may be 10 times larger than measured N CCN .To sum up, although the exact value of κ c cannot be obtained from the measurement of the humidified nephelometer system, the influence of κ c on N CCN can be inferred and is found to be correct enough considering the convenience of this method.More data, especially from observations of more hygroscopic aerosol, are still needed to confirm this method.

Conclusions
N CCN is a key parameter of cloud microphysics and aerosol indirect radiative effect.Direct measurements of N CCN are generally conducted under supersaturated conditions in CCN chambers, and are complex and costly.Accumulation mode aerosol contributes most to both the aerosol scattering ability and the aerosol CCN activity.In view of this, it is possible to predict N CCN based on relationships between aerosol optical properties and the aerosol CCN activity.In this study, a new method is proposed to calculate N CCN based on measurements of a humidified nephelometer system.In this method, N CCN is derived from a lookup table which involves σ sp , Å and κ f , and the required three parameters can be obtained from a three-wavelength humidified nephelometer system.
Relationships between aerosol optical properties and aerosol CCN activity are investigated using datasets on aerosol PNSD measured during several campaigns in the North China Plain.The relationship between σ sp , Å, κ c and N CCN is analyzed.It is found that the ratio between N CCN and σ sp , referred to as AR sp , is determined by κ c and Å.In light of this, it is possible to calculate N CCN based only on measurements of a three-wavelength humidified nephelometer system which provides information about σ sp , the hygroscopicity parameter κ and Å.However, κ derived from measurements of a humidified nephelometer system under sub-saturated conditions (termed κ f ) differs from κ under supersaturated conditions, which indicate aerosol CCN activity (termed κ c ).As a result, the conversion from κ f to κ c is needed.Based on previous studies of aerosol hygroscopicity and aerosol CCN activity, a simple conversion from κ f to κ c with a fixed difference (referred to as κ) of 0.2 is proposed.On the basis of this simple conversion, the method of N CCN prediction based only on measurements of a humidified nephelometer system is achieved under conditions without sea salt aerosol, dust aerosol, externally mixed aerosol or fresh aerosol.
This method is validated with measurements of a humidified nephelometer system and a CCN counter in Gucheng in 2016.During the campaign, both N CCN and σ sp vary with the pollution conditions.AR sp is around 5 and changes with Å and κ f .Based on this new method, N CCN are calculated to compare with its measured values.The agreement between the calculated N CCN and the measured N CCN is achieved with relative deviations less than 30 %. Furthermore, the variation of κ and its influence on N CCN calculation are studied.The difference between κ f and κ c was 0.2 ± 0.1.Sensitivity of calculated N CCN to conversions from κ f to κ c is studied by applying different kinds of conversions.Results show that calculated N CCN varies little and is insensitive to the conversions, which confirms the robustness and applicability of this newly proposed method.
This study has connected aerosol optical properties with N CCN and also proposed a novel method to calculate N CCN based only on measurements of a three-wavelength humidi-fied nephelometer system.Due to the simple operation and stability of the humidified nephelometer system, this method will facilitate the real-time monitoring of N CCN , especially on aircrafts.In addition, measurements of the widely used CCN counter are limited to supersaturations higher than 0.07.In fogs and shallow layer clouds, supersaturations are generally smaller than 0.1 % (Ditas et al., 2012;Hammer et al., 2014a, b;Krüger et al., 2014).For studying aerosol-cloud interaction, this method is more applicable due to its applicability for calculating N CCN at lower supersaturations than 1.0 %.
Data availability.The corresponding data in Fig. 2 can be accessed through the following link: https://pan.baidu.com/s/1mjyQ8uk.The whole dataset can be accessed by request to the corresponding author.
Competing interests.The authors declare that they have no conflict of interest.

Figure 1 .
Figure1.Aerosol PNSD (black lines), the cumulative contribution of σ sp at wavelength of 450 and 700 nm (dark green lines and light green lines, respectively), the cumulative contribution ofN CCN at a supersaturation of 0.07 % (dark red and dark blue lines) and the cumulative contribution of N CCN at a supersaturation of 0.20 % (light red and light blue lines) based on measurement in several campaigns in the North China Plain.Solid lines and dashed lines indicate Å of 1.9 and 0.5, respectively.Blue lines and red lines indicate κ c of 0.1 and 0.5, respectively.

Figure 2 .
Figure 2. Colors represent AR sp (calculated as AR sp = N CCN σ sp at 450 nm wavelength and 0.07 % supersaturation) with different PNSDs (classified by Å values) and different κ c .

Figure 3 .
Figure 3.The schematic chart of the N CCN prediction based on measurements of a humidified nephelometer system.

Figure 5 .
Figure 5. (a) Comparisons of calculated AR sp and measured AR sp with different conversions of κ c from κ f .(b) Regressions of calculated N CCN and measured N CCN with different conversions of κ c from κ f .

Figure 6 .
Figure 6.Differences between κ c and κ f , referred to as κ, with Å (positions of dots) and κ f (colors of dots).Bars represent percentages of κ within different ranges.

Table 1 .
Review of studies that have used aerosol optical parameters to infer N CCN .