Interactive comment on “ Size-resolved and bulk activation properties of aerosols in the North China plain : the importance of aerosol size distribution in the prediction of CCN number concentration ” by Z

This paper discusses the interaction between aerosol particles and cloud formation. This is a very important scientific issue for climate change study. This paper shows the field measurement in a highly polluted region (eastern China). Due to the extremely high aerosols and lack of measurements in this region, the result of the experiment provides important information for better understanding the interaction between aerosols and cloud formation. In addition, this study shows more detailed information of aerosol particles than some previous measurements in this region. This study provide not only bulk aerosol information (such as PM2.5 and PM10), which is normally measured by

size.The slopes of the activation curves for ambient aerosols are not as steep as those observed in calibrations with ammonium sulfate suggesting that the observed aerosols is an external mixture of more hygroscopic and hydrophobic particles.
The calculated CCN number concentrations (N CCN-calc ) based on the size-resolved activation ratio and aerosol number size distribution correlate well with the N CCN-obs , and show an average overestimation of 19%.Sensitivity studies of the CCN closure show that the N CCN at each supersaturation is well predicted with the campaign average of sizeresolved activation curves.These results indicate that the aerosol number size distribution is critical in the prediction of possible CCN.The CCN number concentration can be reliably estimated using time-averaged, size-resolved activation efficiencies without accounting for the temporal variations.

Introduction
The impact of aerosol on cloud and the corresponding feedbacks of cloud are currently considered as the largest uncertainty in climate system (IPCC, 2007).Great efforts have been made to predict the number concentration of cloud condensation nuclei (CCN) for modeling applications (Boucher and Lohmann, 1995;Khvorostyanov and Curry, 2006).Closure studies where measured and predicted CCN number concentrations (N CCN ) are compared, provide a test for quantitative understanding of CCN activation properties, and in particular, for parameterization schemes used in large-scale Published by Copernicus Publications on behalf of the European Geosciences Union.Z. Z. Deng et al.: Size-resolved and bulk activation properties of aerosols in the North China Plain models.Closure between the measured and the predicted CCN number concentrations would be achieved, when the differences between them fall within the uncertainties of measurements and predictions.
It has been well documented that the Raoult and Kelvin effects would together determine how an aerosol particle could turn into a possible CCN (Rogers and Yau, 1989).The relative importance of aerosol number size distribution and aerosol chemical composition in aerosol activation has already been discussed in several studies.Aerosol chemical composition is more important at lower supersaturations than at higher supersaturations, because the relative change in CCN number concentration induced by the change of aerosol composition is larger for circumstances with low CCN number concentration at lower supersaturations (Kuwata et al., 2005).The ability of particles to act as CCN is largely controlled by aerosol size rather than composition (Junge and McLaren, 1971;Fitzgerald, 1973;Dusek et al., 2006).Mixing state indicating the heterogeneity of the chemical composition of a particle distribution also needs to be accounted for (Anttila, 2010;Medina et al., 2007).
The measurements of aerosol size distribution and chemical composition are often utilized to predict the CCN number concentration.Bulk chemical composition of aerosol particles with diameter smaller than 10 or 1 µm from filter sampling is often used in closure studies (Bougiatioti et al., 2009), while the knowledge of a size-resolved composition could possibly improve the prediction of CCN number concentration (Medina et al., 2007).Stroud et al. (2007) measured chemical composition of aerosols with an aerosol mass spectrometer (AMS), and predicted CCN number concentration with a kinetic model.CCN number concentrations were substantially over predicted (by 35.8±28.5%)using size-averaged chemical composition, and by introducing size-dependent chemical composition the closure was improved considerably (average error 17.4±27%).
Size-resolved activation ratios (the fraction of the activated particles in the total aerosol number) are frequently determined in laboratory and field studies.Such methods, described in detail by Frank et al. (2006), are used in instrument calibrations in laboratory and applied in measurements of aerosol activation properties.Size-resolved activation properties of known compounds, such as water-soluble organic and inorganic substances (Hori et al., 2003;Cruz and Pandis, 1997), mixtures of known compounds (Giebl et al., 2002), and natural mixtures (Dinar et al., 2006;Wex et al., 2007;Ziese et al. 2008) are intensively investigated in laboratory studies.
The concentrations of various pollutants are dramatically increasing in recent decades in China due to rapid economic development.The North China Plain (NCP) is one of the most polluted regions in the world, according to the satellite data of the aerosol loading and trace gas concentrations (CO, SO 2 , NO x , etc.) (Xu et al., 2011).The high level of aerosol loading (mass and number) and trace gases concentrations could possibly change the physical and chemical properties of the atmosphere, as well as cloud processes.A case in point is that the precipitation in North China has decreased significantly during the last 40 years and the reduction trend of precipitation is found to be correlated to increasing aerosol concentrations (Zhao et al., 2006).
In this work, the aerosol activation properties in the NCP are investigated, using the aerosol number size distributions, the size-resolved activation ratios, and the bulk CCN number concentrations.This work presents a method to better understand the relationship between aerosol number size distribution and CCN number concentration.Finally, a closure study is performed between the measured (N CCN-obs ) and calculated CCN number concentrations involving aerosol size distribution and size-resolved activation ratio.

Relationship between aerosol size distribution and CCN number concentration
This section presents the relationship between the aerosol number size distribution and CCN number concentration to help understanding the current work.
A bulk CCN number concentration can be measured employing a CCN counter (CCNC) set at a given supersaturation.The CCN is a subset of the total aerosol population.A schematic plot shows the relationship between aerosol number size distribution and CCN in Fig. 2.

Internally mixed aerosol
Assuming uniform chemical composition throughout the size range, a critical dry particle diameter D m (pink line in Fig. 2) can be calculated from the N CCN-obs and aerosol size distribution.The number concentration of aerosol particles with sizes larger than D m equals to N CCN-obs .
where D p is the diameter of aerosol particle, and n(logD p ) is the function of the aerosol number size distribution.

Partially externally mixed aerosol
Atmospheric aerosol particles have complicated sizedependent chemical compositions due to various physical and chemical processes involved.Even at a certain particle size, their chemical composition may be quite different if the aerosol is heterogeneous mixed.For atmospheric aerosol particles with various chemical compositions, the CCN concentration can be calculated using the following equation, where n CCN (logD p ) is the CCN number size distribution function, and A(logD p ) is the size-resolved activation ratio.
The size-resolved activation ratio A(logD p ) is determined by aerosol particle size and chemical composition.In order to understand the role of size and composition on the sizeresolved activation ratio, two extreme conditions for aerosol composition are introduced and discussed here.First, we consider highly soluble particle substance (HSP), such as NaCl aerosols or ammonia sulfate aerosols.A critical dry diameter D HSP for the highly soluble particles can be calculated using Köhler equation (blue line in Fig. 2).Particles with sizes smaller than D HSP cannot be activated at the corresponding supersaturation.
For another extreme case, we consider an insoluble but wettable particle (IBW).Here, a Kelvin diameter (D Kelvin , green line in Fig. 2) is determined using the Kelvin equation (Rogers and Yau, 1989;Pruppacher and Klett, 1997;Seinfeld and Pandis, 2006).The particles larger than D Kelvin are all activated.
The critical dry diameters of NaCl, (NH 4 ) 2 SO 4 and IBW aerosol particles at various supersaturations are shown in Table 1.Typical supersaturation for stratiform clouds, cumulus clouds, and fog are 0.05%, 0.25-0.8%,and 0.1%, respectively (Seinfeld and Pandis, 2006).Ammonium sulfate particles larger than 34 nm, respectively sodium chloride particles for sizes larger than 26 nm may be activated at supersaturation of 0.8%.The size of an IBW particle needs to be above several micrometers to be activated at very low supersaturations in stratiform clouds.The activation ratio of aerosols is 0 at D HSP and 1 at D Kelvin .The activation ability of ambient aerosols in the real atmosphere varies between these two extreme cases of highly soluble substance and IBW.In this paper, ambient aerosol activation properties are investigated in field measurements using CCNC and mobility size spectrometer.3 Measurements and data processing

The field site
The NCP has been undergoing a rapid development during the last three decades.Heavy industries and dense population have been causing severe particulate and gaseous pollution episodes, especially over the main cities in this area (Xu et al., 2011).Wuqing is a town located in the NCP between the two Megacities of Beijing and Tianjin (Fig. 1).Investigations of the physical and chemical properties of the atmosphere were conducted at a regional/suburban site in Wuqing (39 • 23 N, 117 • 01 E, 7.4 m a.s.l.).The site is at the edge of the town with low traffic flow, and there are no large emission sources in the immediate surrounding areas.
The field study, focusing on aerosol, CCN activation properties and aerosol optical properties, was carried out in January 2010.The aerosol number size distribution and the bulk CCN number concentration were measured from Dec. 31, 2009 to Jan. 20, 2010.The size-resolved activation ratios were measured only at daytime.

Instrumentations
The data used in this work include the aerosol number size distribution, the CCN number concentration and the sizeresolved CCN activation ratio.The set-up of instruments is shown in Fig. 3.The instruments were equipped in the air-conditioned measurement container with a temperature around 20   7 m above the ground level, and subsequently passes through a silica gel diffusion drier, maintaining a relative humidity (RH) below 30%.
Aerosol number size distributions (13.8-750 nm) were obtained by a scanning mobility particle sizer (SMPS, Model 3936, TSI, USA) with a time resolution of five minutes.The SMPS consist mainly of differential mobility analyzer (DMA, Model 3081, TSI, USA) and condensation particle counter (CPC, Model 3772, TSI, USA).The DMA sheath and sample flows were 3 lpm and 0.3 lpm, respectively.
A continuous-flow dual CCN counter (CCN-200) (Roberts and Nenes, 2005;Lance et al., 2006) manufactured by Droplet Measurement Technologies (DMT, USA) was utilized to measure the CCN activation properties.The CCN-200 has two columns to measure different samples at different supersaturations at the same time.One column directly measures the dry polydisperse aerosol sample to obtain the bulk CCN concentration, while the other measures the sizeresolved activation properties.Both columns operated at the same supersaturations at the same time.Five supersaturations (nominally 0.07, 0.10, 0.20, 0.40, and 0.80%) made up a cycle of half an hour, taking 10 min for 0.07% and 5 min for other supersaturations.The bulk CCN number concentrations at five supersaturations were available every half an hour. 1 Figure 3 Instrumentation Set-up 2 3 Quasi-monodisperse aerosol particles with diameters of 30,40,50,75,100,150,200 and 300 nm were selected by another DMA (Model 3081, TSI, USA).The selected size of aerosol particles after the DMA was also changed every 30 minutes, during which the activation ratios for one size at five supersaturations were measured.Particle sizes with number concentrations with less than 10 cm −3 were skipped.The sheath and sample flow rates in DMA were 8 lpm and 0.8 lpm, respectively.The sample flow was then split into two parts, 0.5 lpm for CCNC and 0.3 lpm for CPC (Model 3776, TSI, USA).CCNC reports the CCN number concentration for these size-selected aerosol particles (N CCN-mono ), and CPC reports the corresponding condensation nuclei number concentration (N CN-mono ).The activation ratio is defined as the ratio between N CCN-mono and N CN-mono .Activation ratios of all the diameters at five supersaturations were available every 3-4 h depending on the number of selected particle sizes.
The CCNC was calibrated with ammonium sulfate particles (Rose et al., 2008) before and after the campaign.The critical dry diameters determined from the activation curves of ammonium sulfate, are converted to effective supersaturation (SS e ) utilizing the Köhler equation (Pruppacher and Klett, 1997).The Köhler equation employs the temperature dependent surface tension of water (IAPWS Secretariat, 1994), temperature dependent solubility of ammonium sulfate in water (Seinfeld and Pandis, 2006), and molality dependent van't Hoff factor (Young and Warren, 1992;Low, 1969).
The temperature gradients (TG) and SS e were linearly fitted.The SS e of the atmospheric measurements is calculate from the TG with this TG∼SS e relationship.The calibration shows that the effective supersaturations were 0.058, 0.085, 0.18, 0.36 and 0.72% for size-resolved measurements, and 0.056, 0.083, 0.17, 0.35 and 0.70% for bulk measurements.

Data processing
For each supersaturation, N CCN-obs is recorded every second.To ensure the instrument and data stability, these records are filtered with different criterions of temperature and flow, e.g., the temperatures and flow rates need to be close to the set values.The average N CCN-obs at each supersaturation is computed using the processed records.
The CCN activation ratio is calculated based on both the N CCN-mono and N CN-mono of the quasi-monodisperse aerosol particles.Each aerosol sample consists of aerosol particles with a small range of electrical mobility, due to the DMA transfer function.The particles may however carry different number of electric charges.This means that even for the same mobility, these particles can have different particle sizes.The DMA transfer function width and the multiple charges skew the activation curves.
A multiple charge correction is then applied for the CCN activation ratio without considering the width of DMA transfer function (as the Appendix A).The presence of multiply charged particles, which usually have higher activation ratio than the singly charged particle, induces a falsely higher measured activation ratio for singly charged diameters.The correction will reduce the activation ratio especially for the smaller particle sizes.

Summary of bulk CCN measurements
Figure 4 shows the time series of the wind, aerosol number concentrations (N CN ) and N CCN-obs during the measurement period.The statistical results for the N CN and N CCN-obs are summarized in Table 2.The N CN ranged from 2000 to 59 000 cm −3 .Most of the time, the N CN was however between 10 000 and 40 000 cm −3 .
The N CCN-obs depended strongly in the different weather systems during the measurement period.High N CCN-obs were observed during periods of heavy aerosol pollution when the wind speed was low.The N CCN-obs was found to be as high as 28 000 cm −3 at 0.70% supersaturation.Normally, the N CCN-obs was however about 2000, 3000 and 6000 cm −3 at supersaturation of 0.056, 0.083 and 0.17%, and more than 10 000 cm −3 at supersaturations above 0.35%.On other hand, under meteorological situation with strong winds, the N CCN-obs can be as low as around 100 cm −3 at supersaturations of 0.056 and 0.083%, and less than 2000 cm −3 at 0.70% supersaturation, because the aerosol number concentration in the accumulation mode range becomes relatively low.
The inferred critical diameters D m , as defined in Eq. (1) in Sect.2.1, are calculated based on the N CCN-obs and the corresponding aerosol number size distribution.The D m at each supersaturation varies dramatically (Fig. 5).Variations of D m at supersaturations above 0.17% are larger than  that at 0.056 and 0.083% supersaturations.The D m are in the ranges of 190-280, 160-260, 95-180, 65-120 and 50-100 nm at supersaturations of 0.056, 0.083, 0.17, 0.35 and 0.7%, with their mean values 230.1, 198.4, 128.4, 86.4 and 69.2 nm, respectively.The average aerosol number concentration within these size ranges are 2000, 2900, 5800, 6900 and 8100 cm −3 .These values are comparable to the campaign average N CCN-obs .The predicted CCN number concentrations (using Eq. 1) with the mean critical dry diameters inferred from the measurements result in an average relative deviation of nearly 69%, and a bias of −26% (see the definition in caption of Fig. 9).This indicates that it is impossible to predict CCN number concentration from the aerosol number size distribution using a fixed critical dry diameter.

Size-resolved activation ratio
Figure 6 shows the time series of the activation ratios for 75, 100, and 200 nm particles at different supersaturations.
At lower supersaturations and for smaller particles, e.g.75 nm at 0.058 and 0.085% supersaturations, the activation ratios are close to 0, because the particles are too small to be activated.Particles larger than 75 nm are mostly activated at supersaturations above 0.36%.It can be seen in Fig. 6 that the activation ratios for 200 nm particles at 0.056%and 0.085%, for 100 nm particles at 0.18%, and for 75 nm particles at 0.36% mainly ranged between 0.2 and 0.8.
Figure 7 shows the size-resolved activation curve at each supersaturation averaged for the campaign.The activation curves for ambient aerosols are shown in colored lines.The activation curves at different supersaturations are distinct.Particles smaller than 150 nm are rarely activated at supersaturation 0.058%, while 40 nm particles have activation ratios of 0.4 at 0.72% supersaturation.
Most 300 nm particles activate at all measured supersaturations.Although 300 nm is much smaller than the Kelvin diameter for most of the measured supersaturations (Table 1), small soluble fraction enables the particle to be activated.For example, ammonium sulfate fractions of 18, 8, 2, 0.3 and 0.03% (and the rest is insoluble) are sufficient to activate a 300 nm particle at supersaturations of 0.07, 0.1, 0.2, 0.4 and 0.6%, respectively.Almost no particles of 30 nm are activated at the measured supersaturations, because even pure ammonium sulfate particles of 30 nm are unable to be activated at 0.8% supersaturation.The activation ratios are strongly dependent on the particle size.The activation ratio increases with increasing diameter.
The slope of the activation curves of ammonium sulfate represents internally mixed aerosol (gray curves in Fig. 7).The slopes for ambient aerosols are not as steep as that of ammonium sulfate, suggesting that the aerosol is chemically and/or morphologically externally mixed (Frank et al., 2006).For each size, hygroscopic growth and activation of particles depend on their chemical components and mixing state.The external mixing is also observed in the hygroscopicity measurements in Wuqing (Liu et al., 2011).And the GF-PDF (Probability Distribution Function of Growth Factor) of a size selected aerosol, in turn, can provide the activation ratio at various supersaturations (Su et al., 2010).

Calculation of CCN number concentration based on aerosol number size distribution and size-resolved activation ratio
The CCN number concentration can be calculated from the aerosol number size distribution and the size-resolved activation ratios (Eq.2).The calculation of N CCN using this method is evaluated in this study with parallel measurements of N CCN and size-resolved activation properties (Fig. 8).
The two columns of the CCNC are independent and they are used for bulk and size-resolved measurements.Both columns are set to the same five supersaturations, nominally 0.07, 0.10, 0.20, 0.40 and 0.80%, during the measurement.However, the calibration showed that the effective supersaturations are different (Sect.3.2).
The measured N CCN is compared with the calculated N CCN at the same supersaturation in CCN closure study.The measured N CCN and effective supersaturation are fitted with an empirical function where S is supersaturation, N 0 , k and S 0 are fitted parameters.This function describes the N CCN ∼S relationship in this study better than N CCN = CS k suggested by Twomey (1959).N CCN at the effective supersaturations of the size-resolved measurements are achieved by fitting the CCN spectra with Eq. ( 3).This is referred to as the "measured" N CCN (N CCN-meas ), and then used to be compared with the calculated N CCN (N CCN-calc ).

Calculation with measured aerosol number size distribution and size-resolved activation ratio
N CCN-calc can be calculated from the above corrected data with Eq. ( 2).The calculated N CCN-calc (N CCN-calc−realtime ) based on the measured aerosol number size distribution and the size-resolved activation ratio, along with the bulk measurements, is shown in Fig. 9a.The N CCN-calc−realtime is highly correlated with the measurements (R 2 = 0.9501).However, the calculation generally overestimates the N CCN .The linear fitted lines have slopes larger than 1 for each supersaturation and 1.169 for all the data.
The difference between measured and calculated N CCN might result from the measurement uncertainties.The  uncertainty for aerosol number size distribution is under controlled conditions within 10% (Wiedensohler et al., 2011).The uncertainty for CCN measurements comes from the uncertainty of supersaturation, the water depletion inside the CCNC, and the particle counting and flow rate.The uncertainty of calibrated supersaturation, by comparing the calibration before and after the campaign, is small in this study.The water depletion may occur in the CCNC in the bulk CCN measurement.The high particle number concentration also may reduce the counting rate of the CCNC (manual of CCNC).Taking these sources into account, the uncertainty of bulk and size-selected CCN number concentration might exceed that of aerosol size distribution measurement.Moore et al. (2010) reported uncertainties of 0.17 for N CCN-mono , 0.067 for N CN-mono and thus 18% for activation ratio when the N CN-mono is 100 cm −3 .Other uncertainties arise from the coarse size resolution of the activation ratio, the absence of DMA transfer function correction for the activation ratio and the linear interpolation of the activation ratio on the scale of logD p .The uncertainties are estimated to be >10% for bulk N CCN-meas , and >21% for calculated N CCN-calc .The calculated CCN number concentrations agree well with the measured one within the estimated uncertainties of the measurements and the data processing.

Sensitivity study
The calculation of N CCN-calc employs the activation ratio curves and the aerosol number size distribution.The activation ratio curves (AR) represent the chemical composition and mixing state of aerosol.The aerosol size distribution can be described with two factors, i.e. the population of aerosol and the normalized aerosol size distribution (NASD) Sensitivity tests are performed to explore the relative importance of these three factors (AR, N CN and NASD).The N CCN-calc are calculated when one of the above factors is replaced by the average conditions.
The average AR based on 20-day measurements in January 2010 are given in Fig. 7. Figure 9b shows the calculated N CCN-calc (N CCN-calc−ConstAR ) utilizing these averaged activation curves and the real-time measurement of aerosol size distribution.There are more scattered data than the base case (Fig. 9a).The relative bias is larger than the base case and the correlation coefficient (R 2 ) is lower.Nevertheless, both relative bias and R 2 are close to those of the result using all real-time data.The replacement of the average activation ratio does not cause significant changes to the results.These average size-resolved activation ratio curves provide a good estimation of activation properties.
Figure 9c shows the result when particle number concentrations are fixed to the average one.The aerosol number size distributions are replaced with the product of the NASD and the average particle number concentration (N CN ).
where bar represents average in time.The N CCN-calc−ConstNcn is linearly related to particle number concentration.The N CCN-calc−ConstNcn is limited by the prescribed aerosol number concentration.The average relative deviation is larger than the base case and the correlation coefficient is lower.The linear fitted lines have slopes and intercepts highly biased from 1 and 0, respectively.
The average NASD is obtained from the average of all normalized aerosol number size distributions.The aerosol number size distribution in the calculation is replaced with the product of the average NASD and the original particle number concentration.
Compared to the previous cases, the average NASD case has much more scattered data; both the average relative bias and the average relative deviation are also larger (Fig. 9d).
From the results discussed for Fig. 9c and d, it can be seen that the aerosol number size distribution plays a critical role in calculation of N CCN .The evolution of aerosol number size distribution depends on the sources, coagulation, growth, aging and deposition processes.It is improper to calculate the N CCN with prescribed aerosol size distribution due to its significant variation.

Summary and conclusion
The aerosol-cloud interaction is an essential issue in climate change research.The relationship between aerosol and CCN is complicated, because the aerosols origin from various emissions, and undergo atmospheric physical and chemical processes.Measurements of size-resolved activation help Atmos.Chem. Phys., 11, 3835-3846, 2011 www.atmos-chem-phys.net/11/3835/2011/us to better understand the ability of aerosol particles acting as CCN.The bulk and size-resolved activation properties of submicron aerosols were investigated in January 2010 at a regional/suburban site in the NCP.High aerosol mass and number concentrations are connected with high N CCN-obs in the NCP.The N CCN-obs occasionally exceeds 20000 cm −3 at supersaturations above 0.35% during pollution episodes.Such high N CCN-obs are also observed in the vicinity of Guangzhou (Rose et al., 2010) and south of Beijing (Wiedensohler et al., 2009).
However, the relationship between this abundant CCN at the surface and the cloud properties is not clear yet.Deng et al. (2009) presented the aircraft measurements of cloud droplet number concentration (CDNC) around Beijing.The CDNC are 376±290, 257±226, 147±112, 60±35 and 60±84 cm −3 , for cumulus, stratocumulus, altocumulus, altostratus, and nimbostratus clouds, respectively.This observed CDNC around Beijing area are far lower than the surface measured CCN number concentration.Most of the aerosols are trapped inside the boundary layer.The aircraft measurements show that the aerosol number concentration decreases with height (Liu et al., 2009).Aerosol particles in the boundary layer do not always have opportunity to be activated into the cloud droplets above the boundary layer.There are also some mechanisms to transfer the surface aerosol into the free troposphere, such as convection.Local circulations like mountain valley breeze and sea land breeze may also alter the vertical profiles of aerosol.Chen et al. (2009) shows that the pollutants in the boundary layer can be injected from the planetary boundary layer and form an elevated pollution layer in the free troposphere due to the Mountain Chimney Effect.
The size-resolved activation measurements and CCN closure study provide insight of the detailed activation ability.More than 50% of the particles larger than 200, 170, 90, 70, and 45 nm are activated at supersaturations of 0.058, 0.085, 0.18, 0.36 and 0.72%, respectively.These diameters are a little larger than but close to the critical diameters of ammonium sulfate particles (Table 1).This implies that the aerosols in the North China Plain consist of highly soluble material.Soluble fractions of more than 83%, calculated based on the Köhler Theory with assumed aerosol composition of ammonium sulfate and an insoluble core, are needed to activate these particles.The water soluble organics and the influence of surface tension are also expected to contribute to the activation (Petters and Kreidenweis, 2007;Gunthe et al., 2011).
The size-resolved activation curves, based on the measured aerosol size distributions, provide a method to calculate CCN size distribution and N CCN .Sensitivity studies of this method were performed to explore the relative importance of the size-resolved activation ratio, the aerosol number concentration and normalized aerosol size distribution.The calculated N CCN are highly biased when the aerosol number concentration or normalized aerosol size distribution are fixed to the average level.This shows that both the aerosol number concentration and normalized aerosol size distribution are of great importance in the prediction of CCN number concentration.Junge and McLaren (1971) found that aerosol size distribution is the most important factor in determining the CCN spectra, with compositional variations being significant only for aerosols with less than 10% soluble material.Fitzgerald's (1973) study also showed that the shape of the CCN spectra is quite insensitive to aerosol solubility.Recent work also concluded that size matters more than chemistry for cloud-nucleating ability of aerosol particles (Dusek et al., 2006;McFigans et al., 2006;Ervens et al., 2007;Andreaeand Rosenfeld;2008).Thus the campaign-average size-resolved activation ratios can be used to describe the activation properties of the aerosols in the NCP.The variation of aerosol chemical composition affects the solubility, the surface tension and the non-ideality of the solution.The variation of size-resolved activation ratio caused by aerosol chemical composition has weak impacts on bulk aerosol activation.This average size-resolved activation ratios during this campaign and measured aerosol size distribution can be used to predict N CCN successfully.These results would help us to understand the role of size and chemical compositions in their activation processes, and enables us to develop an aerosol-CCN scheme based on such size-resolved measurements.

Appendix A The procedure of multiple charge correction
The aerosol sample selected by DMA is a quasi-monodisperse aerosol with a width of mobility range and several charges for each particle.A simple multiple charge correction is applied for the CCN activation ratio without consideration of the DMA transfer function.Thus only the central mobility is considered in the aerosol sample.
Assuming the activation ratio for the particle with j charges passing through channel i is A ij ,i = 1,2,. . .,I , the measured activation ratio can be expressed as where J is the maximum number of charges on one particle, here we use 10.N CPCij is the number of particles passing through channel i with j charges.It can be calculated from the parallel aerosol size distribution and the charge probability (Wiedensohler, 1988), considering the DMA transfer function.
Z. Z. Deng et al.: Size-resolved and bulk activation properties of aerosols in the North China Plain The relative multiple charge fraction is and A ij can be expressed as the linear interpolation of the activation ratios at the measured diameters, A ij = A i(j ) + A i(j )+1 − A i(j ) logD ij − logD i(j ) logD i(j )+1 − logD i(j ) (A4) logD i(j )+1 − logD ij logD i(j )+1 − logD i(j ) + A i(j )+1 logD ij − logD i(j ) logD i(j )+1 − logD i(j ) = A i(j ) log D i(j )+1 /D ij log D i(j )+1 /D i(j ) + A i(j )+1 log D ij /D i(j ) log D i(j )+1 /D i(j ) where D ij is the diameter of the particles passing through channel i with j charges, i(j ) is the index of the largest one among the measured diameters which are smaller than or equals to D ij , A i indicates the activation ratio of the singly charged particles in the corresponding channels.When i(j ) equals to the number of the measured sizes, D i(j )+1 and A i(j )+1 can be replaced with the corresponding theoretical critical dry diameter of water ball (Kelvin equation) D K and the activation ratio of 1.When no measured diameter is smaller than or equals to D ij , D i(j ) and A i(j ) are replaced with D HSP and 0, D i(j )+1 and A i(j )+1 are D 1 and A 1 .
With Eq. (A4), Eq. (A1) can be written as where S ij and T i are both expressed as the results of P ij , Q ij and F ij .T i comes from the terms where D i(j )+1 is replaced with Kelvin diameter.
A new response is written as R i = M i − T i .This equation set is then expressed as where R and A are I ×1 vectors and S is an I × I matrix.Solving the equation set with non-negative least square method will get the activation ratio of singly charged particles.

Figure 2
Figure 2 Schematic of the Relationship between Aerosol and CCNThe black curve represents the aerosol size distribution, while only the particles under the red curve act as CCN.Dm is regarded as an inferred critical dry diameter at the given SS.The number concentration of the aerosols larger than Dm equals to the NCCN.DNaCl is the critical dry diameter of NaCl particle at the given SS.DKelvin is the critical diameter for an insoluble but wettable particle (IBW) at the given SS.All the aerosol particles with diameter larger than DKelvin (area A) can be activated, while the atmospheric aerosol particles smaller than DNaCl (area E) cannot be activated.The area C and D equals to each other.

Fig. 2 .
Fig. 2. Schematic of the relationship between aerosol and CCNThe black curve represents the aerosol size distribution, while only the particles under the red curve act as CCN.D m is regarded as an inferred critical dry diameter at the given SS.The number concentration of the aerosols larger than D m equals to the N CCN .D NaCl is the critical dry diameter of NaCl particle at the given SS.D Kelvin is the critical diameter for an insoluble but wettable particle (IBW) at the given SS.All the aerosol particles with diameter larger than D Kelvin (area A) can be activated, while the atmospheric aerosol particles smaller than D NaCl (area E) cannot be activated.The area C and D equals to each other.

Figure 5 Fig. 5 .
Figure 5 Probability Distribution of the Inferred Critical Dry Diameter Fig. 5. Probability distribution of the inferred critical dry diameter.

Fig. 7 .
Fig. 7. Average activation curves for different supersaturations calibration curves of ammonia sulfate particles are shown as gray curves labeled with the effective supersaturation.The colored curves are the average activation curves of ambient aerosols.

1Fig. 8 .
Figure 8 the Flowchart for CCN Closure between Bulk and Size-resolved Measurement 2 3 Flowchart for CCN closure between bulk and size-resolved Measurements.

Figure 9
Figure 9 Closure between Measured CCN Number Concentration and the CCN Number Concentration Calculated from Aerosol Number Size Distribution (SD) and Sizeresolved Activation Ratio (SRAR) for Different Supersaturations a: Real-time SD and SRAR; b: Real-time SD and Averaged SRAR; c: Average NCN (keep NASD) and Real-time SRAR; d: Average NASD (keep NCN) and Real-time SRAR.There are 1527 pairs of data in each panel.The title of each panel shows the fitted function, correlation coefficient, average relative bias (Bias=(NCCN-cal-NCCN-meas)/NCCN-meas) and average relative deviation (Dev=|NCCN-cal-NCCN-meas|/NCCN-meas).

Fig. 9 .
Fig. 9. Closure between Measured CCN Number Concentration and the CCN Number Concentration Calculated from Aerosol Number Size Distribution (SD) and Size-resolved Activation Ratio (SRAR) for Different Supersaturations (a): Realtime SD and SRAR; (b): Real-time SD and Averaged SRAR; (c): Average N CN (keep NASD) and Real-time SRAR; (d): Average NASD (keep N CN ) and Real-time SRAR.There are 1527 pairs of data in each panel.The title of each panel shows the fitted function, correlation coefficient, average relative bias (Bias = (N CCN-cal − N CCN-meas )/N CCN-meas ) and average relative deviation (Dev = |N CCN-cal − N CCN-meas |/N CCN-meas ).

Table 1 .
logD p d logD p Critical Dry Diameter of NaCl, (NH 4 ) 2 SO 4 and an Insoluble but Wettable (IBW) Particle.

Table 2 .
Statistics of the Aerosol Number Concentration and CCN Number Concentration.The N CCN (cm −3 ) at five supersaturations and the aerosol number concentration (N CN , cm −3 ) are presented.The minimum, maximum, mean value and the corresponding standard deviation are presented.The last line is the number of samples.