Ccn Predictions Using Simplified Assumptions of Organic Aerosol Composition and Mixing State: a Synthesis from Six Different Locations

An accurate but simple quantification of the fraction of aerosol particles that can act as cloud condensation nuclei (CCN) is needed for implementation in large-scale models. Data on aerosol size distribution, chemical composition , and CCN concentration from six different locations have been analyzed to explore the extent to which simple assumptions of composition and mixing state of the organic fraction can reproduce measured CCN number concentrations. Fresher pollution aerosol as encountered in Riverside, CA, and the ship channel in Houston, TX, cannot be represented without knowledge of more complex (size-resolved) composition. For aerosol that has experienced processing (Mexico City, Holme Moss (UK), Point Reyes (CA), and Chebogue Point (Canada)), CCN can be predicted within a factor of two assuming either externally or internally mixed soluble or-ganics although these simplified compositions/mixing states might not represent the actual properties of ambient aerosol populations, in agreement with many previous CCN studies in the literature. Under typical conditions, a factor of two uncertainty in CCN concentration due to composition assumptions translates to an uncertainty of ∼15% in cloud drop concentration , which might be adequate for large-scale models given the much larger uncertainty in cloudiness.


Introduction
Aerosol-cloud interactions represent one of the largest uncertainties in estimating the effects of aerosol on radiative forcing.One key parameter for this estimate is to determine what fraction of aerosol particles can act as cloud condensation nuclei (CCN) and form cloud droplets.The propensity of a particle to form CCN depends on its size, chemical composition and the supersaturation to which it is exposed.Whereas size distributions are routinely measured in field experiments, the full characterization of the chemical composition presents a major challenge since, in particular, the organic fraction of particles can be composed of hundreds of compounds with different physicochemical properties (e.g., surface tension, solubility, degree of dissociation, molecular weight).In laboratory and theoretical studies, it has been shown that these properties can enhance or reduce the CCN ability of organic particles as compared to better-characterized inorganic particles (Corrigan and Novakov, 1999;Cruz and Pandis, 2000).For ambient particle populations, it is not feasible to consider Published by Copernicus Publications on behalf of the European Geosciences Union.
B. Ervens et al.: CCN studies at six different locations all individual compounds due to the far from complete characterization of the organic fraction at the molecular level, and the computational burden the description of hundreds of individual compounds represents in models.
There is no consensus about the importance of detailed knowledge of aerosol composition (including mixing state) in studies that compare measured and modeled CCN number concentrations ("CCN closure").Some studies report that this information is of minor importance for successful CCN closure and that aerosol size distribution largely determines the fraction that can be activated at a given supersaturation (Conant et al., 2004;Dusek et al., 2006;Ervens et al., 2007).Other studies show that measured CCN number concentrations can only be reproduced if detailed organic properties/mixing state are taken into account (Mircea et al., 2005;Stroud et al., 2007;Cubison et al., 2008).
With increasing distance from emission sources, particles become mixed by both physical processes (e.g., coagulation or condensation of semivolatile and low-volatility organic and inorganic compounds) or chemical processes (e.g., oxidation of primary (organic) species yielding more watersoluble products, and particle-phase reactions).These ageing processes lead to growth of the particles, i.e. an increase in their CCN ability at a given supersaturation, and/or to an increase in the hygroscopic fraction and, thus, to a reduction in the size threshold ("critical diameter") above which particles can be activated at a given supersaturation (Petters et al., 2006;Furutani et al., 2008).
Most CCN studies published to date have been limited to sampling at one site and, thus, it is not clear how to generalize their conclusions about CCN activation as a function of aerosol mixing state and organic solubility.In a global model study, it has been shown that different assumptions on mixing state and organic solubility might significantly affect CCN number concentrations (Pierce et al., 2007).The motivation of the current study is to explore the applicability of these simplifying composition/mixing state assumptions in CCN closure studies, using a consistent model approach, based on data sets collected at very different locations and distances from sources.Unlike previous CCN studies (some of which analyzed in detail the same data sets as those considered here), it is not attempted to deduce exact size/composition/mixing state parameters of the CCN-active particle population based on all measurements, but rather to evaluate the extent to which simple assumptions can reproduce measured CCN number concentrations across all data sets.A simple treatment of CCN composition/mixing state as a function of distance from sources would be highly useful for the description of aerosol-cloud interactions in largescale models.

Data sets
CCN data sets at six locations that differ in proximity to pollution sources, aerosol loading and composition have been analyzed; details on these data sets and corresponding publications are summarized in Table 1.Three data sets are split into two subsets: During the first period of the MASE experiment at Point Reyes, CA (PYE), air masses were transported mainly from the west and did not have any land contact over the three days prior to sampling, whereas air masses during the remainder of the experiment came from the north and north east and thus had continental influence (C. Berkowitz, personal communication, 2010).For some periods during the ICARTT experiment at Chebogue Point (CBG), analysis of the organic mass fraction (OMF) of the aerosol using the Aerodyne aerosol mass spectrometer (AMS) allowed their classification as either anthropogenically or biogenically influenced, respectively (Holzinger et al., 2007;Williams et al., 2007;Zhang, 2010).Note that not all data points could be unambiguously ascribed to such air masses.During Go-MACCS, CCN data were collected on the NOAA research vessel Ronald H. Brown both in the Houston Ship Channel (HSC) and along the Houston Gulf Coast (HGC).It has been shown that aerosol composition and processing can differ significantly in these two areas due to different emissions (Bates et al., 2008;Bahreini et al., 2009).At Mexico City T0 (MEX) and Riverside (RVS), the sampling took place at ground sites that were located near and downwind of significant pollution sources.Emissions at the mountain-top at Holme Moss, UK, (HOM) are characterized by the plumes of Manchester, a conurbation of 2.5 million people (distance ∼35 km), and nearby towns.

Model
The CCN model employed here is described in detail in previous studies (Ervens et al., 2007;Cubison et al., 2008).In brief, the model is initialized with measured size distributions and CCN number concentrations at a given supersaturation (S).In the current study, we compare calculated and measured CCN number concentrations at one S for each study in the range of 0.27%≤ S ≤0.44% (Table 1).This S (range) is the only one available for all data sets.Such low S is encountered in stratus clouds that have a significant influence on the global radiative forcing.Depending on the data set, S is either a constant value for the whole time period or variations in the CCN counter are taken into account.At this relatively low S, CCN number concentrations are most sensitive as only a small fraction of the aerosol population is activated and, thus, any change in the number of activated particles (e.g., due to changes in hygroscopicity) could translate to a significant change in activated fraction (Ervens et al., 2007).Aerosol composition in the model is constrained with time-dependent bulk (i.e., not size-resolved) mass fractions of sub-micron non-refractory inorganic ions (sulfate, nitrate, ammonium, chloride) and organics from Aerodyne AMSs (Canagaratna et al., 2007).The mass of black carbon (BC) has been derived based on absorption measurements for the studies in which this data was available.
The water uptake of the particles is calculated using Köhler theory and defining all inorganics as being fully dissolved.The organic fraction is considered as either insoluble or composed of hygroscopic organics (e.g., fulvic acid and small dicarboxylic acids) which translates to hygroscopicity parameters κ org = 0 or κ org = 0.12, respectively (Petters and Kreidenweis, 2007).The carbonaceous (organics+BC) fraction is either internally or externally mixed with the inorganic fraction.The four resulting 'composition assumptions' regarding the organic fraction are identical to those in a previous model study (Pierce et al., 2007): 1. Externally mixed, insoluble (κ org = 0) organics (EM-I) 2. Externally mixed, soluble (κ org = 0.12) organics (EM-S) 3. Internally mixed, insoluble (κ org = 0) organics (IM-I) 4. Internally mixed, soluble (κ org = 0.12) organics (IM-S) The composition/mixing state of ambient aerosol populations is likely to be more complex than any of these assumptions.However, in this study, the extent to which these sim-plified composition models lead to reasonable closure for a variety of locations and aerosol types will be explored.

CCN closure results
In Table 2, the concentration ratios "CCN (calculated)/CCN (measured)" are shown for the data sets in Table 1 and four composition cases.For aerosols sampled in source regions as encountered in RVS, MEX, and HSC, there is a high variability in the observed closure depending on the study.Cubison et al. (2008) showed for the RVS data set that freshly emitted, hydrocarbon-like organics at RVS comprise an externally mixed population with a significant contribution to the total number concentration of particles with a diameter of D ∼ 100 nm.A similar situation is encountered in Mexico City and the Houston Ship Channel where a significant fraction of the particles are fresh (especially from the late evening to the early morning) and have not yet undergone much physical or chemical transformation.In such scenarios, even the assumption of insoluble, externally mixed organics (EM-I) with bulk composition may lead to a significant overestimate of CCN number concentration.In those cases size-resolved composition and mixing state information is required to accurately predict CCN (Cubison et al., 2008;Twohy and Anderson, 2008).There is significant variability in the CCN prediction biases at these locations, which relate to differences in size-resolved composition and mixing Aerosol size distribution External mixture, κ org =0.12 (EM-S) III.

II.
Particle size state which are not captured by any of the simplified assumptions of this study.Whereas MEX and RVS resemble one another in terms of average organic fraction and distance from sources, single particle analysis at both locations has shown that the former location is more influenced by (aged) biomass burning particles (Moffet et al., 2008) whereas the latter one showed high fractions of elemental carbon in the diameter range below 200 nm, i.e. around the critical diameter for particles that activate at S = 0.3% (Spencer et al., 2007).

Number concentration
While inappropriate assumptions about organic composition/mixing state could lead to the overprediction of the CCN number concentration, there is also the possibility that an apparent overprediction is really a result of the measured CCN number concentration being too low due to instrumental limitations at high particle loading.However, at S ∼ 0.3% a significant underprediction only occurs for CCN number concentrations on the order of 30 000 cm −3 (Droplet Measurement Technology Inc, 2004).Even though the total particle number concentration occasionally exceeded this value significantly, the average activated fraction at S ∼ 0.3% never exceeded 0.2 (Cubison et al., 2008) which results in a maximum CCN number concentration of ∼ 6000 cm −3 .
In Fig. 1, a schematic size distribution is shown and subpopulations that are predicted to activate for each of the four composition assumptions are marked.If two composition/mixing state assumptions result in similar predicted CCN number concentrations, it does not imply that the same subset of the particle distribution is predicted to activate.It is evident that canceling effects leading to comparable predicted CCN numbers depend on the shape of the size distribution and the magnitude of the organic fraction.None of the four suggested assumptions represents the real composition/mixing state of an atmospheric particle population.There is an infinite number of other (more complex) composition/mixing states that can lead to the same predicted CCN number.
At locations with small organic fractions (HGC, PYE, HOM), the different composition/mixing state assumptions only lead to small changes in the overall quality of the CCN closure.At locations with higher organic fractions, internally and externally mixed insoluble organics or internally and externally mixed soluble organics, respectively, consistently give similar predicted CCN number concentrations, i.e. the areas I and III, and the areas II and IV, respectively, in Fig. 1 are similar on average for all observed size distributions which shows that the assumed mixing state is less important than the assumed hygroscopicity of the organics.
In some cases canceling effects of predicting different parts of the size distribution to activate (Fig. 1) can lead to similar predicted CCN number concentrations that are within a factor of two to the measured ones with several assumptions.
With increasing distance from pollution sources, the prediction of CCN number concentration under the assumption that all particles contain some hygroscopic material is improved, but no clear statement can be made whether physical or chemical mixing/ageing dominates as similar CCN ratios are predicted by applying cases EM-S or IM-I.The relative importance of mixing/ageing processes depends on factors that cannot be quantified in the present study, such as different photochemical activity and/or oxidant levels due to seasonal effects or concentration levels of precursors.Field studies and model simulations using results from laboratory experiments have suggested that chemical ageing of organic aerosols is too slow and limited to account for efficient hydrophobic-to-hydrophilic conversion as compared to physical mixing processes, especially condensation of hygroscopic secondary inorganic species across the whole particle population (Petters et al., 2006;DeGouw and Jimenez, 2009).

Spatial scale of ageing
In large-scale models, a time scale on the order of 1-2 days is assumed to convert particles from hydrophobic to hygroscopic, and, thus into potential CCN (Wilson et al., 2001).Aerosol age depends not only on distance from source but also on transport and processing time to the sampling site.However, wind data or highly time-resolved back trajectories that could allow an estimate of transport age are only available for a subset of the data sets investigated here.The relative age of air masses is often characterized by its 'photochemical age', which is calculated based on the ratio of NO x /NO y , benzene/toluene, BC/CO or oxidized/total organic aerosol mass.This photochemical age is not an absolute value that can be compared for different locations since it is also function of oxidant levels.Since none of these parameters is available for all the data sets used in this study, the present analysis explores spatial ageing scales by comparing distances from sources.
In Fig. 2, the range of the CCN (calculated)/CCN (measured) ratios, weighted by the frequency in the CCN closure studies, is shown for internally and externally mixed organics.No specific distance is ascribed to the sampling locations close to pollution sources (MEX, HSC, and RVS) because of the various pollution sources close to or within a few kilometers of the sampling location.
For studies downwind of but relatively close to major source areas (HOM and HGC), best CCN closure is achieved if all particles are assumed to be hygroscopic.This might be reasonable because of chemical and/or physical particle processing or due to the fact that the initial particle population dilutes and the resulting aerosol population is mostly determined by aged background aerosol.Applying IM-I (or EM-I) for remote locations as has been done in many global model applications will lead to an underestimate of CCN number concentrations.Our analysis indicates that, based on two studies (HGC and HOM), the ageing scale of particles is much shorter than several days and could be on the order of hours in agreement with a recent model study that explores the ageing time scale for soot particles (Riemer et al., 2010).This result for locations where photochemistry is active confirms studies that have shown that the addition of a few percent of soluble material to a hydrophobic particle significantly enhances its CCN ability (Bilde and Svenningsson, 2004).

Role of organic fraction
The data sets explored here, cover a wide range of OMF ranging from 7±4% to 79±10% (Table 1).For an aerosol with small OMF, the assumption of organic composition/mixing state is not crucial since the fractions of the size distributions that are predicted to activate due to hygroscopic and/or internally mixed organics are small (Fig. 1).For high OMF, however, predicted CCN number concentrations are quite sensitive to the assumptions on mixing state/composition and quite different closure results are found.
In Fig. 3a-d, the ranges of predicted CCN (calculated)/CCN (measured) ratio are shown as a function of OMF for all data sets and all composition cases.Despite much scatter around unity, the predicted CCN number agrees within a factor of two or better for small OMF under all assumptions (as also reflected in Table 2).As organic fractions increase above ∼50% (MEX, CBG, HSC), it is evident that CCN number concentrations are increasingly underestimated if insoluble organics (EM-I or IM-I) are assumed (Fig. 3a and b), but reasonably well predicted for the EM-S and IM-S assumptions.This is in agreement with the study by Wang et al. (2008) who found that the best closure for aerosol with OMF >70% can be achieved if a hygroscopicity of κ org = 0.12 (IM-S) is assumed.The overestimate of CCN number concentration for some of the fresh aerosol (HSC, RVS), as discussed in Sect.4.1, decreases slightly as OMF increases but this improvement may be a fortuitous result of compensating factors.

Comparison to previous CCN studies
In Table 3, we have summarized results of multiple previous CCN studies together with the approximate distance from major pollution sources and the assumptions on organic hygroscopicity and mixing state in the respective CCN studies.Only a few studies have been performed very close to major pollution sources (Broekhuizen et al., 2006;Cubison et al., 2008;Quinn et al., 2008;Lance et al., 2009).
www.atmos-chem-phys.net/10/4795/2010/Atmos.Chem.Phys., 10, 4795-4807, 2010  These studies agree that best closure can be achieved if size-resolved chemical composition is taken into account with particular consideration of freshly emitted hydrophobic organics.Size-resolved particle analysis of particle data sets in Tokyo and Guanzhou has confirmed the existence of such a mode around D ∼ 100 nm (Kuwata and Kondo, 2008;Rose et al., 2010).Several studies of hygroscopic growth factor measurements in urban environments confirm the existence of a less hygroscopic mode that is composed of freshly-emitted hydrophobic particles (Swietlicki et al., 1999;Cocker et al., 2001;Väkevä et al., 2002).Since the critical diameter of CCN is usually in the size range of ∼50-200 nm (depending on S and composition), the consideration of this 'small-size' mode is crucial for CCN closure studies and ignoring it will lead to an overestimate of the CCN number concentration.A recent CCN study of the data set in Mexico City has shown that this mode is most prominent in the morning and best closure is achieved if hydrocarbon-like organics (HOA) and BC is assumed to be externally mixed with the inorganic and oxygenated organic fraction.In the afternoon, this composition/mixing state assumption leads to an underestimate of CCN and the assumption of internally mixed, size-resolved composition gives best closure results (Wang et al., 2010).The good closure results in the latter study that are obtained by assuming bulk composition and an external mixture of all components might be fortuitous due to canceling effects of an overestimate by assuming bulk composition and an underestimate due to externally mixed components according to the schematic in Fig. 1.These studies for polluted conditions and fresh emissions are consistent with findings from a global model study where it has been shown that the largest error in CCN prediction occurs under polluted conditions and CCN mixing state needs to be taken into account in order to reduce this error to <10% (Sotiropulou et al., 2007).

2009).
The assumption of an external mixture of soluble organics leads to an underestimate of the CCN number but increasing the hygroscopicity of the internally mixed model organics leads to better agreement (Wang et al., 2008).An internal mixture of insoluble organics suggests that indeed physical mixing processes (i.e.condensation of soluble lowvolatility or semivolatile compounds or coagulation) are predominant rather than chemical ageing processes that would result in an external mixture of soluble organics.The dominance of condensation and coagulation is also apparent in fast size-resolved chemistry data (e.g., Zhang et al., 2004).
At remote continental locations with some impact of anthropogenic emissions, CCN closure studies have been successful with the assumption of internally mixed organics with κ org ∼ 0.09 (Kammermann et al., 2010).In that study, composition measurements were not available; however, the low hygroscopicity parameters (0.07 < κ all < 0.21) determined in their studies point to a small inorganic fraction.Those authors have also shown that the sensitivity to the mixing state is not of importance and very similar closure results are found by assuming externally mixed, soluble organics, in agreement with our results for EM-S and IM-S in Figs. 2 and  3.In regions with very high organic fractions such as in the Amazon, the assumption of internally mixed organics with κ org ≤ 0.1 leads to CCN overprediction of ≤17% (Mircea et al., 2002;Rissler et al., 2006;Gunthe et al., 2009).This range of κ org is in agreement with the hygroscopicity suggested for secondary organic aerosol (Petters and Kreidenweis, 2007).
During studies at remote locations, size-resolved composition measurements were available.Even though all aged particles are to some extent internally mixed, larger particles generally exhibit a higher hygroscopicity due to their growth by condensation of soluble compounds (sulfate, organics) (Furutani et al., 2008;Gunthe et al., 2009;Kammermann et al., 2010).An average hygroscopicity might be biased to larger values if it is averaged based on volume of the size distribution.If particles around the critical diameter have a distinctly smaller hygroscopicity, applying this average value for the whole size distribution will lead to an overestimate (Medina et al., 2007).
The trends in κ org in Table 3, together with the findings in Fig. 2, can be used as general guidance for the treatment of the organic fraction in CCN studies.All data sets confirm that size-resolved organic composition and mixing state are of importance in highly polluted areas with fresh emissions, whereas condensation and/or coagulation is efficient enough to convert hydrophobic organic particles within short distances into hygroscopic particles (internal mixture, κ org = 0).With increasing distance from pollutions sources, the initially hydrophobic organic particles become hygroscopic due to additional hygroscopic material and the organic fraction can be represented with an overall organic hygroscopicity 0 < κ org < 0.2.

Effects of uncertainty in CCN number concentration on drop number concentration (N d )
While CCN studies are helpful in order to test our understanding of the physico-chemical properties of aerosol particles that affect their CCN ability, the supersaturation in a cloud is not only controlled by the condensational sink of water vapour but to a large extent by dynamic processes, such as the cooling rate due to the updraft.In previous theoretical studies, it has been shown that any chemical effects on CCN number concentration are reduced when cloud drop numbers (and not CCN in equilibrium) are compared (Ervens et al., 2005;Sotiropulou et al., 2007;Cubison et al., 2008;Wang et al., 2008).By means of a theoretical model approach, we explore the extent to which an error of a factor of two due to inappropriate composition assumptions in CCN closure studies (Figs. 2   and 3) translates into an error in drop number concentration.This model approach has been used before to describe the activation of aerosol particles at a constant updraft velocity (Ervens et al., 2005;Cubison et al., 2008).The initial size distribution for these exemplary model runs is lognormal with geometrically distributed diameters between 0.02-2 µm.It is assumed that all particles are internally mixed and have the same composition throughout the size range.
A reference composition (κ = 0.18) has been defined that translates into a critical diameter D1 at S = 0.3% according to Köhler theory.The number concentration of the aerosol distribution is chosen in a way that this base case has a CCN number concentration of 400 cm −3 .In sensitivity studies to simulate more/less polluted scenarios, the total particle number has been scaled up/down by a factor 10 (4000 cm −3 , 40 cm −3 ; Fig. 4a, b).
For sensitivity studies, an error of two in the base case CCN number is introduced by varying κ in a way that the resulting critical diameters D2 and D05 describe a concentration that is twice/half as large as that constrained by D1 at S = 0.3% (Fig. 4a, b).The two size distributions show that the values of D1 and D2 depend on the shape of the size distribution since different fractions are predicted to activate.The calculations are performed for two different size distributions in order to explore the impact of the size distributions.Unlike in previous studies that have explored the effect on cloud drop number concentration due to an error in aerosol number concentration (e.g., Feingold, 2003;Ervens et al., 2005), in the current study different compositions with a constant aerosol number concentration are input parameters for the sensitivity runs and the difference in predicted CCN number concentration only hold for S = 0.3%.At different S, the ratio of the predicted CCN number concentration will differ from two.
The compositions (κ1, κ05, κ2) and size distributions are used as input to the cloud model and simulations are performed for updraft velocities w in the range of 10 cm s −1 < w < 300 cm s −1 .Drop number concentrations from each simulation (N d (1), N d (05), N d (2)) are compared at a maximum liquid water content of 0.3 g m −3 .In Fig. 4c and d A value of ±100% corresponds to the same uncertainty as in the comparison of the CCN number concentration whereas 50% denotes that the error in cloud drop number prediction is only half of that as in CCN number prediction.At w = 10 cm s −1 , the difference in drop number concentration is greatest for both initial size distributions and might be as large as a factor of two.As opposed to findings that suggested the largest effect at high particle number concentration, i.e. if condensation might significantly impact the supersaturation (Ervens et al., 2005), the results in Fig. 4c and d do not show a clear trend in terms of the total particle number concentration.
With increasing updraft velocity, the supersaturation is mostly controlled by the cooling rate and the sink term due to condensation of water vapour becomes negligible.At w ∼300 cm s −1 , the change in drop number concentration due to different assumptions of particle composition (κ) is reduced to about 10-20% as compared to the ratio of 2 in the CCN number concentrations.This range is in agreement with findings from similar studies (Ervens et al., 2005;Sotiropoulou et al., 2006).This uncertainty might translate into an error of regional indirect forcing of ∼0.5 W m −2 ; however, these are regions where the total indirect radiation is high, and thus the relative error in indirect forcing is small (Sotiropoulou et al., 2006;2007).In the latter studies, it has been concluded that the error in CCN prediction is small for the indirect forcing because the clouds that contribute most to the indirect effect are those at moderate pollution levels.As shown in the current study, in these regions, however, CCN can be predicted reasonably well without detailed knowledge of composition and mixing state.

Summary and conclusions
CCN closure results for six different locations are compared using four simplified composition/mixing state assumptions for the carbonaceous (organics+BC) aerosol fraction (soluble/insoluble, internally/externally mixed with inorganic fraction).Despite very different locations and air masses, the following trends can be identified: -Very close to pollution sources, simple assumptions of organic mixing state/ solubility and bulk composition are not sufficient to predict CCN number concentrations.More complex assumptions about composition and mixing state (e.g., size-resolved) need to be made.
-Externally mixed, hydrophobic organic particles are likely to be sufficiently processed by chemical and/or physical ageing within a few tens of kilometers downwind of emission sources such that CCN composition can be reasonably well represented by externally mixed, hygroscopic organics.
-Different assumptions for organic solubility and mixing state often lead to similar CCN number concentrations since different subsets of the aerosol population are predicted to activate.Thus, reasonable CCN closure may be achieved due to such compensating factors even though the assumed composition/mixing state might not represent the true properties of the aerosol population.
-A factor of two error in CCN concentration due to composition effects will translate to an error of about 10-20% in cloud drop concentration in agreement with previous studies that compared effects on drop number concentration due to different aerosol number concentrations (Ervens et al., 2005;Cubison et al., 2008).
Our results provide a general framework that allows prediction of CCN number concentrations to better than a factor of two on average for a variety of scenarios where the aerosol has undergone some degree of ageing by making simple assumptions about the solubility and mixing state of the organic fraction.Given the rather poor representation of clouds in large-scale models, the error in drop number concentration due to uncertainties in CCN number concentrations is relatively small compared to radiative forcing uncertainties associated with macroscale cloud properties such as cloud fraction and depth.

Fig. 1 .
Fig. 1.Schematic of areas of activated number concentrations for different composition/mixing state assumptions.

Fig. 4 .
Fig. 4. (a) and (b) Example size distributions that are used as input data to the cloud parcel model.D1 denotes the critical diameter for particles that are activated at S = 0.3%, κ = 0.18 ("base case").D05 and D2 denote the critical diameters for particles with a composition that result in 50% or 200%, respectively, of the activated number concentration as compared to the base case.(c) and (d) Relative difference between predicted drop number concentration for the compositions κ05 and κ2 to predicted drop number concentration using κ1 as a function of updraft velocity in the cloud parcel model.

Table 1 .
Characteristics of the data sets that have been used for CCN closure in the current study.

Table 2 .
Average ratios (±1 std dev) of calculated to measured CCN number concentrations for several locations and four different assumptions of composition/mixing state (κ org : hygroscopicity parameter of organic fraction).Best agreement is marked in gray shaded cells, poorest in bold for each location.

Table 3 .
Summary of previous CCN closure studies."Dist" is the approximate distance from major emission sources, κ org is the hygroscopicity parameter of the organic fraction, κ all is the hygroscopicity parameter of the total aerosol (if κ was not provided in the original literature it was derived here based on reported composition/hygroscopicity data); "slope" is the ratio of CCN (calculated)/CCN (measured), and S is the supersaturation (range).If not otherwise noted, all studies assume bulk composition.