Atmospheric Chemistry and Physics Estimation of Cloud Condensation Nuclei Concentration from Aerosol Optical Quantities: Influential Factors and Uncertainties

Large-scale measurements of cloud condensation nuclei (CCN) are difficult to obtain on a routine basis, whereas aerosol optical quantities are more readily available. This study investigates the relationship between CCN and aerosol optical quantities for some distinct aerosol types using extensive observational data collected at multiple Atmospheric Radiation Measurement (ARM) Climate Research Facility (CRF) sites around the world. The influences of relative humidity (RH), aerosol hygroscopicity (f RH) and single scattering albedo (SSA) on the relationship are analyzed. Better relationships are found between aerosol optical depth (AOD) and CCN at the Southern Great Plains (US), Ganges Valley (India) and Black Forest sites (Germany) than those at the Graciosa Island (the Azores) and Niamey (Niger) sites, where sea salt and dust aerosols dominate, respectively. In general, the correlation between AOD and CCN decreases as the wavelength of the AOD measurement increases, suggesting that AOD at a shorter wavelength is a better proxy for CCN. The correlation is significantly improved if aerosol index (AI) is used together with AOD. The highest correlation exists between CCN and aerosol scattering coefficients (σ sp) and scattering AI measured in situ. The CCN–AOD (AI) relationship deteriorates with increasing RH. If RH exceeds 75 %, the relationship where AOD is used as a proxy for CCN becomes invalid, whereas a tight σ sp –CCN relationship exists for dry particles. Aerosol hygroscopicity has a weak impact on the σ sp –CCN relationship. Particles with low SSA are generally associated with higher CCN concentrations, suggesting that SSA affects the relationship between CCN concentration and aerosol optical quantities. It may thus be used as a constraint to reduce uncertainties in the relationship. A significant increase in σ sp and decrease in CCN with increasing SSA is observed, leading to a significant decrease in their ratio (CCN / σ sp) with increasing SSA. Parameterized relationships are developed for estimating CCN, which account for RH, particle size, and SSA.


Introduction
Aerosols play important roles in Earth's climate and the hydrological cycle via their direct and indirect effects (IPCC, 2007).Aerosol particles can scatter and absorb solar radiation, and alter the vertical distribution of solar energy and atmospheric stability (Ramanathan et al., 2001;Liu et al., 2012).These are known as direct effects.Aerosols can modify microphysical and macroscopic cloud properties, such as cloud particle size, cloud albedo (Twomey, 1977;Twomey et al., 1984;Rosenfeld et al., 2001;Andreae et al., 2004;Koren et al., 2005) and cloud-top heights (Andreae et al., 2004;Lin et al., 2006;Li et al., 2011).They can also influence warmand cold-rain processes (Rosenfeld and Woodley, 2000;Andreae et al., 2004;Lin et al., 2006;Bell et al., 2008;Li et al., 2011), the depth of the mixed-phase region in a cloud (Andreae et al., 2004;Koren et al., 2005Koren et al., , 2008Koren et al., , 2010;;Niu and Li, 2012) and the occurrence of lightning (Orville et al., 2001;Steiger and Orville, 2003;Yuan et al., 2011;Yang et al., 2013).These are known as aerosol's indirect effects, which are the largest sources of uncertainty in the forcing of Earth's climate system.Determining CCN (cloud condensation nuclei) concentrations and their spatial and temporal variations are key challenges in quantifying aerosol's indirect effects.
CCN concentration has been measured chiefly through field experiments by counting the number of droplets formed in a chamber using optical counters at various levels of water vapor supersaturation (S) (Hudson and Yum, 2002;Ross et al., 2003;Yum et al., 2007;Rose et al., 2008;Liu et al., 2011).However, such in situ measurements of CCN concentration are few and localized and thus may not represent large areas.Extensive measurements of CCN concentration are not currently feasible because of the high cost and complex nature of the operation.CCN is determined by the aerosol size distribution and chemical composition and is governed by the Köhler theory.Aerosol particles in the ambient environment are often very complex and are comprised of inorganic and organic species (Kanakidou et al., 2005;Zhang et al., 2007), so the Köhler theory has been extended to include the influence of these species (Shulman et al., 1996;Facchini et al., 1999;Svenningsson et al., 2006).The mixing state and a detailed knowledge of how different compounds interact with water also matter (McFiggans et al., 2006;Andreae and Rosenfeld, 2008;Ward et al., 2010;Yang et al., 2012).A modified Köhler theory, called the "κ-Köhler" theory, was proposed by Petter and Kriedenweis (2007), which uses a single parameter, κ, to describe the solubility effect on CCN activation.
Unlike CCN concentration and size-resolved aerosol composition, aerosol optical quantities, such as aerosol optical depth (AOD) and aerosol scattering/extinction coefficients, are much more readily available using ground-based and space-borne remote sensing instruments.Aerosol optical quantities, especially AOD, have often been used as a proxy for CCN in large-scale model simulations (Quaas et al., 2009;Wang et al., 2011;Tao et al., 2012;Grandey et al., 2013) and in studying aerosol's indirect effects (Nakajima, 2001;Bréon et al., 2002;Feingold et al., 2003;Yuan et al., 2008).However, AOD represents the vertically integrated attenuation and depends not only on the number of particles but also on relative humidity (RH), size distribution, etc., and might not be a good proxy for CCN (Jeong et al., 2007).The use of aerosol optical measurements to estimate CCN concentrations is appealing but challenging because they are governed by different aerosol attributes (Ghan et al., 2006;Kapustin et al., 2006;Andreae, 2009).Nevertheless, attempts at relating CCN concentration to AOD or aerosol extinction/scattering properties have shown gross correlations between CCN concentration and aerosol optical quantities (Ghan and Collins, 2004;Ghan et al., 2006;Shinozuka et al., 2009;Andreae, 2009;Jefferson, 2010;Liu et al., 2011).The correlation is often fraught with uncertainties that could be reduced by accounting for some influential factors, such as aerosol size and/or composition, as well as environmental variables (e.g., RH).Previous attempts have been made to try to account for the influence of RH (Ghan and Collins, 2004;Ghan et al., 2006), but few systematic investigations have been conducted (Andreae, 2009), due partially to the dearth of measurements available at the time.
Thanks to the US Department of Energy, which is responsible for the deployment of the Atmospheric Radiation Measurement (ARM) Climate Research Facility (at fixed and mobile locations), CCN and many pertinent variables have been measured in recent years, allowing for the study presented here.The goal of this study is to gain further insights into the relationship between CCN and aerosol optical quantities, such as columnar AOD and aerosol scattering coefficients, by exploiting rich ARM data acquired around the world with different background aerosol types.To reduce the uncertainty in CCN estimations from aerosol optical measurements, we investigate the influence of RH, aerosol hygroscopicity and aerosol single scattering albedo (SSA) on the relationship between CCN and aerosol optical measurements.Measurements and methods used are described in Sect. 2. Section 3 presents results from various analyses and a summary is given in Sect. 4.

Data
ARM data from five sites are used, representing different regions (e.g., continental and marine) dominated by different types of aerosols: the US Southern Great Plains (SGP, permanent site, typical rural continental aerosols over farm land), Graciosa Island in the Azores (GRW, mobile facility site, sea salt aerosols and local pollution from airport traffic and long-range transport from Europe), the Black Forest in Germany (FKB, mobile facility, agricultural and forested regions with rich biogenic aerosols), the Ganges Valley in India (GVAX, mobile facility site, anthropogenic pollution, high concentrations of sulfate, nitrate, organic and black carbon particles), and Niamey in Niger (NIM, mobile facility site, dust aerosols).The locations and observation periods, as well as measurements used in this study, are listed in Table 1.More detailed information about each site can be found at http://www.arm.gov/sites.
AOD and the Angstrom wavelength exponent (α) data were obtained from the National Aeronautics and Space Administration's Aerosol Robotic Network (AERONET) database (Holben et al., 1998;http://aeronet.gsfc.nasa.gov).The quality and consistency of AERONET AOD data are well controlled and continuously monitored.There were no AERONET retrievals available for the FKB site.Cimel sunphotometers used in the AERONET measure direct solar and sky radiances at discrete wavelengths (340, 380, 440, 500, 670, 870, 940 and 1020 nm) from which AOD is retrieved at each wavelength with an uncertainty of 0.01-0.02(Dubovik and King, 2000).At the FKB site, AOD and α were retrieved from the multifilter rotating shadow band radiometer (MFRSR).The MFRSR measures total and diffuse solar broadband irradiances at 415, 500, 610, 673, 870, and 940 nm with an AOD retrieval accuracy of ∼ 0.01 (Alexander  et al., 2008).The consistency of AOD and α retrieved from the Cimel sun-photometer and the MFRSR has been investigated by Lee et al. (2010).Close agreements were found at all wavelengths except at 415 nm.MFRSR-derived α used in this study was calculated using data at 500 and 675 nm.CCN and aerosol condensation nuclei (CN) concentrations, aerosol scattering and absorption properties, as well as the aerosol hygroscopic growth factor (f RH ), are measured by a suite of instruments comprising the aerosol observing system (AOS), which is the primary ARM platform measuring in situ aerosol properties at the surface (Jefferson, 2011).CN concentrations are measured by the compact and rugged TSI Model 3010 instrument, which counts the number of particles with diameters in the size range of 10 nm to 3 µm.CCN concentrations are measured by the Droplet Measurement Technology (DMT) CCN counter at seven levels of supersaturation (S; Roberts and Nenes, 2005).The observation interval is 5 min at each level of S. It is calibrated at the beginning and at the end of each mobile facility deployment and annually at the SGP site (Jefferson, 2011).
Aerosol scattering coefficients (σ sp ) integrated over the scattering angle range of 7-170 • are measured with TSI Model 3565 three-wavelength (450, 550 and 700 nm) nephelometers that separate aerosols by particle diameter for total aerosols (D p ≤ 10 µm) and submicrometer aerosols (D p ≤ 1 µm).Two nephelometers are deployed, with one serving as the "reference" that measures dry σ sp and the other connected to a humidity scanning system and measuring changes in σ sp with RH.The humidifier scans RH from low (∼ 40 %) to high (∼ 90 %) and back to low RH on an hourly basis.Aerosol light absorption coefficients (σ ap ) at 470, 528 and 660 nm are measured by a filter-based Radiances Research particle/soot absorption photometer.The 470 nm σ ap was normalized to 450 nm to match the σ sp measured by the nephelometer.Anderson et al. (1996) and Heintzenberg et al. (2006) have reported that the uncertainty in nephelometermeasured σ sp ranges from 1 to 4 Mm −1 for one-minute aver-aged data.The uncertainty also depends on the magnitudes of σ sp and σ ap (Jefferson et al., 2011).
The aerosol hygroscopic growth factor, f RH , is a parameter commonly used to quantify the increase in aerosol scattering relative to dry scattering with changes in RH, and is defined as the ratio of the σ sp at a given RH to that at a low reference RH: The hygroscopic growth factor at RH = 85 % and RH Ref = 40 % is then written as f RH(85 %/40 %) .To calculate the RH dependence of σ sp , a two-parameter empirical fit is used: where a and bare determined from σ sp measured at varying RH levels (Jefferson, 2011).RH values measured by a nephelometer have an error on the order of 10 % because the instrument sensor is not well calibrated.However, binaveraged f RH(85 %/40 %) has been calculated in this study using a large amount of data, so the effects of the uncertainty on results are minor.Knowing the fitting parameters, a and b, one can estimate σ sp at any ambient RH: (3)

Data analysis
After matching data from multiple instruments according to observation time, they are sorted into different discrete bins in which means and standard deviations are calculated.A period void of data is excluded from subsequent analyses.CCN measurements were made at different values of S, and AOD at different wavelengths, but to easily compare our finding with the study by Andreae (2009), the data used here were made at S = 0.4 % and at 500 nm, respectively.Note that S = 0.4 % is more representative of convective clouds, but is too high a value for stratiform clouds.To compensate for this, low S values (S = 0.1 %) were considered in deriving the general aerosol optical quantities-CCN relationship for practical applications, as presented in Sect.3.5.CCN measured at any S is adjusted to a fixed S of 0.4 and 0.1 % through the following equation: where N 0 , b and k are empirically fitted parameters (Ji and Shaw, 1998).This function describes the N CCN -S relationship better than the traditional formula CCN S = CS k suggested by Twomey (1959) (C and k are fitted parameters).The latter overestimates CCN concentration at large S because there is no constraint on CCN as total aerosol concentration increases.Mean fitting errors in this study are 9.5, 3.2, 6.3, 23.8 and −10.7 % at SGP, GRW, NIM, GVAX and FKB sites, respectively.small at the GRW site because there is less anthropogenic pollution, but the ratio of CCN to CN is high.This suggests that a large fraction of aerosol particles at this site can be activated into CCN.CN concentrations at the NIM site are the largest because dust events are frequent.The ability of dust particles to serve as CCN strongly depends on the amount of minor soluble substances contained in the dust particles (Rosenfeld et al., 2001;Kelly et al., 2007).CCN generally increases with CN during dust events, but the ratio of CCN to CN tends to decrease sharply with increasing CN, implying that less CCN become available under dusty conditions (Liu et al., 2011).This is why the smallest ratio of CCN to CN is found at the NIM site even though the CCN 0.4 concentration is moderately high.

Relationship between columnar aerosol optical quantities and CCN
For easy comparison with Andreae (2009), AOD-CCN relationships were obtained based on the function AOD = a • (CCN 0.4 ) b (Andreae, 2009) for AOD at 440, 500, 675, 870 and 1020 nm. Figure 1 presents the relationships between CCN 0.4 and AOD at 500 nm (AOD 500 ), between CCN 0.4 and AI, and their corresponding correlation coefficients (R 2 ) for different sites.AI is defined as the product of AOD 500 and α (500-675 nm), which serves as a better proxy for CCN (Nakajima, 2001).AOD 500 and CCN 0.4 are positively correlated and the correlations are best at the SGP, GVAX and FKB sites.Although a moderate correlation exists at the NIM site, the largest standard deviations and the smallest ratio of CCN to CN representative of the site suggests that dust aerosols are not efficient CCN.They are, however, efficient in light scattering.The small value of mean α indicates that dust aerosols dominated this area during the study period.Biomass burning aerosols are also present in this area and may complicate the analysis of NIM data.The lowest correlations between CCN 0.4 and AOD 500 / AI observed at the GRW site may be attributed to sea salt aerosols.Because of their large size, their scattering may be strong relative to the low number concentration of large particles that are converted into CCN.In general, for most of the sites considered in this study, the correlation between AOD 500 and CCN deteriorates with increasing wavelength.CCN is more closely correlated with AOD measurements at shorter wavelengths because the CCN concentration is dictated by fine-mode aerosols (Andreae, 2009).The relationship varies considerably from site to site and so large errors would be incurred if one global mean relationship was used, attesting to the need of different functions for different aerosol types/regions.Both the ability of an aerosol particle to act as a CCN at a given S level and its contribution to extinction depends on the aerosol particle size distribution.Particle size is thus also a key factor influencing the AOD-CCN relationship.To assess this potential impact, Fig. 1c and d show correlation coefficients from linear regressions of CCN 0.4 and AOD 500 / AI, respectively, as a function of wavelength.Like AOD 500 , AI generally increases with increasing CCN and the correlation is better than with AOD 500 at all sites.AI is more sensitive than AOD to the accumulation mode aerosol concentration, which is typically responsible for most CCN.Since α contains aerosol size information and AI conveys both aerosol loading and particle size information, the correlation between AI and CCN depends much weakly on wavelength.Compared with other pollution aerosols, dust AOD shows a slight decreasing trend with increasing wavelength, which may contribute to the slight increase in the correlation between CCN and AI at the NIM site.

Relationship between in situ aerosol scattering properties and CCN
Given that CCN is measured near the surface and that AOD represents total light extinction in the whole atmospheric column, the AOD-CCN relationship must be affected by the vertical distribution of aerosols.To avoid such mismatch, Fig. 2 shows results from the same analysis performed in Fig. 1, but using in situ measurements of σ sp at 450 nm in lieu of AOD (Fig. 2a) and the scattering aerosol index, Scat_AI (Fig. 2b).Correlation coefficients for the linear regressions of CCN 0.4 and σ sp (Fig. 2c) and Scat_AI (Fig. 2d) for dry aerosol particles with D p ≤ 1 µm as a function of wavelength are shown in Fig. 2c and d.Scat_AI is the product of σ sp and the scattering wavelength exponent, α Scat , which is expressed as where σ sp,λ 1 and σ sp,λ 1 are scattering coefficients at wavelengths λ 1 and λ 2 (here, λ 1 = 450 nm and λ 2 = 700 nm).The number of CCN bins and sample sizes for each CCN bin are shown in Table 3.At all sites, correlations between σ sp and CCN and Scat_AI and CCN are greater than those for the AOD-CCN and AI-CCN relationships (Fig. 1).The highest correlations are found for the Scat_AI-CCN relationships, which also exhibit much less wavelength dependence.The sound relationship between aerosol optical quantities and CCN concentration indicates that if the vertical profile of aerosol scattering properties is known, the CCN profile may be estimated.Note that the ARM program has adopted the method of Ghan et al. (2006) to produce vertical profiles of CCN at its long-term sites.The method is based on aerosol extinction profiles, as well as surface CCN measurements.While their method and ours differ significantly because they rely on different types of scattering received by active and passive sensors, the fundamental principle is the same, namely, making use of optical measurements to derive CCN.In general, scattering is much more readily measured than CCN.While this sounds encouraging, the uncertainty is large, up to a factor of two (Andreae, 2009).Accounting for some influential factors would help reduce the uncertainty.

Influence of ambient RH
The aerosol humidification effect is defined as the change in AOD in response to changing RH.A hygroscopic particle can swell in size through the uptake of water, which enhances its scattering efficiency and thus increases its contribution to total extinction and AOD.On the other hand, its capability of being activated to become a CCN does not depend on RH because it activates at S. This implies that changes in ambient RH can result in variations in AOD 500 or AI, even when CCN 0.4 concentrations remain the same.As such, the relationship between CCN and AOD or σ sp is affected by RH, which is qualitatively investigated in the following way.
AOD and AI data originally averaged over different CCN concentration ranges were further binned within each CCN interval according to RH range (0-35 %, 35-75 %, and 75-100 %). Figure 3 shows AOD 500 and AI as a function of CCN concentration for these different RH bins using data from the SGP site.Both AOD 500 and AI increase with increasing ambient RH within the same ranges of CCN 0.4 concentration.The correlation between AOD 500 and CCN concentration becomes weak when ambient RH values are above 75 % due to the strong aerosol swelling effect on AOD 500 (Jeong et al., 2007).The increase in particle size implies that α decreases, which has been demonstrated by others (Noh et al., 2011).This increase in AOD and decrease in α with increasing RH complicates the relationship between AI and CCN 0.4 .Unless RH is very high, e.g., greater than 95 %, changes in humidity do not influence the wavelength dependence of scattering in any significant way because scattering coefficients at all wavelengths change by similar factors and absorption is usually a minor fraction of extinction (Shinozuka et al., 2007).AOD 500 or AI values under lower ambient RH conditions are more representative of the real effects of aerosols.
Figure 4 shows the correlation coefficients of the relationships between in situ σ sp and CCN for aerosol particles with D p ≤ 1 µm and at ambient RH conditions as a function of wavelength at all sites.The CCN bins used are the same as in Fig. 2 and ambient σ sp are averaged in each CCN bin.Aerosol σ sp measurements, CCN concentrations, ambient RH measurements, and calculated aerosol hygroscopic growth factors were temporally matched.The aerosol hygroscopic growth factor is calculated at 1 h intervals.Scattering coefficients corrected for ambient RH have a temporal resolution of one minute and are matched with the closest hourly value of aerosol hygroscopic growth factor.The correlation coefficients of σ sp -CCN relationships at ambient RH levels are generally lower than those under dry RH conditions (Fig. 2c).For example, at the GRW site, there is almost no relationship between CCN 0.4 and σ sp at ambient conditions because particles over the site have a strong hygroscopicity.The σ sp -CCN relationship at the NIM site is least affected by RH because RH is low in that region and the prevalent dust aerosols have a relatively low hygroscopicity.These results suggest that the influence of RH on the relationship between aerosol optical quantities and CCN concentration needs to be taken into consideration unless RH is low enough for humidification to be negligible.

Influence of aerosol hygroscopicity
Hygroscopicity and RH jointly determine the swelling effect, which affects AOD and σ sp , and thus the AOD (σ sp )-CCN relationship.Having addressed the effect of RH, hygroscopicity is investigated by minimizing the influence of ambient RH through use of in situ measurements of σ sp under fixed moderately dry conditions (∼ 40 %). Figure 5 shows σ sp -CCN 0.4 relationships for different ranges of f RH for dry aerosol particles with D p ≤ 1 µm (Fig. 5a) and D p ≤ 10 µm (Fig. 5b) at the SGP site.The sample sizes in Fig. 5a and b are given in Table 4.No clear influence of f RH on any σ sp -CCN relationship for dry particles with D p ≤ 1 µm and D p ≤ 10 µm is seen.
The aerosol property f RH depends strongly on aerosol chemical composition (Jeong et al., 2007;Liu et al., 2011) and conveys information about the enhancement of aerosol light scattering/extinction as RH increases.Fundamentally, if aerosol particles are highly hygroscopic, they should be more readily activated into CCN.To further assess the influence of f RH on the σ sp -CCN relationship, the CCN concentration and σ sp at 450 nm for dry particles with D p ≤ 10 µm (Fig. 6a) and the ratio of CCN to σ sp (Fig. 6b) as a function of f RH are plotted.No significant changes in CCN and σ sp with increasing f RH are found, especially when f RH is greater than 1.5 (Fig. 6a).Since there is no significant variation in CCN and σ sp with changes in f RH , the ratio of CCN to σ sp is insensitive to increasing f RH .This supports the finding that f RH has a weak influence on the σ sp -CCN relationship.The scattering wavelength exponent associated with each value of f RH is 1.69 ± 0.40, 1.67 ± 0.40, 1.70 ± 0.40 and 1.76 ± 0.34, respectively, which shows almost no change with variations in f RH .
It is still unclear whether f RH is useful for inferring CCN properties (Ervens et al., 2007).Studies have shown that the most important piece of information for CCN closure is the aerosol size distribution, followed by aerosol composition (Dusek et al., 2006).Both affect aerosol hygroscopicity (Ervens et al., 2007).As natural aerosols are usually well mixed, the true effect of chemical composition may not stand out clearly, especially if its signal is weaker than the other uncertainties.Aerosol composition at the SGP site does not vary dramatically, so f RH there may be more dependent on changes in the aerosol size (Hegg et al., 1993).Mean α does change slightly in each bin, which may indicate that there are differences in aerosol composition after all.Also, α may not completely describe the aerosol particle size, especially Table 4. Sample size for the data points in Fig. 5a and b.

Influence of aerosol SSA
In addition to AOD and α, aerosol SSA, defined as the ratio of scattering to extinction, is another independent aerosol attribute denoting aerosol composition and size.SSA can thus potentially affect the CCN-AOD (σ sp ) relationship.SSA can be estimated from surface measurements made by a scanning sun-photometer, such as those used in the AERONET (Dubovik and King, 2000), by a combination of direct-beam and diffuse radiation (Zhao and Li, 2007), or a combination of surface-measured total attenuation and satellite-measured atmospheric reflection (Lee et al., 2007).Since both AOD and SSA are influenced by ambient RH, only surface measured σ sp and SSA at a fixed RH (∼ = 40 %) are used here to eliminate the influence of ambient RH. Figure 7 shows σ sp at 450 nm as a function of CCN 0.4 for different ranges of SSA at 450 nm with D p ≤ 1 µm.Figure 8a shows CCN 0.4 concentrations, σ sp , and their ratio (CCN / σ sp ) at 450 nm as a function of SSA for D p ≤ 1 µm.CCN 0.4 concentrations decrease slightly with increasing SSA, while σ sp increases significantly with increasing SSA.Their ratio decreases significantly with increasing SSA.One explanation for these dependencies involves an air mass containing light-absorbing soot particles coated with volatile material (e.g., sulfates and organics) (Clarke et al., 2007).These particles can act as CCN, but scatter radiation poorly, therefore they have a lower SSA (Shinozuka, 2008).As they age, the particles grow in size due to deposition of soluble mass, such as sulfate and nitrate.They can then scatter more even while their number concentration remains constant or decreases due to coagulation (Shinozuka, 2008).To constrain any influence of particle size, which also affects CCN and aerosol optical quantities, the same relationships as in Fig. 8a are plotted in Fig. 8b, but using only data with α ranging from 1.6 to 1.8.Similar trends are found, eliminating particle size as a driving force behind the relationships.
Results presented here suggest that SSA has a significant influence on the relationship between CCN concentration and aerosol optical quantities and if used as a constraint, may reduce uncertainties in the relationship.Similar results were reported by Shinozuka (2008), who showed that by using SSA as a constraint, the estimation of CCN concentration from aerosol extinction coefficients for pollution particles in Mexico is improved by up to 20-30 %.

Parameterizations for estimating CCN
The above analyses serve a guide toward developing more accurate relationships between CCN and aerosol optical properties by accounting for the major influential factors.A relationship between CCN and AOD is first developed by considering the influences of particle size and aerosol SSA.Correcting for the strong influence of RH cannot be generalized because it depends on aerosol type.On the other hand, the swelling effect is only significant for large RH (> 90 %).
Here, the parameterization is limited to RH < 80 %, i.e., only measurements made under dry to moderately moist conditions are used.The parameterization based upon the large data set from the ARM SGP site may be valid for other rural continental regions.
The parameterization is given as R 2 is 0.94 and the mean relative error (RE), defined as (CCN C -CCN M )/CCN M , is 0.85.CCN C and CCN M represent calculated CCN concentration using Eq. ( 6) and measured CCN concentration, respectively.SSA is limited to 0.85-0.95,which represents most aerosol particles with moderate scattering and absorbing properties.
The relatively large error is mainly attributed to the fact that CCN is measured near the surface, but AOD represents total light extinction in the whole atmospheric column.Any unaccounted for swelling effect is not expected to be very large due to the constraint in RH.Compared to the use of a single fixed relationship between CCN and AOD, R 2 is improved by 9.3 % (0.94 vs. 0.86) and RE is improved about 11.5 % (0.85 vs. 0.96).
If there are in situ aerosol optical measurements available, such as σ sp at 450 nm, estimation of CCN can be further improved by the following parameterization: R 2 is improved (increasing from 0.94 to 0.99) and mean RE is reduced from 0.85 to 0.20, relative to Eq. ( 6).When compared to a single fixed CCN-σ sp relationship that does not account for any influential factors, the R 2 from Eq. ( 7) does not differ considerably (0.99 vs. 0.97); the mean RE is significantly decreased by as much as 74.7 % (0.20 vs. 0.79).

Summary and conclusions
Aerosol loading has often been used as a proxy or predictor of CCN in cloud-aerosol interaction studies due to the dearth of CCN measurements.Based on extensive measurements of aerosol optical quantities and CCN number concentrations made at different ARM Climate Research Facility sites, the relationships between aerosol optical quantities, including columnar AOD, surface-measured aerosol scattering parameters, and CCN concentrations are assessed.For the purpose of constraining and reducing the variability and uncertainties in relating aerosol optical quantities and CCN concentrations, the influences of RH, aerosol hygroscopicity and SSA are investigated using more extensive routine measurements made at the permanent ARM SGP site.
In general, mean AOD-CCN relationships at the SGP, GVAX and FKB sites show a variable degree of correlation.A weaker correlation is found at the GRW and NIM sites where relatively large particles dominate.In general, the correlation decreases as the wavelength at which AOD is measured increases.So use of AOD values measured at the shortest wavelengths is recommended.Moreover, it is better to use AI derived from AOD measurements at two wavelengths than AOD at a single wavelength because the relationship between AI and CCN is systematically better than the CCN-AOD relationship.The best predictors of CCN are in situ aerosol scattering/extinction coefficients and aerosol indices measured simultaneously with CCN.
AOD and AI are significantly influenced by ambient RH levels.The correlation between AOD (AI) and CCN becomes weak when ambient RH values are high, e.g., greater than 75 %, due to strong aerosol swelling effects on AOD.The correlation between aerosol optical quantities and CCN concentration is much tighter for dry air than for humid air.This implies that aerosol optical quantities measured at low RH are better representatives of the real effects due to aerosols.No significant influence of the aerosol hygroscopic growth factor on any CCN-σ sp relationship is found.Particles with low SSA are generally associated with higher CCN concentrations for the same scattering coefficient and lower σ sp values.Aerosol SSA has a significant influence on the relationship between CCN concentration and aerosol optical loading variables, and can thus be used to reduce uncertainties in the estimate of CCN.Note that both f RH and SSA are related to aerosol chemical composition.
The influential factors are accounted for in developing parameterization schemes for estimating CCN from any aerosol optical property (AOD, α, and σ sp ).The best results are achieved by using σ sp and SSA.The parameterization is valid for RH < 80 %.If the humidification function and humidity are known, one can correct for the effect to any higher values of RH.
This study reveals the potential and limitations of using aerosol optical property measurements to infer CCN concentration with a focus on the impact of ambient RH, aerosol hygroscopic response, and SSA.Further evaluation and analyses will require aerosol composition and aerosol size distribution information, together with aerosol optical parameters and meteorological parameters for each aerosol type and region.

Fig. 1 .
Fig. 1.(a) Relationship between AOD at 500 nm and CCN 0.4 , (b) relationship between AI and CCN 0.4 (c) their correlation coefficients, and (d) same as (c), but for AI in lieu of AOD.

Fig. 2 .
Fig. 2. Same as Fig. 1, but AOD is replaced by aerosol scattering coefficients for dry aerosol particles with diameters of less than 1 µm measured by nephelometers.

Fig. 3 .
Fig. 3. (a) AOD at 500 nm and (b) AI as a function of CCN 0.4 concentration for different ranges of ambient RH.Data are from the SGP site.

Fig. 4 .
Fig. 4. Correlation coefficients of the relationship between surfacemeasured aerosol scattering coefficients and CCN 0.4 concentrations as a function of wavelength for ambient RH conditions and with aerosol particle diameters of less than 1 µm.

Fig. 5 .
Fig. 5. Relationship between CCN 0.4 concentrations and aerosol scattering coefficients at 450 nm for dry aerosol particles with (a) D P ≤ 1 µm and (b) D P ≤ 10 µm for different ranges of aerosol hygroscopic growth factor.Data are from the SGP site.

Fig. 6 .
Fig. 6.(a) CCN 0.4 concentrations and aerosol scattering coefficients, and (b) their ratio as a function of f RH for dry particles with D P ≤ 10 µm.Data are from the SGP site.

Fig. 7 .
Fig. 7. Relationship between aerosol scattering coefficients at 450 nm and CCN 0.4 concentrations for different ranges of SSA and for dry particles with D P ≤ 1 µm.

Fig. 8 .
Fig. 8. CCN 0.4 concentration, aerosol scattering coefficient and their ratio as a function of SSA at 450 nm for all dry particles with D P ≤ 1 µm for (a) all values of the extinction Angstrom exponent and (b) values of the extinction Angstrom exponent that fall between 1.6 and 1.8.The sample number in each SSA bin for each case is given in each panel.

Table 1 .
Description of ARM 1 data sets selected for this study.Angstrom wavelength exponent; 5 AERONET Aerosol Robotic Network; 6 CCN cloud condensation nuclei; 7 CN condensation nuclei; 8 σ sp aerosol light scattering coefficients; σ ap aerosol light absorption coefficients; 9 SSA single scattering albedo, equal to the ratio of σ sp to (σ sp + σ ap ); 10 f RH(RH/RH Ref ) aerosol hygroscopic growth factor defined as the ratio of σ sp at a given RH to σ sp at a low reference RH; 11 AOS aerosol observing system, the primary ARM platform for in situ aerosol measurements made at the surface.

Table 2
They are responsible for nearly half of the aerosol scattering at the NIM and GVAX sites.Coarse particles with diameters > 1 µm contribute more to aerosol scattering at the GRW site.The smallest values of SSA are found at the NIM and FKB sites (0.82 ± 0.06 and 0.85 ± 0.06, respectively).As per the values of SSA and α, significantly different aerosol types are present at these sites.SSA at the SGP and GVAX sites is similar (∼ 0.92 ± 0.04) and α is on the same order.On average, there was no significant difference in the magnitude of f RH between these two sites where f RH is generally large, indicating the presence of more hygroscopic particles.The NIM site has the lowest f presents the means and standard deviations of aerosol optical quantities and CCN at all sites.The largest mean AOD occurred at the NIM site (0.39 ± 0.33), which is almost four times greater than that at other sites, and the smallest mean AOD was measured at the GRW site (0.11 ± 0.06).Mean α at these two locations (NIM: 0.47 ± 0.23, GRW: 0.75 ± 0.35) are lower than that at the other sites, indicating more influence by coarse particles (dust particles at the NIM site and sea salt at the GRW site).The largest mean α at the FKB site (1.88 ± 0.27) suggests more fine particles at this site than at the SGP and GVAX sites.Mean σ sp shows that submicron particles (D p ≤ 1 µm) play a dominant role in aerosol scattering at the SGP and FKB sites.RH because dust aerosols are primarily composed of insoluble components or components with low solubility, while the GRW site has the highest f RH because sea salt aerosols with strong hygroscopicity dominate in this area.Mean number concentrations of CN and CCN 0.4 are

Table 2 .
Summary of mean aerosol optical quantities, CN concentration, and CCN concentration at 0.4 % supersaturation during the study period.

Table 3 .
Number of CCN bins and sample sizes for each bin in Figs. 2 and 4.

Table 5 .
Sample sizes for the data points in Fig.7.
Table 5 lists sample sizes.σ sp generally increases with increasing SSA for the same range of CCN 0.4 concentration.Low SSA values are generally associated with high CCN concentrations, and vice versa.