Global organic and inorganic aerosol hygroscopicity and its effect on radiative forcing

Domain: earth_science
Published: 2023-10-02
Editorial outcome: accept

Abstract
The climate effects of atmospheric aerosol particles serving as cloud condensation nuclei (CCN) depend on chemical composition and hygroscopicity, which are highly variable on spatial and temporal scales. Here we present global CCN measurements, covering diverse environments from pristine to highly polluted conditions. We show that the effective aerosol hygroscopicity, κ, can be derived accurately from the fine aerosol mass fractions of organic particulate matter (ϵorg) and inorganic ions (ϵinorg) through a linear combination, κ = ϵorg ⋅ κorg + ϵinorg ⋅ κinorg. In spite of the chemical complexity of organic matter, its hygroscopicity is well captured and represented by a global average value of κorg = 0.12 ± 0.02 with κinorg = 0.63 ± 0.01 as the corresponding value for inorganic ions. By showing that the sensitivity of global climate forcing to changes in κorg and κinorg is small, we constrain a critically important aspect of global climate modelling.

Introduction
The radiative energy budget of the Earth is strongly influenced by atmospheric aerosol particles, which scatter and absorb solar radiation, act as nuclei in the formation of cloud droplets and ice crystals, and cause a variety of rapid adjustments in environmental variables1,2. In our understanding of the climate system and our ability to model its human-driven change, the roles of aerosols, such as aerosol–radiation interactions (ari) and particularly the highly dynamic aerosol–cloud interactions (aci), have remained strikingly uncertain3,4. The aerosol hygroscopicity and, thus, the water content of the particles in response to the atmospheric conditions, influence the aerosol-related effective radiative forcing (ERFaer) in the climate system via two mechanisms: First, more hygroscopic aerosol particles grow to larger diameters at relative humidity < 100%, leading to a greater scattering cross section and thus stronger radiative forcing by aerosol–radiation interactions (RFari). Second, particles of the same size but higher hygroscopicity act more readily as cloud condensation nuclei (CCN), which activate into cloud droplets, leading to a larger cloud droplet number, longer-lived clouds and stronger forcing by aerosol–cloud interactions (RFaci)5, and, together with the cloud adjustments, this entails a stronger ERFaer.

The Köhler equation

s = aw exp(Ke) (1)

represents the dependence of s—which is the ratio of equilibrium water vapour pressure over a curved solution to that above a flat, pure-water surface—on the Raoult and Kelvin effects6. The equation combines the solute (Raoult) term, which quantifies the decreased water activity, aw, leading to a decreased water vapor pressure above the water surface as a function of particle size and chemical composition, and the curvature (Kelvin) term, Ke, which quantifies the water vapor pressure enhancement above a curved surface as a function of surface tension. Equation (1) is of fundamental importance in cloud microphysics, as it thermodynamically describes the activation of CCN into cloud droplets at a given water vapor supersaturation, S = s − 1. Petters and Kreidenweis7 introduced the hygroscopicity parameter, κ, to parameterize aw of a solution droplet according to

aw = 1 / (1 + κ(Vs / Vw)) (2)

where Vs and Vw are the volumes of the dry solute and pure water, respectively. In combination with particle size and number concentration, κ has been very useful to predict CCN number concentrations in aerosol populations8–10. Experimentally, κ has been retrieved via two different strategies: (i) from ambient measurements of entire aerosol populations, resulting in overall effective κ values, typically ranging from ~0.1 to ~0.9, and (ii) from laboratory experiments yielding compound-specific κ values ranging from ~0.02 to ~0.4 for organic and from ~0.3 to ~0.9 for inorganic reference substances7,11,12. Typical inorganics are salts comprising sulfate (SO42−), nitrate (NO3−), ammonium (NH4+), or chloride (Cl−). For the calculation of κ as an effective parameter, often the surface tension of pure water has been assumed, as is also done here.

The κ of a mixture of chemical components, i, in an aerosol population is given by the additive mixing rule

κ = Σ ϵi κi (3)

which includes the dry component volume fraction ϵi = Vsi / Vs with Vsi as the volume of the individual components and Vs as the total particle volume7,13,14. This formula is based on the Zdanovskii-Stokes-Robinson (ZSR) approach assuming additive water uptake of individual components in mixtures15. Aerosol chemical composition is measured routinely by aerosol mass spectrometers (AMS), providing time series of the quantitative mass concentrations, m, of the major aerosol constituents organics (Org), SO42−, NO3−, NH4+, and Cl−. While the mass fraction of inorganic ions is usually limited to a few well characterized compounds, the organic mass fraction might comprise thousands of different molecules, of which most are not fully identified. Standardized AMS observations worldwide have improved the understanding of global aerosol composition profoundly11. This has particularly helped to constrain the ambient aerosol hygroscopicity, since the AMS-derived data on aerosol composition can be directly linked to an ambient κ using the simplified version of Eq. (3)

κ = ϵorg κorg + ϵinorg κinorg (4)

with the organic mass fraction ϵorg = morg / mtotal, the inorganic mass fraction ϵinorg = (mtotal − morg) / mtotal, and the total aerosol mass concentration mtotal = morg + mSO42− + mNO3− + mNH4+ + mCl−16. Note that Eq. (4) is an approximation and assumes that the inorganics are composed solely of hygroscopic salts. As mineral components and elemental carbon are not detected by the AMS, the presence of non- or weakly-hygroscopic compounds as minor constituents is subsumed into the deduced value of κorg and/or κinorg. The upper size limit of AMS measurements (i.e., 50% transmission) and therefore the data used in Eq. (4) is typically around 600 nm17. Further, whereas Eq. (3) is based on volume fractions, Eq. (4) uses mass fractions, which is an approximation. This is justified here as the densities, ρ, are sufficiently similar (i.e., ρorg ≈ 1.4 g cm−3, ρinorg ≈ 1.77 g cm−3)16,18. For lower ϵorg, average ϵorg (i.e., ≈ 0.25), however, the difference between volume and mass fractions can be up to 15% (with volume fractions being larger), which has to be considered in the interpretation of the results.

Equation (4) has been applied in both directions: either as a retrieval of κorg and κinorg based on ambient measurements of an overall κ and aerosol chemical composition or as an application of previously derived κorg and κinorg values to parameterize the effective aerosol hygroscopicity, e.g., for the purpose of radiative transfer calculations. In fact, aerosol–climate models use Eq. (3) to parameterize the aerosol hygroscopicity through species-specific κ values (see Methods). Several retrievals of κorg and κinorg have been reported, from remote tropical forests to moderately or even heavily polluted urban areas (Table S1). These campaign-specific results show large ranges in κorg from 0.04 to 0.25 and for κinorg, from 0.46 to 0.71, and further emphasize the need of a robust and accurate representation of the aerosol hygroscopicity in aerosol–climate models. This raises two fundamental questions:

1. Is there a pair of robust κorg and κinorg values that is globally representative of aerosol water contents above and below water saturation and, thus, a suitable choice for general application in aerosol–climate models?

2. How sensitive are the model predictions in terms of CCN concentrations as well as direct and indirect radiative forcing to the choice of κorg and κinorg?

This study addresses both questions. First, we conducted a systematic retrieval of κ by merging extensive datasets from AMS and size-resolved CCN measurements obtained in contrasting environments (Fig. 1A) to calculate a pair of broadly representative κorg and κinorg values. Secondly, we applied this optimized retrieval along with other pairs of κorg and κinorg in the ECHAM–HAM aerosol–climate model to test the corresponding sensitivity of CCN concentrations and radiative forcing.

Results
Retrieval of globally representative κorg and κinorg values

Figure 1B shows how κorg and κinorg were retrieved through a linear bivariate regression fit of measured ϵorg and κ data, combining contrasting data from remote rainforest (Amazon) to urban-polluted air (Chinese megacities). The extrapolation of the fit to ϵorg = 0 yields κinorg and the extrapolation to ϵorg = 1 yields κorg16,19. The optimized retrieval shows a clearly linear relationship, consistent with Eq. (4), as well as a remarkably tight scatter plot and corresponding low uncertainty. It yields κorg = 0.12 ± 0.02 and κinorg = 0.63 ± 0.01 as robust values, constrained by a wide distribution of ϵorg data points from ~0.2 to ~1.0.

Figure 1C underlines how robustly and broadly our optimized retrieval represents the average aerosol hygroscopicity worldwide by means of a good agreement between the regression line from Fig. 1B and measurement data from 11 additional field campaigns, including remote background locations (i.e., boreal forest10,20, semi-arid Northern American forest21, marine22, alpine23), rural locations (in Europe24 and North America25) as well as strongly polluted regions (i.e. Indo-Gangetic Plain and central Mexico25). The individual data sets are shown in Fig. S3. The data from the marine background site on Barbados as well as a polluted site in the Indo-Gangetic Plain (Delhi) are of particular significance as only few aerosol and CCN data exist from these locations. Note that the aerosols with relatively high fractions of refractory particles (i.e., sea salt from marine sites and mineral dust at an alpine location) follow the regression line fairly well, even though a certain fraction is not quantitatively evaporated in the AMS and, thus is not included in ϵinorg. The good agreement can be explained as it is primarily the soluble matter in the dust aerosol that affects the CCN population, whereas large dust particles, which could nucleate droplets, are not well documented by κ in the AMS. For aerosols, it has been shown that a mixture of secondary sulfate and organic aerosols—both quantified by the AMS—accounts for most of the CCN27,28. Note here that sea spray and mineral dust aerosol populations typically reach far into the supermicron size range, which implies that the AMS measurement with its upper cut-off size at about 600 nm—defined here as 50% transmission17—excludes significant parts of both aerosol components. Since primary and secondary organic aerosols (POA and SOA) cannot be distinguished by the AMS and thus are combined in the measured organic mass concentration, we recommend to use κorg = 0.12 for both SOA and POA, e.g., in model parametrizations. Following the approach in Gunthe et al.16 and interpreting κorg = 0.12 as an “effective Raoult parameter", we calculated an effective average molecular mass of the organic compounds of Morg = 212 ± 42 g mol−1, assuming a density of 1.4 g cm−318, in good agreement with previous studies16,29,30.

Overall, the good agreement among all datasets in Fig. 1C provides strong evidence that our optimized retrieval of κorg = 0.12 ± 0.02 and κinorg = 0.63 ± 0.01 is a widely applicable representation of the average effective hygroscopicity of aerosols consisting of mixtures of organic and inorganic components over oceans and continents worldwide. This mixing state of the aerosol components affects ari and aci and its representation in models is associated with large uncertainties31–33. Generally, an aerosol population tends to become more and more internally mixed with atmospheric residence time, even within tens of kilometers or after few hours of transport34,35. At the same time, studies suggest that the mixing state of atmospheric aerosols is not fully represented by either the assumption or parameterization of a completely external mixture or internal mixture36,37. Our parameterization of κorg and κinorg is based on a wide variety of atmospheric conditions at different locations and, therefore, represents an atmospherically relevant distribution of prevalent aerosol mixing states. At the same time, special aerosol populations, such as freshly emitted and externally mixed particles, might deviate from the average retrieval. Further note that AMS measurements barely account for the chemical complexity of the organic fraction as they, for instance, do not differentiate between inorganic sulfate or nitrate vs sulfate or nitrate fragments emerging from organosulfates or organonitrates. Vogel et al.38 argue that this effect causes a systematic underestimation of ϵorg for significant levels of organosulfates or organonitrate (Fig. S4), which after correction is still consistent with the linear relationship reported here. Nevertheless, this aspect is worth addressing in follow-up studies in (nitrooxy)-organosulfate-rich environments with targeted instrumentation.

Climate model sensitivity to changes in κorg and κinorg

Changes in the aerosol hygroscopicity affect the growth of the particles in the subsaturated regime and therefore RFari as well as their activation to cloud droplets under supersaturated conditions and therefore RFaci. Accordingly, an improved determination of κ better constrains the aerosol effects on the radiative forcing and therefore for the climate. The aerosol–climate model ECHAM–HAM, which is the ECHAM atmospheric general-circulation model39 coupled to the HAM aerosol module40, was used to estimate the sensitivity of the radiative forcing in climate models to changes in aerosol hygroscopicity. The model parameterizes the overall κ through Eq. (3) based on compound-specific κ values for sea salt, black carbon, mineral dust, organic carbon, and sulfate aerosols (details in experimental section). Replacing the model’s standard values, which are 0.06 for organics and 0.6 for inorganics, by our optimized values κorg = 0.12 and κinorg = 0.63 yields absolute changes in the global mean radiative forcing at the top of the atmosphere of ΔRFari = −0.011 W m−2 and ΔERFaer = −0.026 W m−2 (Table 1). This corresponds to relative changes in RFari of 8% for a replacement of κinorg and 1% for a replacement of κorg as well as a relative change in ERFaer of 1% for a replacement of both, κinorg and κorg. The absolute changes are close to the range of the model variability for the 30-year model runs. Further note the ΔRFari and ΔERFaer from ECHAM–HAM can be rather considered as lower limit values and corresponding results from other climate models might be higher. Myhre et al.41 showed in a model comparison study that ECHAM-HAM yields a global mean anthropogenic RF (all-sky) of −0.15 W m−2, in comparison to the 16-model mean of −0.27 ± 0.15 W m−2 (± one standard deviation). Along these lines, the RFari of ≃ −0.11 W m−2 derived here from ECHAM-HAM (Table 1) is much less than the value of −0.3 W m−2 given in the recent report of the Intergovernmental Panel on Climate Change (IPCC).

In principle, the aerosol effects through ari and aci could be treated approximately additively, which allows to retrieve RFaci as ERFaer − RFari from Table 1. We refrain from reporting these values here, however, as this approach does not account for the various adjustments in the system upon ari or aci changes and also cannot be obtained directly from the model. In terms of indirect effects, the replacement of κ yields the geographic distributions of the changes in CCN concentrations (ΔNCCN) and in the effective radiative forcing (ΔERFSW) shown in Fig. 2B, C. These changes in ΔNCCN and ΔERFSW are comparatively small, which is not surprising since out of the aerosol-related factors that control the CCN spectrum—which are total number concentration, particle size, and particle hygroscopicity—the sensitivity to number is the largest. Moreover, the simplified Köhler equation (Eq. (9)) underlines that the exact value of κ is generally the least important determinant of CCN activity as S varies with D to the power of three and just linearly with κ42. The largest ΔNCCN and ΔERFSW values observed in Fig. 2B, C were found in regions with a high organic aerosol burden and the corresponding values (filtered for high OC) of ΔRFari = −0.049 W m−2 and ΔERFaer = −0.149 W m−2 are higher than the global mean values (Table S3). In terms of direct effects, in contrast, larger local changes were observed, as shown in Fig. 2D (shown here as a quantified sensitivity introduced below). This can be interpreted to emerge because, especially for times and locations with relatively high humidity (i.e., RH > 85%), the increase in hygroscopic growth from increases in κorg and κinorg, leads directly to an increase in total aerosol-phase mass, thus increasing the aerosol optical depth (AOD) even in the absence of a change in mass scattering efficiency. In essence, Fig. 2 illustrates that the response in total light scattering, and therefore ari, to an increase in κ is much more direct than the response of CCN concentrations, and thus aci, to the same factor. Figure 2D also shows some regions with positive values, but the pattern structure suggests that these are due to weather noise. Further note in this context that previous studies documented for organic compounds that the hygroscopicity measured above water saturation, as deduced from observed CCN activity, is higher than that observed in the subsaturated regime, as deduced from light scattering or hygroscopic tandem differential mobility analyser (HTDMA) data43–45. This means that the κorg derived here from CCN activity is likely an upper estimate when used for direct forcing calculations. However, while Table 1 suggest that the Δκ between super- and subsaturated retrievals barely changes the global mean direct effects, it is still worth noting as it might affect conclusions on local effects as suggested by Fig. 2D.

We quantified the sensitivities ξ(RF, κ) of the radiative forcing at the top of the atmosphere in relation to changes in κ (i.e., the change in radiative forcing per unit change in κ) as follows:

ξ(RF, κ) = ΔRF / Δκ (5)

where RF can be either RFari or ERFaer and κ can be either κinorg, κorg or κorg,inorg as the mass-weighted combination of κorg and κinorg. We obtained a globally averaged sensitivity of the RFari to changes in κinorg of ξ(RFari, κinorg) = −0.29 ± 0.003 W m−2, which is about 20 times larger than the corresponding sensitivity to changes in κorg of ξ(RFari, κorg) = −0.017 ± 0.13 W m−2. The much higher ξ(RFari, κinorg) compared to ξ(RFari, κorg) relates to the fact that also κinorg is higher than κorg, which entails a higher hygroscopic growth of inorganic than organic particles in the subsaturated humidity regime and, thus, a higher scattering cross section in aerosol–radiation interaction. When both κ values are changed at the same time, we obtained ξ(RFari, κorg,inorg) = −0.30 ± 0.02 W m−2. Figure 2D shows that the local sensitivity can be substantially higher than the global average ξ(RFari, κ) values. For the overall aerosol-related effective radiative forcing, we obtained a sensitivity to changes in κinorg of ξ(ERFaer, κinorg) = −0.47 ± 0.01 W m−2, which is about 3 times larger than the corresponding sensitivity to changes in κorg of ξ(ERFaer, κorg) = −0.15 ± 0.62 W m−2. Note here the much larger uncertainty in ξ(ERFaer, κorg). For a change in both κ values, we obtained ξ(ERFaer, κorg,inorg) = −0.68 ± 0.29 W m−2. As all these sensitivities are negative, an increase in aerosol hygroscopicity entails a decrease of the radiation at the top of the atmosphere and, therefore, an atmospheric cooling.

In essence, the aerosol hygroscopicity is of major importance for the atmospheric radiative budget. Our results here constrain and simplify κ as an important prescribed parameter in global climate models. First, we provide a globally representative linear relationship of the additive hygroscopicity of organics and inorganic mass fractions, yielding κorg = 0.12 ± 0.02 and κinorg = 0.63 ± 0.01 as recommended parameters for future model applications. Here, κorg should be used for both, primary and secondary organic aerosols. Second, the higher sensitivity of the model to changes in κinorg relative to changes in κorg stresses the importance of a correct representation of the abundance and hygroscopicity of the small number of relevant inorganic aerosol components (i.e., sulfates, nitrates, ammonium) in the models. In turn, this also implies that an experimental determination of the κ of individual compounds within the thousands of different organics—with many of them being unidentified—is not essential to reduce uncertainties in the effective radiative forcing of aerosol particles. The variability of κ within the organic aerosol fraction might be efficiently represented by average chemical properties such as the oxygen-to-carbon ratio11,46. More effort should be dedicated to correctly understand and represent the processes determining the abundance of the organics in the atmospheric multiphase systems and their representation in models, where the largest uncertainties are located in order to better predict the remaining important effects of particle organics as good as possible.

Methods
Aerosol mass spectrometric and size-resolved CCN data

The aerosol mass spectrometric (AMS) and size-resolved CCN data used in this study were obtained from the field studies listed below. AMS data on the non-refractory submicron aerosol fraction (i.e., mass concentrations of organics, nitrate, sulfate, ammonium, and chloride) were obtained either size-resolved from a quadrupole aerosol mass spectrometer (Q-AMS, Aerodyne Research Inc., Billerica, MA, USA), a high-resolution time-of-flight aerosol mass spectrometer (HR-ToF-AMS), or non-size-resolved from an aerosol chemical speciation monitor (ACSM, Aerodyne Research Inc.)47,48. Note that the AMS measurement of Cl− is typically not quantitative due to a merely partial evaporation of the refractory NaCl as a major compound of sea salt aerosols.

CCN concentrations in the studies were measured with a continuous-flow streamwise thermal gradient CCN counter (CCNC, models CCN-100 or CCN-200, DMT, Longmont, CO, USA). In the instrument, the supersaturation (S) was cycled through different S values, typically between 0.1 and 1.1%, defined by controlled temperature gradients inside the CCNC column. Particles with a critical supersaturation Sc ≥ S in the column are activated and form water droplets. Droplets with diameters larger 1 μm are detected by an optical particle counter (OPC) at the exit of the column. Further information on the CCN measurements and instrumentation can be found elsewhere49,50. Note that the CCN measurements were conducted in size-resolved mode, which is one established approach to retrieve κ, as outlined in detail elsewhere16,19,51. This applies to all three main datasets used here for the κorg and κinorg retrieval (i.e., ATTO, PRIDE-PRD-2006, and CARE-Beijing-2006, shown in Fig. 1B) as well as for most of datasets from previous field studies outlined below.

Field studies and datasets

This study integrates 16 field measurements worldwide, during which size-resolved CCN measurements and an aerosol mass spectrometer were operated. These studies can be broadly grouped into two categories: (i) three studies were selected for the retrieval of κorg and κinorg according to criteria outlined below and (ii) 13 further data sets were implemented to evaluate to what extent the retrieved κorg and κinorg values are representative worldwide. The original datasets of the following three studies represent the basis for the κorg and κinorg retrieval:

ATTO, Brazil: The Amazon Tall Tower Observatory (ATTO) site is located in a remote area of the central Amazon rainforest (2.143° S, 59.000° W), ~150 km northeast of the city of Manaus, Brazil. Previous studies provide detailed information on the ATTO site52, the footprint area of its atmospheric observations53, as well as the multi-year ACSM and size-resolved CCN measurements (March 2014 to February 2015)9,19. The conditions probed at ATTO ranged from pristine rain forest air to heavily polluted biomass burning smoke54–56.

Guangzhou, China: The Program of Regional Integrated Experiments of Air Quality over the Pearl River Delta (PRIDE-PRD2006, short here PRD) in Guangzhou was conducted in July 2006 at a rural receptor site (23.550° N, 113.070° E) in the small village Backgarden ~60 km northwest of the megacity Guangzhou on the outskirts of the densely populated center of the Pearl River Delta (PRD). Details on the campaign as well as CCN and AMS datasets can be found elsewhere57–59.

Beijing, China: The Campaign of Air Quality Research in Beijing (CAREBeijing-2006, short here BEI) was conducted from 10 August to 09 September 2006 at a suburban site (39.510° N, 116.310° E) located on the campus of Huang Pu University in Yufa, ~50 km south of the city center of Beijing (BEI). Details on the campaign as well as CCN and AMS datasets can be found elsewhere60,61.

The following two datasets—which are published here for the first time—were included in the analysis as they add particularly relevant locations to the list of investigated environments:

Delhi, India: The Delhi-2018 campaign was performed to characterize the aerosol hygroscopicity in a strongly polluted region in India, comprehensive aerosol measurements during the Delhi-2018 campaign in the Indo-Gangetic plain were conducted62,63. The campaign site was on the campus of the India Meteorological Department (IMD, Delhi, India), which is located in the midst of heavy traffic and small industries. Instruments were placed in an air-conditioned container at ~28 °C. The measurement periods spanned from 05 Feb to 02 Mar 2018. This period marked the end of the winter in the Indo-Gangetic Plain and is characterized by light winds, mildly cold temperature, and high humidity64.

Barbados: The measurements were conducted at the Barbados Atmospheric Chemistry Observatory (BACO, 13.165° N, −59.432° E) during th EUREC4A campaign. The measurement period spanned from 21 Jan to 22 Feb 2020 and a comprehensive campaign overview can be found in Stevens et al.65. Different aerosol populations were measured, spanning from clean marine background conditions to long-range transported aerosols, comprising dust as well as the episodic occurrence of mixtures of dust and black carbon66.

The datasets from previously published studies outlined below were further merged into the present literature and data syntheses. Our analysis either started from the original data (if available) or was based on digitized data points from relevant figures of the corresponding manuscripts, using the WebPlotDigitizer (https://automeris.io/WebPlotDigitizer/, last access 06 Feb 2022). This includes the following locations and measurements:

Puerto Rico: The Puerto Rico Aerosol Cloud Interaction Study (PRACS) took place in Puerto Rico from 9 to 18 Dec 2004. The relevant CCN and aerosol composition data has been reported in Allan et al.22. The site was dominated by north-easterly trade winds bringing clean, marine air masses, interrupted only by few episodes with moderate anthropogenic pollution. The aerosol probed during PRACS can be characterized as comprising mostly sea salt and non-sea salt sulfate. The amounts of organic matter in the aerosol were very low, which makes the data points from this study particularly relevant for the present analysis as the they represent the lowest ϵorg levels in our data synthesis. For our analysis, the data points were digitized from figures in Allan et al.22.

Taunus, Germany: The Feldberg Aerosol Characterization Experiment (FACE-2005) took place in June-July 2005 at the Taunus Observatory field site, which is a small mountain in a forested area. It represents a rural background site about 30–50 km of the Rhine-Main metropolitan area. The site receives diverse aerosol conditions, including urban plumes as well as aged rural air masses. The relevant CCN and aerosol composition data has been reported in Dusek et al.24. This dataset can be regarded as characteristic for many other rural and/or semi-urban locations worldwide. For our analysis, the original data has been re-processed.

Jungfraujoch, Switzerland: The Cloud and Aerosol Characterization Experiment (CLACE-06) took place from 03 to 13 Mar 2007. The high-elevation research station is considered to be prevalently in the free troposphere, receiving aged background aerosol. The relevant CCN and aerosol composition data has been reported in Rose et al.23. For our analysis, the original data has been re-processed.

ZF2, Brazil: The Amazonian Aerosol Characterization Experiment (AMAZE-08) took place from 14 Feb to 12 Mar 2008 at the ZF2 site north of Manaus67. The relevant CCN and aerosol composition data has been reported in Gunthe et al.16. During the campaign, the site received clean rainforest air, interrupted by long-range transported plumes of African dust and biomass burning smoke. This data complements the ATTO data that was used for the κorg and κinorg retrieval. For our analysis, the original data has been re-processed.

Hyytiälä, Finland: The SMEAR II station in the boreal forest in Hyytiälä, Finland is part of the European Integrated project on Aerosol Cloud Climate and Air Quality Interactions (EUCAARI) network and has recorded long term size-resolved CCN measurements. The data used belongs to the measurements from February 2009 to April 2012. The site is a rural background site that received clean and polluted air masses. The relevant CCN and aerosol composition data has been retrieved from a combination of papers10,20,68.

Mexico (aircraft): The Megacities Impact on Regional and Global Environment (MIRAGE) Experiment took place over central Mexico in March 2006 in the course of research flights between 3 and 5 km altitude. MIRAGE was part of the Megacity Initiative: Local and Global Research Observations (MILAGRO) campaign69. The relevant CCN and aerosol composition data has been reported in Shinozuka et al.25. For our analysis, the data points were digitized from figures in Shinozuka et al.25.

Mexico City, Mexico: The measurements outside of Mexico City were conducted from 16 to 31 Mar 2006 in the course of the MILAGRO and MIRAGE campaigns69. The relevant CCN and aerosol composition data has been reported in Lance et al.70. The measurements primarily probed “dense atmospheric pollutants trapped at high altitude, where rapid photochemical oxidation can take place", according to Lance et al.70. For our analysis, the data points were digitized from figures in Lance et al.70. Size-resolved ϵorg-κ relationships are reported in Lance et al.70 for particle diameters of 40, 60, 80, and 100 nm. For comparability with the other studies, these ϵorg-κ relationships were averaged in ϵorg bins here.

USA (aircraft): The second part of the Intercontinental Chemical Transport Experiment—Phase B (INTEX-B) took place from 17 Apr to 15 May 2006 over the US West Coast in the course of research flights below 6 km altitude71. INTEX-B used the same instrumentation as during MILAGRO (see above). The relevant CCN and aerosol composition data has been reported in Shinozuka et al.25. The flights probed anthropogenic and biogenic emissions over extended areas as well as the influence of long-range transport from Asia. For our analysis, the data points were digitized from figures in Shinozuka et al.25.

Taunus, Germany, shown in Fig. S4: The Ice Nuclei Research Unit—Taunus Observatory (INUIT-TO) campaign took place in August 2012 at the Taunus Observatory field site on Mt Kleiner Feldberg in a forested area in central Germany. The relevant CCN and aerosol composition data has been reported in Vogel et al.38 (Fig. S4). During the campaign, fresh and aged aerosol populations were probed. Especially high fractions of sulfate covalently bonded to organic molecules are a focal point of this study as they cause substantially lower κ-values. Vogel et al.38 argue that high fraction of organic acids, organosulfates, and nitrooxy-organosulfate affect the quantification of the organic and inorganic mass fractions by AMS. This limitation of standard AMS measurements can be solved by more sophisticated instrumentation on the chemical composition of aerosol particles and further systematic studies are required to resolve these effects.

SMEAR II, Finland, not shown here: The measurements were conducted from Mar to May 2007 and probed clean and polluted conditions. The relevant CCN and aerosol composition data has been reported in Cerully et al.72 and the data points were digitized from the corresponding figures. This study was critically evaluated, though not included in our analysis because of a clear deviation from the overall linear relationship, as shown in Fig. S4. This is in line with the discussion in Cerully et al.72, stating that especially “the κinorg values are too low for typical inorganic compounds", likely due to a mismatch in the size ranges of the AMS and CCN counter measurements. The authors further conclude that “bulk measurements should be used with caution for representing characteristics of small mode particles."

Colorado, USA: In the course of the BEACHON (Bio-hydro-atmosphere Interactions of Energy, Aerosols, Carbon, H2O, Organics, and Nitrogen) project in the semi-arid Manitou Experimental Forest, measurements were conducted from Mar 2010 to Feb 2011. The BEACHON site is representative of the Central Rocky Mountains montane zone and vegetation. It was chosen as it has minimal impact from nearby anthropogenic emissions and is located in a region with significant biogenic volatile organic compound (BVOC) emissions. Accordingly, the ambient submicron aerosol is expected to be dominated by organic compounds of mostly biogenic origin. The relevant CCN and aerosol composition data has been reported in Levin et al.73 and 21, from where we digitized the data points for the present analysis.

For further details on the experimental conditions and measurements of aforementioned campaigns, refer to the original studies.

Retrieval of κorg and κinorg

The following statistical procedure has been developed to obtain robust and widely representative results for κorg and κinorg:

Suitable datasets providing combined size-resolved CCN counter and AMS measurements in relevant environments were identified. The statistically largest CCN and AMS datasets were used for the retrieval. Specifically, the number of ϵorg vs κ data points n served as a criterion. Datasets with n > 100 were selected. This includes the ATTO (n = 1503), PRD (n = 410), and BEI (n = 261) data sets (see Table S2), while smaller datasets with n < 100 were omitted.

As shown by Gunthe et al.61, the AMS and CCN counter measurements are most comparable for the largest particle diameters measured at the lowest supersaturation (i.e., S~0.1%), which corresponds to accumulation mode particles serving as CCN. Note here that κ is typically size-dependent and, therefore, focussing on one particular size range can introduce some bias. At the same time, κ values are typically relatively constant across a given size mode19,59. Accordingly, the approach chosen here can be regarded as representative for accumulation mode particles as the prime source of CCN. This approach was also applied here. Note further that due to the AMS and ACSM detection limits, only data points with f_org > 0.2 were used16. The AMS time series were binned according to the time resolution of the CCN measurements, which yielded data points every 2.5–5 h, depending on the mode of operation.

For the three datasets with n > 100, the κ data was binned onto an ϵorg grid, with ϵorg increments of 0.01, and the data were averaged within each bin (see Fig. S2). The binned data from ATTO, PRD, and BEI were merged, which yielded our optimized retrieval (see Fig. S1 and Fig. S2). The binning ensures that the data across the entire ϵorg range is weighted equally and that the regression is not biased by differences in the density of the original n data points.

A bivariate linear regression fit according to Cantrell74 was applied, which takes experimental errors in ϵorg and κ into account. Note that a binning and fitting of all datasets, compared to an averaging and fitting of the binned three largest datasets only (see above), did not yield a significantly different κorg and κinorg retrieval within the range of the uncertainty. This shows that the optimized retrieval is statistically robust, independent of whether the smaller datasets are included or not. Binning all datasets with comparable counting error and averaging the binned results afterwards, however, seems to be the statistical most valid approach at this point.

Retrieval of Morg from κorg

Following the approach in Gunthe et al.16 and by interpreting κorg as an “effective Raoult parameter", we calculated an effective average molecular mass of the organic compounds (Morg) by adapting and applying the following equation from Rose et al.51

κ = (ni / ns) (Vw / Vs) = (νs Φs ρs Mw) / (ρw Ms) (6)

with n as the numbers of moles, ρ as the densities, and M as molar masses of the dry solutes (s) and pure water (w) as well as the van’t Hoff factor of the solute (is) with νs as the number of ions and Φs as the molar osmotic coefficient in aqueous solution, as follows

Morg ≈ (is Mw) / (ρw κorg) ≈ (νs Φs Morg w) / (ρorg κorg) (7)

with the is ≈ νs Φs ≈ 1, the molar density of water molecules in liquid water ρw/Mw ≈ 55 mol cm−3, assuming the surface tension of pure water75,76, and ρorg ≈ 1.4 g cm−377. Note that κ in Petters and Kreidenweis7 has been defined based on the ratio of molar volumes. In the course of this study, we use the ratio of masses, which are routinely measured in aerosol studies.

Maps and geographic information system (GIS) data

The analysis of geographic information system (GIS) data sets was conducted with the QGIS software package (version 3.12, QGIS development team, https://www.qgis.org/, last access 29 Jul 2023) using the coordinate reference of the World Geodetic System from 1984 (WGS84). The following GIS datasets have been used in this study:

Topography: The global topography data was obtained from Natural Earth (Free vector and raster map data, https://www.naturalearthdata.com, last access 29 Jul 2023).

Coastlines and country borders: coastlines and country border data were obtained from Natural Earth (Free vector and raster map data, https://www.naturalearthdata.com, last access 29 Jul 2023).

Global water bodies: Maps of global water bodies were obtained from the European Space Agency (ESA) (https://www.esa-landcover-cci.org/?q=node/162, last access: 29 Jul 2023).

ECHAM-HAM aerosol-climate model runs

We performed several model runs with the ECHAM–HAM model, version echam6.1–ham2.2–moz0.978. The model is based on the ECHAM atmospheric general circulation model39, the HAM interactive aerosol module79,80, and the trace gas chemistry module MOZ81 (the latter was disabled in these runs). Of most direct relevance to our study are the following parameterized processes contributing to warm-cloud–aerosol interactions: aerosol activation into cloud droplets according to Abdul-Razzak and Ghan82; diagnostic warm rain processes (autoconversion and accretion) according to Khairoutdinov and Kogan83; and aerosol scavenging according to Croft et al.84,85. We used the stratiform cloud scheme according to Lohmann and Roeckner86, which was extended to double-moment microphysics by Lohmann et al.87 and Lohmann and Hoose88, with the Sundqvist et al.89 critical-relative-humidity cloud cover parameterization. Thus, the model is capable, in principle, of representing both RFaci and rapid ACI adjustments. In terms of aerosol-radiation interactions, the scattering and absorption properties of the aerosol are computed in the model using Mie theory80. The scattering size parameter and volume-averaged refractive index are computed assuming an internally mixed aerosol, and taking into account the aerosol water content. Since the refractive index of aerosol water is very small—2.0⋅10−7 according to Zhang et al.80—and effects such as absorption enhancement in droplets is considered negligible, the effect of changes in κ on absorption is expected to be very small compared to the impact on scattering. The optical properties used for the radiation computation are computed using all seven modes of the aerosol module. It is noted that the results are dependent on the predicted aerosol size distribution, as the wet radii change with the κ value. Thus, the model is capable, in principle, of representing both RFari and RFaci, as well as rapid adjustments to both.

To reduce internal variability and to achieve low statistical uncertainty on the forcing components within a reasonable integration time, we used monthly varying but yearly repeating sea-surface temperature (SST) and sea ice cover (SIC) from the observed climatology and nudged the upper-level wind fields to the present-day ERA-Interim reanalysis90 wind fields of the years 1980–2015. This reduces the internal variability without over constraining the behavior of lower-tropospheric warm cloud and allow significant changes in global-mean forcing to emerge after a shorter integration time than would otherwise be required91,92. For the geographic distribution of CCN, 30-year runs (1985–2015) were required for robust patterns to emerge. Estimates of radiative forcing were computed by performing a pair of model runs with present-day SST, SIC, and wind fields, and aerosol (precursor) emissions estimates for either the year 2000 or the year 1850. Emissions were obtained from the AEROCOM-II ACCMIP dataset; anthropogenic emissions follow93.

Model runs in various configurations were conducted: with the default Lin and Leaitch94 or ref. Abdul-Razzak and Ghan82 activation scheme, no or Petersik et al.95 subgrid relative humidity variability for aerosol water uptake, and various κ settings. We estimate RFari in each configuration following Ghan96 using two runs, one with present-day (PD) emissions and one with preindustrial (PI) emissions, with a climatological annual cycle of SST and with large-scale wind fields nudged to ERA Interim reanalysis.

The original model considers the following aerosol species with their compound-specific κ: sea salt (κSS = 1.12), mineral dust (κDU = 0), black carbon (κBC = 0), primary organic aerosol (κPOA = 0.06), and sulfate (κSU = 0.60)7,80,97. Note that the model uses sulfate (SU) as a surrogate species for all inorganic ions other than sea salt and dust. The overall κ is then parameterized based on the additive mixing rule in Eq. (3). To take into account the effect of the optimized κorg and κinorg on activation and thus RFaci as well as ERF, κ had to be implemented in the Abdul-Razzak and Ghan82 activation scheme.

We evaluated the effects of changing κ of only the organic mass fraction, only the inorganic mass fraction, and both, the organic and inorganic mass fractions (see Table 1 and Table S3). The model’s sensitivity was then assessed by means of the global mean direct radiative forcing (radiative forcing due to aerosol-radiation interactions, RFari) as well as effective radiative forcing due to the entire aerosol perturbation (ERFaer), including both aerosol-radiation and aerosol-cloud interactions. As expected, the changes in both κorg (from 0.06 to 0.12) and κinorg (from 0.6 to 0.63) yield increases in magnitude of both RFari (owing to increased hygroscopic growth in the subsaturated regime) and ERFaer (which includes in addition an increase in CCN). The absolute change in ERFaer is only 0.2%, however the effect on the direct radiative effect is 10%. These changes are not very large, due to the fact that CCN concentrations are primarily determined by the aerosol number size distribution with particle chemical composition playing a secondary role42. For RFari, future measurements are needed to validate the retrieved values for subsaturated conditions.

The model is using the hygroscopicity parameter B which was translated to a hygroscopicity parameter κ as follows: From Petters and Kreidenweis7, the saturation ratio S can be expressed as a function of κ in a modified Köhler equation:

S(Dwet) = (Dwet^3 - Ds^3) / (Dwet^3 - Ds^3(1 - κ)) * exp(4σ Mw / (RT ρw Dwet)) (8)

For slightly supersaturated conditions with respect to water vapor saturation, as encountered in warm clouds, we can ~ln S = ln(1 + s) ≈ s (where s is the supersaturation), so that Eq. (8) becomes

s(D) ≈ ln((Dwet^3 - Ds^3) / (Dwet^3 - Ds^3(1 - κ))) + (4σ Mw / (RT ρw Dwet))

≈ ln(1 + (κ Ds^3) / (Dwet^3 - Ds^3)) + (4σ Mw / (RT ρw Dwet))

≈ (κ Ds^3) / (Dwet^3 - Ds^3) + (4σ Mw / (RT ρw Dwet)) (9)

≈ κ (Ds^3 / Dwet^3) + (4σ Mw / (RT ρw Dwet))

with the first term being the solute term, describing the Raoult effect, and the second term the curvature term for the Kelvin effect. Under conditions for which the ~s ≪ 1 and D3 ≪ D3wet hold, B = κ.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "The authors have used data from a number of field campaigns spanning a wide variety of site types (urban, forested, coastal, among others). They show that observed overall hygroscopicities can be recovered via a simple 2-component linear mixing rule, combining an averaged inorganic k_inorg = 0.63 with an averaged organic k_org = 0.12, weighted by their mass fractions. Further, they have conducted estimates of the perturbations to direct and indirect radiative forcings, modifying the assumed component hygroscopicities. The authors conclude that forcing predictions, on a global scale, are not very sensitive to the exact choice of organic component hygroscopicity, and suggest this finding can be used to focus ongoing research toward more sensitive factors in order to reduce remaining uncertainties.\n\nThe paper is interesting and makes good use of data from past studies to present them in a new way. I think there will be interest in this topic, especially from those outside the aerosol-cloud interaction community. The paper also aims to provide specific recommendations for future directions, and these will likely generate numerous additional citations.\n\nI recommend that this manuscript be accepted for publication, but suggest that the authors modify / qualify their helpful recommendations, as I explain below in Major Comments. I also offer some other comments for their consideration.\n\nMajor Comments\n\nThe paper argues that “the aerosol hygroscopicity is of major importance for the atmospheric radiative budget.” This is certainly true for direct radiative effects, which are sensitive to relative humidity (RH) and to the representation of the response of aerosol water contents to changing RH. It is also argued, quite reasonably, that further refining the precise hygroscopicity of the complex mixtures of organic species typically comprising the atmospheric aerosol is less important than other factors. The final statement is:\n\n“Instead, more effort should be dedicated to correctly understand and represent the processes determining the abundance of the organics in the atmospheric multiphase systems and their representation in models, where the largest uncertainties are located in order to better predict the remaining important effects of particle organics [on radiative forcing] as good as possible.”\n\nWith respect to the effects of composition on CCN concentrations, and hence on the simulated indirect forcings, the statement of the importance of the aerosol hygrosopicity seems to contradict the last line of the first paragraph:\n\n“The sensitivity of global climate forcing to changes in k_org and k_inorg is small, which constrains a critically important aspect of global climate modelling.”\n\nTo avoid possible confusion, I suggest that differences between direct and indirect forcing calculations be made more explicit, as follows.\n\nFor indirect forcing / CCN concentration predictions: I agree with the observation that overall, the sensitivity to aerosol composition (outside of extremes) should be small. Of the three factors (other than temperature) that control the CCN spectrum, namely total number concentration, particle size, and particle hygroscopicity, the sensitivity to number is easily the largest. Further, the simplified Kohler relationship between critical supersaturation and aerosol properties shows that the critical supersaturation varies with particle size to the -3/2 power, but hygroscopicity only to the -1/2 power. The authors also note these factors in the methods, on page 14, lines 24-25, citing Dusek et al. (2006). Hence the exact value of hygroscopicity is generally the least important determinant of CCN activity, and the results in Figure 2B, which show close to zero changes in simulated CCN active at 0.3% supersaturation, are not surprising. I think it would be helpful to make the total sensitivities clear and to include these other factors when discussion the recommendations for future work to constrain indirect forcing.\n\nThe above discussion clarifies why, in the simulations, the results shown in Figure 2C indicate that in all locations the sensitivity of the indirect forcing to changes in hygroscopicity is small. This because the CCN spectrum that is input to the model at each grid point does not change that much when only hygroscopicity is modified over a relatively small range, if all other more sensitive factors (total number concentrations and aerosol size distributions) are the same.\n\nFor direct forcing: In contrast, there are larger local changes in direct forcing due to hygroscopicity changes, as discussed for Figure 2D. I interpret this finding to emerge because, especially for times and locations with relatively high humidity (RH > 85%), the increase in hygroscopic growth from increasing the hygroscopicity of both components, leads directly to an increase in total aerosol-phase mass, thus increasing AOD even in the absence of a change in mass scattering efficiency. In other words: the response in total light scattering (or AOD) to an increase in hygroscopicity is much more direct, than is the response of CCN concentrations to the same factor.\n\nIt’s not entirely clear how the model handles the direct forcing calculation; I assume that a new mass scattering efficiency is also selected due to the change in wet particle diameter with a more hygroscopic aerosol. However, as long as the size distribution initially peaks near its most-effective diameters, the variation in mass scattering efficiency should be relatively small. Regions in Figure 2D with positive sensitivities are therefore somewhat curious (do those contradict the statement on page 2, line 8?) Any dependence on mass scattering efficiency will highlight the importance of simulating the aerosol size distribution accurately for accurate direct forcing estimates. As for the most important factors to resolve for direct forcing, I would strongly concur with the concluding statement recommending attention to the accurate simulation of total aerosol-phase mass, as it directly multiplies the mass scattering efficiency.\n\nIf the authors agree with the above interpretations of Figure 2, I believe it would be helpful to provide some of these additional interpretations in the main text, and to write separate conclusions and recommendations for the direct and indirect forcings.\n\nOther comments\n\n1. The title refers to “radiative forcing” in general but the introduction and data focus on CCN observations. As noted above, calculations are presented for both the direct (subsaturated) and indirect (CCN-related) forcings. I think it would be helpful to distinguish the direct and indirect cases more clearly. Also, I think only contributions from non-absorbing species are considered here. There remain significant uncertainties in estimating aerosol absorption and its role in radiative forcing, so it might be prudent to mention that here.\n\n2. Page 2, line 8: Particles of the same size but higher hygroscopicity act more readily as CCN (need to point out role of size here).\n\n3. Page 2, line 26: for work on resolving the value of k_org based on organic compound characteristics, please include this reference:\nPetters, SS, D Pagonis, MS Claflin, EJT Levin, MD Petters, PJ Ziemann, SM Kreidenweis, Hygroscopicity of organic compounds as a function of carbon chain length, carboxyl, hydroperoxy, and carbonyl functional groups, J. Phys. Chem. A, 2017, 121(27), 5164-5174; doi 10.1021/acs.jpca.7b04114.\n\n4. Page 3, equation 4: This assumes that the inorganic component is composed solely of hygroscopic salts. There are often mineral components and elemental carbon, which are not detected by the AMS. Therefore this equation is an approximation, and in general, the presence of non- or weakly-hygroscopic compounds as minor constituents is probably subsumed into the deduced value of k_org and/or k_inorg. This equation merits some additional explanation of the assumptions inherent here, including the upper limit on aerosol size that is imposed by the AMS, and the next point below.\n\n5. As noted in several places in the manuscript, the use of mass fraction instead of volume fraction to weight water contents is an approximation, compared with the ZSR rule that is typically invoked. It is argued that the difference is small. For the densities assumed here, that is true for high mass fractions of organics (e_org > 0.75). For lower mass fractions, down to their limit of e_org > 0.2, the differences can be as large as 15% with the volume fractions larger than the corresponding mass faction, since the organic is less dense. Using mass fraction as the independent variable for a linear fit has, I believe, the effect of predicting slightly lower k_inorg (possibly suggested in Figure 1C?), which may partially compensate for nonhygroscopic components that are not explicitly included in the mixing rule.\n\n6. Page 3, lines 22-26: the authors pose two questions. Question 1 could be phrased more explicitly, that is, “Is there a pair of robust k_org and k_inorg values that is globally representative of aerosol water contents, above and below water saturation?” In Question 2, does “radiative forcing” only mean direct radiative forcing? If both direct and indirect, please specify more clearly.\n\n7. Bottom of page 3, and comprising the description of how k was retrieved, as well as Methods on page 9, lines 10-15: It seems like there is something missing in the description that may make this misleading to those from other communities. It is stated that AMS and CCN counter measurements were needed for the regression (e.g., page 9, line 17; page 12, line 24). However, neither of these is a measurement of kappa; additional data or methodologies are needed, most likely size distributions that can be used to derive effective kappas, or a size-resolved CCN measurement, which I believe is what was used here. Gunthe et al (2011), cited herein, use size-resolved CCN spectra to obtain paired supersaturations and activation diameters, from which effective hygroscopicities could be deduced. It is also possible to measure total CCN at a particular supersaturation and also the total aerosol size distribution, assume that the largest particles activate first, and estimate an activation diameter in this way in order to compute the effective hygroscopicity. In the methods on page 9, the operation of the CCN counter is not asa a size-resolved measurement. If the Gunthe et al. approach was used for all the data sets, then please make this clear in the description on page 9, and also note that this requires an experimental setup that is different than simply operating a CCN counter to obtain total activated particles as a function of supersaturation, which is implied here.\n\n8. Page 5, line 15 and following: It is argued why the method works even though dust and sea salt are not represented in the AMS data. This is likely a result of the upper size limit of the AMS, since it has been shown that sea spray composition varies strongly with size. This size dependence is implied with the statement “accounts for most of the CCN”. Further, Table S2 explains the sizes that the data are specific to, which also limits the expected composition.\n\n9. Page 6, lines 4-5: Note that for organic compounds, it has frequently been documented that the hygroscopicity measured above water saturation – that is, deduced from observed CCN activity – is higher than that observed in the subsaturated regime, i.e., deduced from light scattering or HTDMA data. The authors should note this as a caveat to their methodology, in that the derived k_org is likely an upper estimate when used for direct forcing calculations. As seen in Table 1, the global mean value for direct effects is barely changed even with the higher k_org, but this may affect conclusions around local effects (Figure 2D). The authors could perhaps show, in the Supplement, the equivalents of Figure 2D for the second and third cases in Table 1 to address this possibility.\n\n10. Page 8, lines 12-14: the hygroscopicity of the inorganic components (when measured ions are interpreted as various salts, but excluding sodium compounds which are also excluded herein) does not vary that much, which is also stated on page 3, line 20.\n\n11. Just an observation: For a nonabsorbing aerosol, as assumed here, simulation of the size distribution can be an important factor, in order to select an appropriate mass scattering efficiency. Composition also plays a significant role, of course. Interestingly, prior work showed that the ZSR mixing rule (the basis for the kappa mixing rule) also applies to scattering calculations and the efficiency curves could be weighted by the composition. Also interestingly, depending on how the calculation is set up, there is less dependence on the degree of neutralization of sulfate than might be expected. This is because the lower hygroscopicity of fully neutralized sulfate is balanced by the additional ammonium mass, while the lower ammonium mass per sulfate ion in bisulfate is compensated by the higher water content; variation in refractive index between those cases is a minor factor.\n\n12. If you would like to add a North American continental site, the following publication also used AMS and size-resolved CCN data in a two-component model to draw a similar conclusion (k_org = 0.13, assuming k_inorg=0.6):\nLevin, E. J. T., Prenni, A. J., Palm, B. B., Day, D. A., Campuzano-Jost, P., Winkler, P. M., Kreidenweis, S. M., DeMott, P. J., Jimenez, J. L., and Smith, J. N.: Size-resolved aerosol composition and its link to hygroscopicity at a forested site in Colorado, Atmos. Chem. Phys., 14, 2657–2667, https://doi.org/10.5194/acp-14-2657-2014, 2014.\n\nReview prepared by Sonia Kreidenweis", "reviewer_2": "Please see the attached Word document for the detailed review comments."}, "author_response": "Responses to the review of the manuscript “Global organic and inorganic aerosol hygroscopicity and its effect on radiative forcing”, by Pöhlker et al., submitted for publication in Nature Communications\n\nDear editor, we would like to thank you and both referees for the valuable comments and useful suggestions to improve our manuscript. Below, you will find our responses to the individual comments of the referees along with a description of changes that we did in the manuscript. We have used the following color code:\n• Black: the referee’s comments.\n• Blue: the authors’ responses.\n• Red: Quotes from the original manuscript.\n• Red & italic: Text modifications in the manuscript related to the referee comments.\n\nResponses to Referee #1 (Sonia Kreidenweis)\n\nThe authors have used data from a number of field campaigns spanning a wide variety of site types (urban, forested, coastal, among others). They show that observed overall hygroscopicities can be recovered via a simple 2-component linear mixing rule, combining an averaged inorganic k_inorg = 0.63 with an averaged organic k_org = 0.12, weighted by their mass fractions. Further, they have conducted estimates of the perturbations to direct and indirect radiative forcings, modifying the assumed component hygroscopicities. The authors conclude that forcing predictions, on a global scale, are not very sensitive to the exact choice of organic component hygroscopicity, and suggest this finding can be used to focus ongoing research toward more sensitive factors in order to reduce remaining uncertainties.\n\nThe paper is interesting and makes good use of data from past studies to present them in a new way. I think there will be interest in this topic, especially from those outside the aerosol-cloud interaction community. The paper also aims to provide specific recommendations for future directions, and these will likely generate numerous additional citations.\n\nI recommend that this manuscript be accepted for publication, but suggest that the authors modify / qualify their helpful recommendations, as I explain below in Major Comments. I also offer some other comments for their consideration.\n\nWe appreciate the positive evaluation and the valuable comments by referee #1. The specific comments are addressed below in detail.\n\nMajor Comments\n\n[R1.1] The paper argues that “the aerosol hygroscopicity is of major importance for the atmospheric radiative budget.” This is certainly true for direct radiative effects, which are sensitive to relative humidity (RH) and to the representation of the response of aerosol water contents to changing RH. It is also argued, quite reasonably, that further refining the precise hygroscopicity of the complex mixtures of organic species typically comprising the atmospheric aerosol is less important than other factors. The final statement is:\n\n“Instead, more effort should be dedicated to correctly understand and represent the processes determining the abundance of the organics in the atmospheric multiphase systems and their representation in models, where the largest uncertainties are located in order to better predict the remaining important effects of particle organics [on radiative forcing] as good as possible.”\n\nWith respect to the effects of composition on CCN concentrations, and hence on the simulated indirect forcings, the statement of the importance of the aerosol hygrosopicity seems to contradict the last line of the first paragraph:\n\n“The sensitivity of global climate forcing to changes in k_org and k_inorg is small, which constrains a critically important aspect of global climate modelling.”\n\n[A1.1a] We improved the last statement of the abstract as shown below and hope that this clarifies this issue.\n\n“By showing that the sensitivity of global climate forcing to changes in k_org and k_inorg is small, we constrain a critically important aspect of global climate modelling.”\n\nTo avoid possible confusion, I suggest that differences between direct and indirect forcing calculations be made more explicit, as follows.\n\nFor indirect forcing / CCN concentration predictions: I agree with the observation that overall, the sensitivity to aerosol composition (outside of extremes) should be small. Of the three factors (other than temperature) that control the CCN spectrum, namely total number concentration, particle size, and particle hygroscopicity, the sensitivity to number is easily the largest. Further, the simplified Kohler relationship between critical supersaturation and aerosol properties shows that the critical supersaturation varies with particle size to the -3/2 power, but hygroscopicity only to the -1/2 power. The authors also note these factors in the methods, on page 14, lines 24-25, citing Dusek et al. (2006). Hence the exact value of hygroscopicity is generally the least important determinant of CCN activity, and the results in Figure 2B, which show close to zero changes in simulated CCN active at 0.3% supersaturation, are not surprising. I think it would be helpful to make the total sensitivities clear and to include these other factors when discussion the recommendations for future work to constrain indirect forcing.\n\nThe above discussion clarifies why, in the simulations, the results shown in Figure 2C indicate that in all locations the sensitivity of the indirect forcing to changes in hygroscopicity is small. This because the CCN spectrum that is input to the model at each grid point does not change that much when only hygroscopicity is modified over a relatively small range, if all other more sensitive factors (total number concentrations and aerosol size distributions) are the same.\n\nFor direct forcing: In contrast, there are larger local changes in direct forcing due to hygroscopicity changes, as discussed for Figure 2D. I interpret this finding to emerge because, especially for times and locations with relatively high humidity (RH > 85%), the increase in hygroscopic growth from increasing the hygroscopicity of both components, leads directly to an increase in total aerosol-phase mass, thus increasing AOD even in the absence of a change in mass scattering efficiency. In other words: the response in total light scattering (or AOD) to an increase in hygroscopicity is much more direct, than is the response of CCN concentrations to the same factor.\n\n[A1.1b] Thanks for these helpful comments and valuable suggestions. We have modified the entire paragraph on page 6 to make the differences between direct and indirect forcing more explicit. We have implemented the thoughts and arguments as follows:\n\n“In principle, the aerosol effects through ari and aci could be treated approximately additively, which allows to retrieve RFaci as ERFaer − RFari from Table 1. We refrain from reporting these values here, however, as this approach does not account for the various adjustments in the system upon ari or aci changes and also cannot be obtained directly from the model. In terms of aci, the replacement of κ yields the geographic distributions of the changes in CCN concentrations (∆N ) and in the effective CCN radiative forcing (∆ERF ) shown in Fig. 2B and C. These changes in ∆N and ∆ERF are SW CCN SW comparatively small, which is not surprising since out of the aerosol-related factors that control the CCN spectrum – which are total number concentration, particle size, and particle hygroscopicity – the sensitivity to number is the largest. Moreover, the simplified Köhler equation (Eq. 9) underlines that the exact value of κ is generally the least important determinant of CCN activity as S varies with D to the power of three and just linearly with κ. The largest ∆NCCN and ∆ERFSW values observed in Fig. 2B and C were found in regions with a high organic aerosol burden and corresponding values (filtered for high OC) of ∆RFari=−0.049Wm−2 and ∆ERFaer=−0.149Wm−2 are higher than the global mean values (Table S4). In terms of ari, in contrast, larger local changes were observed as shown in Fig. 2D (shown here as a quantified sensitivity introduced below). This can be interpreted to emerge because, especially for times and locations with relatively high humidity (i.e., RH > 85 %), the increase in hygroscopic growth from increases in κorg and κinorg, leads directly to an increase in total aerosol-phase mass, thus increasing the aerosol optical depth (AOD) even in the absence of a change in mass scattering efficiency. In essence, Fig. 2 illustrates that the response in total light scattering, and therefore ari, to an increase in κ is much more direct, than the response of CCN concentrations, and aci, to the same factor.\n\n[R1.2] It’s not entirely clear how the model handles the direct forcing calculation; I assume that a new mass scattering efficiency is also selected due to the change in wet particle diameter with a more hygroscopic aerosol. However, as long as the size distribution initially peaks near its most-effective diameters, the variation in mass scattering efficiency should be relatively small. Regions in Figure 2D with positive sensitivities are therefore somewhat curious (do those contradict the statement on page 2, line 8? “First, more hygroscopic aerosol particles grow to larger diameters at relative humidity <100 %, leading to a greater scattering cross section and thus stronger radiative forcing by aerosol-radiation interactions (RFari).”). Any dependence on mass scattering efficiency will highlight the importance of simulating the aerosol size distribution accurately for accurate direct forcing estimates. As for the most important factors to resolve for direct forcing, I would strongly concur with the concluding statement recommending attention to the accurate simulation of total aerosol-phase mass, as it directly multiplies the mass scattering efficiency. If the authors agree with the above interpretations of Figure 2, I believe it would be helpful to provide some of these additional interpretations in the main text, and to write separate conclusions and recommendations for the direct and indirect forcings.\n\n[A1.2] The way the radiative effect of aerosols is computed in the model indeed has been described too superficially. We added the relevant information in the supplemental section \"ECHAM-HAM aerosol-climate model runs\" for better clarification as follows:\n\n“In terms of aerosol-radiation interactions, the scattering and absorption properties of the aerosol are computed in the model using Mie theory (Zhang et al., 2012). The scattering size parameter and volume-averaged refractive index are computed assuming internally mixed aerosol, and taking into account the aerosol water content. With this, both aspects of aerosol-radiation interactions may be affected. The optical properties used for the radiation computation are computed using all seven modes of the aerosol module. It is noted that the results are dependent on the predicted aerosol size distribution, as the wet radii change with the k value. Thus, the model is capable, in principle, of representing both RFari and RFaci, as well as rapid adjustments to both.”\n\nSo the reviewer is completely right, that the mass scattering efficiency changes, since the aerosol water content is altered. As for the regions with positive values in Fig. 2D, we believe these to be due to weather noise, rather than to be a clear signal. The following sentence on this has been inserted into the revised manuscript on page 8:\n\n“Figure 2D also shows some regions with positive values, but the pattern structure suggests that these are due to weather noise.”\n\nOther comments\n\n[R1.3] The title refers to “radiative forcing” in general but the introduction and data focus on CCN observations. As noted above, calculations are presented for both the direct (subsaturated) and indirect (CCN-related) forcings. I think it would be helpful to distinguish the direct and indirect cases more clearly. Also, I think only contributions from non-absorbing species are considered here. There remain significant uncertainties in estimating aerosol absorption and its role in radiative forcing, so it might be prudent to mention that here.\n\n[A1.3] The reviewer is right, we look into both, direct and indirect radiative forcings. However, with our method it is only possible to separate direct radiative forcing, and total effective radiative forcing. The indirect radiative forcing cannot be singled out. One might assume that the semi-direct effect (adjustments to aerosol-radiation interactions in the IPCC nomenclature) is small, and so assume the total ERF minus the RFari is the ERFaci. But since we report all numbers we can obtain, we think we did as best as we could.\n\nWe consider both absorbing and non-absorbing species, but the impact of altered aerosol water uptake on the scattering is much larger than the one on absorption. This is now clarified in the model description on page 15 in the supplement through the following statement:\n\n“Since the refractive index of aerosol water is very small - 2.0·10-7 according to Zhang et al., 2012 - and effects such as absorption enhancement in droplets is considered negligible, the effect of changes in κ on absorption is expected to be very small compared to the impact on scattering.”\n\n[R1.4] Page 2, line 8: Particles of the same size but higher hygroscopicity act more readily as CCN (need to point out role of size here).\n\n[A1.4] Thanks. We modified the sentence as suggested to avoid confusion. It reads now as follow:\n\n“Second, particles of the same size but higher hygroscopicity act more readily as cloud condensation nuclei (CCN), which activate into cloud droplets, leading to a larger cloud droplet number, longer-lived clouds and stronger forcing by aerosol--cloud interactions (RFaci), and, together with the cloud adjustments, this entails a stronger ERFaer.”\n\n[R1.5] Page 2, line 26: for work on resolving the value of k_org based on organic compound characteristics, please include this reference:\nPetters, SS, D Pagonis, MS Claflin, EJT Levin, MD Petters, PJ Ziemann, SM Kreidenweis, Hygroscopicity of organic compounds as a function of carbon chain length, carboxyl, hydroperoxy, and carbonyl functional groups, J. Phys. Chem. A, 2017, 121(27), 5164-5174; doi 10.1021/acs.jpca.7b04114.\n\n[A1.5] We have included the reference as suggested.\n\n[R1.6] Page 3, equation 4: This assumes that the inorganic component is composed solely of hygroscopic salts. There are often mineral components and elemental carbon, which are not detected by the AMS. Therefore this equation is an approximation, and in general, the presence of non- or weakly-hygroscopic compounds as minor constituents is probably subsumed into the deduced value of k_org and/or k_inorg. This equation merits some additional explanation of the assumptions inherent here, including the upper limit on aerosol size that is imposed by the AMS, and the next point below.\n\n[A1.6a] We have modified the corresponding statements as suggested to make the inherent assumptions transparent by adding the following statement:\n\n“Note that Eq. 4 is an approximation and assumes that the inorganic component is composed solely of hygroscopic salts. As mineral components and elemental carbon are not detected by the AMS, the presence of non- or weakly-hygroscopic compounds as minor constituents is subsumed into the deduced value of k_org and/or k_inorg. The upper limit of AMS measurements (i.e., 50 % transmission) and therefore the data used in Eq. 4 is typically ~600 nm (Liu et al., 2007). Further, Eq. 3 is based on volume fractions, whereas Eq. 4 uses mass fractions instead, which is an approximation. It is justified here as the densities, ρ, are sufficiently similar (i.e., ρ = 1.77 g cm-3, ρ = 1.72 g cm-3, (NH4)2SO42− NH4NO3 ρ = 1.4 g cm-3 (17)), especially for high ε (i.e., > 0.75). For lower ε (i.e., ≈ 0.25), however, org,average org org the difference between volume and mass fractions can be up to 15 % (with volume fractions being larger), which has to be considered in the interpretation of the results.”\n\nPage 5 lines 29-30 the authors write, “the assumption of an internally mixed aerosol as an average of the global composition is justified (31).”\n\n[A1.6b] Please refer to [R2.4] and [A2.4], where the aspect of the aerosol mixing state has been addressed in detail.\n\n[R1.7] As noted in several places in the manuscript, the use of mass fraction instead of volume fraction to weight water contents is an approximation, compared with the ZSR rule that is typically invoked. It is argued that the difference is small. For the densities assumed here, that is true for high mass fractions of organics (e_org > 0.75). For lower mass fractions, down to their limit of e_org > 0.2, the differences can be as large as 15% with the volume fractions larger than the corresponding mass faction, since the organic is less dense. Using mass fraction as the independent variable for a linear fit has, I believe, the effect of predicting slightly lower k_inorg (possibly suggested in Figure 1C?), which may partially compensate for nonhygroscopic components that are not explicitly included in the mixing rule.\n\n[A1.7] We appreciate this comment and implemented this thought on page 3, line 8ff, as outlined in the course of our response [A1.6].\n\n[R1.8] Page 3, lines 22-26: the authors pose two questions. Question 1 could be phrased more explicitly, that is, “Is there a pair of robust k_org and k_inorg values that is globally representative of aerosol water contents, above and below water saturation?” In Question 2, does “radiative forcing” only mean direct radiative forcing? If both direct and indirect, please specify more clearly.\n\n[A1.8] We thank the referee for the good advice.\n\nWe have changed question 1 from “Is there a pair of robust κ and κ values that is globally org inorg representative and, thus, a suitable choice for general application in aerosol–climate models?” to “Is there a pair of robust κ and κ values that is globally representative of aerosol water contents, org inorg above and below water saturation and, thus, a suitable choice for general application in aerosol–climate models?”.\n\nThe second question was changed from “How sensitive are the model predictions in terms of CCN concentrations and radiative forcing to the choice of robust κ and κ ?” to “How sensitive are the org inorg model predictions in terms of CCN concentrations as well as direct and indirect radiative forcing to the choice of robust κ and κ ?”.\norg inorg\n\n[R1.9] Bottom of page 3, and comprising the description of how k was retrieved, as well as Methods on page 9, lines 10-15: It seems like there is something missing in the description that may make this misleading to those from other communities. It is stated that AMS and CCN counter measurements were needed for the regression (e.g., page 9, line 17; page 12, line 24). However, neither of these is a measurement of kappa; additional data or methodologies are needed, most likely size distributions that can be used to derive effective kappas, or a size-resolved CCN measurement, which I believe is what was used here. Gunthe et al (2011), cited herein, use size-resolved CCN spectra to obtain paired supersaturations and activation diameters, from which effective hygroscopicities could be deduced. It is also possible to measure total CCN at a particular supersaturation and also the total aerosol size distribution, assume that the largest particles activate first, and estimate an activation diameter in this way in order to compute the effective hygroscopicity. In the methods on page 9, the operation of the CCN counter is not asa a size-resolved measurement. If the Gunthe et al. approach was used for all the data sets, then please make this clear in the description on page 9, and also note that this requires an experimental setup that is different than simply operating a CCN counter to obtain total activated particles as a function of supersaturation, which is implied here.\n\n[A1.9] We agree – the description is incomplete and misleading here. We modified that statement on page 3:\n\n“First, we conducted a systematic retrieval of κ by merging extensive data sets from AMS and CCN counters obtained in contrasting environments (Fig. 1A) to calculate a pair of broadly representative κ and κ values.”\norg inorg\n\nas follows\n\n“First, we conducted a systematic retrieval of κ by merging extensive data sets from AMS and size-resolved CCN measurements obtained in contrasting environments (Fig. 1A) to calculate a pair of broadly representative κ and κ values.”\norg inorg\n\nOn page 9, lines 10 to 15, it is actually mentioned that the CCN measurements were conducted in size-resolved mode. Nevertheless we modified the text to emphasize this aspect even more, as we agree with the referee that this should be concisely stated. The original text on page 5:\n\n“The aerosol mass spectrometric (AMS) and size-resolved CCN data used in this study were obtained from the field studies listed below. […]. CCN concentrations in the studies were measured with a continuous-flow streamwise thermal gradient CCN counter (CCNC, models CCN-100 or CCN-200, DMT, Longmont, CO, USA). In the instrument, the supersaturation (S) was cycled through different S values, typically between 0.1 and 1.1 %, defined by controlled temperature gradients inside the CCNC column. Particles with a critical supersaturation S > S in the column are activated and form water droplets. Droplets with diameters larger 1 µm are detected by an optical particle counter (OPC) at the exit of the column. Further information on the CCN measurements and instrumentation can be found elsewhere (refs).”\n\nwas modified as follows\n\n“The aerosol mass spectrometric (AMS) and size-resolved CCN data used in this study were obtained from the field studies listed below. […]. CCN concentrations in the studies were measured with a continuous-flow streamwise thermal gradient CCN counter (CCNC, models CCN-100 or CCN-200, DMT, Longmont, CO, USA). In the instrument, the supersaturation (S) was cycled through different S values, typically between 0.1 and 1.1 %, defined by controlled temperature gradients inside the CCNC column. Particles with a critical supersaturation S > S in the column are activated and form water droplets. Droplets with diameters larger 1 µm are detected by an optical particle counter (OPC) at the exit of the column. Further information on the CCN measurements and instrumentation can be found elsewhere (refs). Note that the CCN measurements were conducted in size-resolved mode, which is one established approach to retrieve κ, as outlined in detail elsewhere (refs). This applies to all three main data sets used here for the κ and κ retrieval (i.e., ATTO, PRIDE-PRD-2006, and CARE-Beijing-org inorg 2006, shown in Fig. 1B) as well as for most of data sets from previous field studies outlined below.”\n\n[R1.10] Page 5, line 15 and following: It is argued why the method works even though dust and sea salt are not represented in the AMS data. This is likely a result of the upper size limit of the AMS, since it has been shown that sea spray composition varies strongly with size. This size dependence is implied with the statement “accounts for most of the CCN”. Further, Table S2 explains the sizes that the data are specific to, which also limits the expected composition.\n\n[A1.10] Thank you for pointing this out. We implemented this thought into the text on page 5 as follows:\n\n“Note here that sea salt and mineral dust aerosol populations typically reach far into the supermicron size range, which implies that the AMS measurement with its upper cut-off size at about 600 nm (50 % transmission) excludes significant parts of both aerosol components.”\n\n[R1.11] Page 6, lines 4-5 on statement “Changes in the aerosol hygroscopicity affect the growth of the particles in the subsaturated regime and therefore RFari as well as their activation to cloud droplets under supersaturated conditions and therefore RFaci.”: Note that for organic compounds, it has frequently been documented that the hygroscopicity measured above water saturation – that is, deduced from observed CCN activity – is higher than that observed in the subsaturated regime, i.e., deduced from light scattering or HTDMA data. The authors should note this as a caveat to their methodology, in that the derived k_org is likely an upper estimate when used for direct forcing calculations. As seen in Table 1, the global mean value for direct effects is barely changed even with the higher k_org, but this may affect conclusions around local effects (Figure 2D). The authors could perhaps show, in the Supplement, the equivalents of Figure 2D for the second and third cases in Table 1 to address this possibility.\n\n[A1.11] Important aspect – thanks for pointing this out. We clarified the text here by adding the following statement on page 8:\n\n“Previous studies documented for organic compounds that the hygroscopicity measured above water saturation, as deduced from observed CCN activity, is higher than that observed in the subsaturated regime, as deduced from light scattering or hygroscopic tandem differential mobility analyser (HTDMA) data (Zheng et al., 2020; Mikhailov et al., 2021). This means that the κ derived here from org CCN activity is likely an upper estimate when used for direct forcing calculations. Albeit, Table 1 suggests that the Δκ between super- and subsaturated retrievals barely changes the global mean direct effects, it is still worth noting as it might affect conclusions on local effects as indicated by Fig. 2D.”\n\nZheng et al., Long-range transported North American wildfire aerosols observed in marine boundary layer of eastern North Atlantic, Environment International, 139, 2020.\n\nMikhailov et al., Water uptake of subpollen aerosol particles: hygroscopic growth, cloud condensation nuclei activation, and liquid–liquid phase separation, Atm. Chem. Phys, 21, 2021.\n\n[R1.12] Page 8, lines 12-14 on statement “Second, the higher sensitivity of the model to changes in κ relative to changes κ stresses the importance of a correct representation of the abundance and inorg org hygroscopicity of the small number of relevant inorganic aerosol components (i.e., sulfates, nitrates, ammonium) in the models.”: the hygroscopicity of the inorganic components (when measured ions are interpreted as various salts, but excluding sodium compounds which are also excluded herein) does not vary that much, which is also stated on page 3, line 20 “These campaign-specific results show a larger range in κ ranging from 0.06 to 0.19 than for κ , ranging from 0.63 to 0.71 […]”.\norg inorg\n\n[A1.12] Referee 2 indicated in [R2.7] that not all numbers in Table 2 were updated appropriately, after more previous field campaigns were taken into account. We have corrected Table 2 – see [A2.7] – and the range of κ from previous campaigns is now 0.46 to 0.71, which is comparatively wide.\ninorg\n\nAccordingly, the aforementioned statement seems still appropriate.\n\n[R1.13] Just an observation: For a nonabsorbing aerosol, as assumed here, simulation of the size distribution can be an important factor, in order to select an appropriate mass scattering efficiency. Composition also plays a significant role, of course. Interestingly, prior work showed that the ZSR mixing rule (the basis for the kappa mixing rule) also applies to scattering calculations and the efficiency curves could be weighted by the composition. Also interestingly, depending on how the calculation is set up, there is less dependence on the degree of neutralization of sulfate than might be expected. This is because the lower hygroscopicity of fully neutralized sulfate is balanced by the additional ammonium mass, while the lower ammonium mass per sulfate ion in bisulfate is compensated by the higher water content; variation in refractive index between those cases is a minor factor.\n\n[A1.13] Thanks for this observation – interesting indeed and probably a starting point for a follow-up study.\n\n[R1.14] If you would like to add a North American continental site, the following publication also used AMS and size-resolved CCN data in a two-component model to draw a similar conclusion (k_org = 0.13, assuming k_inorg=0.6):\nLevin, E. J. T., Prenni, A. J., Palm, B. B., Day, D. A., Campuzano-Jost, P., Winkler, P. M., Kreidenweis, S. M., DeMott, P. J., Jimenez, J. L., and Smith, J. N.: Size-resolved aerosol composition and its link to hygroscopicity at a forested site in Colorado, Atmos. Chem. Phys., 14, 2657–2667, https://doi.org/10.5194/acp-14-2657-2014, 2014.\n\n[A1.14] Thank you for this hint. We have included the study into the manuscript:\n- The relevant references were included in several places in the manuscript:\nLevin et al.: An annual cycle of size-resolved aerosol hygroscopicity at a forested site\no in Colorado, J. Geophys. Res., 117, D06201, 2012.\nLevin et al.: Size-resolved aerosol composition and its link to hygroscopicity at a\no forested site in Colorado, Atm. Chem. Phys., 14, 2657-2667, 2014.\n- The North American data set was added to Fig. 1C. The revised figure is shown below.\n- A short description of the North American data set was added to the method section.\n- Table S2 was updated in the supplementary information was updated.\n- The new data set was also added to Fig. S5:\n\nResponses to Referee #2\n\nIn this manuscript two globally representative average values of κorg and κinorg are retrieved through a bivariate linear regression fit of extensive data sets of εorg and κ from 15 field sites worldwide. The effective aerosol hygroscopicity (κ) is derived via global CCN measurement using a continuous-flow streamwise thermal gradient CCN counter, and the organic mass fraction (εorg) is measured by aerosol mass spectrometers (AMS). The authors also investigate the sensitivity of radiative forcing to this pair values in the ECHAM-HAM aerosol-climate model, and conclude the sensitivity is small. Overall, this is a well written study, and the main results are clearly presented and discussed. I enjoyed reading this article and I think this manuscript will be appealing to modelers interested in aerosol-climate modelling. As such I believe this manuscript is well suited to Nature Communications, and I kindly ask the authors to carefully address (or consider) minor comments below before final publication.\n\nMinor comments\n\n[R2.1] One of the main contributions of this study is performing the retrieval of global representative κorg and κinorg values. Can the authors further clarify the following questions about it? a) In Figure 1B, the linear regression is only based on data sets of three sites (i.e., Amazon, Beijing, and Guangzhou). Is it more suitable to do a retrieval by using more data from other sites that are included in Figure 1C? On page 12 lines 25-28, the authors list the sample size as one criterion for choosing the retrieval sample. We may lose representative data sets from other sites based on this criterion.\n\n[A2.1] Many thanks for this comment. The criteria to include a data set into the retrieval are quite strict indeed. We decided to include only size-resolved CCN datasets with more than 100 data points, because smaller data sets might be strongly affected by outliers. The three data sets included are characterized by long-term measurements and a variability of the relevant parameters over a wide ε range, which org are both important conditions to obtain statistically robust bivariate regression fits as outlined below. Furthermore, we also conducted the retrieval with all data sets and found that the results did not change significantly.\n\nb) Further, the number of ATTO data points is much larger than those of the other two sites, does this mean the data represent more remote rain forest? This influence looks more obvious when we check details in Table S3. A merged κorg is 0.12 ± 0.02, which is close to κorg = 0.13 ± 0.02 at ATTO but almost twice as κorg =0.06 ± 0.03 and 0.07 ± 0.03 at PRD and BEI, respectively.\n\nThe methods section on page 13 explains how the data was handled:\n\n“For the three data sets with n > 100, the κ data was binned onto an ε grid, with ε increments of org org 0.01, and the data were averaged within each bin (see Fig. S4). The binned data from ATTO, PRD, and BEI were merged, which yielded our optimized retrieval (see Fig. S4 and Fig. S3). The binning ensures that the data across the entire ε range is weighted equally and that the regression is not biased by org differences in the density of the original n data points.”\n\nBy binning the three data sets individually, the influence of different sample size is cancelled.\n\nThe fact that the ATTO data set has more influence on the κ than the PRD and BEI data, as the org reviewer correctly pointed out, is not an effect of the different dataset size (as this is eliminated by the binning), but rather by the different ε being covered. Specifically, the ATTO aerosol has high organic org fractions and accordingly most data points at high ε levels. In contrast, the BEI and PRD data has high org inorganic fractions and therefore most data points at low ε levels. This means that κ can be retrieved org from the ATTO data more reliable, compared to the BEI and PRD data, which require a rather ‘far’ extrapolation to ε = 1 yielding κ . org org\n\nc) The binned method successfully reduces the data density effect, but I am wondering if this will reduce the uncertainty of the linear regression correspondingly. Is that why the data points in Figure 1B have large uncertainties, but the uncertainty of the fit is so small? This discrepancy is also shown clearly in Figure S4. Is there a better way to present the uncertainty?\n\nThe uncertainty of the fit is not directly related to the binning method. The error can also be bigger after binning, which is not the case in this study because the linear relationship describes the data very well after binning and this is the reason for the low error in the fit. The result of the fit is different with and without binning; depending on the scientific question the result with or without binning is better.\n\nFor further clarification, we have added the following paragraph to the section on the retrieval to clarify those points:\n\n“Note that a binning and fitting of all data sets, compared to an averaging and fitting of the binned three largest data sets only (see above), did not yield a significantly different κ and κ retrieval org inorg within the range of the uncertainty. This shows that the optimized retrieval is statistically robust, independent of whether the smaller data sets are included or not. Binning all data sets with comparable counting error and averaging the binned results afterwards, however, seems to be the statistical most valid approach at this point.”\n\n[R2.2] Page 9 line 16. The section of “Field studies and data sets” is a bit long. Adding a large table similar to Table S2 may help us to quickly grab campaign information (e.g., date, geographical location, data sources and special conditions) and make comparisons readily. For different stations, a summary of particle size distribution, chemical composition and potential particle sources may help to show how representative the dataset is. I feel the current section generally provides fragmented information though it lists all sites and related information. Also, readers may want to see how the campaign data sets are effectively integrated and to judge the validity of results without having to consult another paper. I would suggest the authors add some critical information (e.g., the sample size of different stations in Fig. 1C, more detailed data filtering met od, and visualized CCN and AMS data from important stations) in SI, and this will help to fill the gap between campaign results and the paper conclusion.\n\n[A2.2] Thanks you for the suggestion. We have added a table as suggested by the referee with the most essential information, but also kept the text section in its current form for more detailed information.\n\n[R2.3] On page 12 line 28-30, the authors mention “the AMS and CCN counter measurements are most comparable for the largest particle diameters measured at the lowest supersaturation (i.e., S ~ 0.1 %), which corresponds to accumulation mode particles.” Will this method of data selection bring some bias? Additionally, the data sets for the retrieval were obtained in 2006 and in 2014-2015, and we know the AMS was updated frequently during these years, so I am just curious if the update will affect the data analysis process.\n\n[A2.3] To clarify this aspect, we introduced the following statement into page 15:\n\n“Note here that κ is typically size-dependent and, therefore, focussing on one particular size range can introduce some bias. At the same time, κ values are typically rather constant across a given size mode (Rose et al., 2010; Pöhlker et al., 2016). Accordingly, the approach chosen here can be regarded as representative for accumulation mode particles as the prime source of CCN.”\n\nWe do not have any indications that the AMS data sets from 2006 and 2014/15 might be not comparable due to instrumental updates.\n\n[R2.4] Page 5 lines 29-30 the authors write, “the assumption of an internally mixed aerosol as an average of the global composition is justified (31).” In contrast, recent studies showed that neither external nor internal mixtures fully represent the mixing state of atmospheric aerosols.1-5 It would be appropriate for the authors to provide a bit more discussion as to the validity of their assumption or at least list some potential caveats. Similarly, the organic coating and its effect on surface tension may also raise questions while assuming the surface tension of pure water on page 2 line 28.\n\n[A2.4] This is a valid objective. We modified and extended the original statement:\n\n“In principle, the retrieval might differ for freshly emitted, externally mixed aerosol particles that have distinct compositions. Since aerosol populations tend to become internally mixed within tens of kilometers or few hours away from emission sources, however, the assumption of an internally mixed aerosol as an average of the global composition is justified (ref).”\n\nas follows\n\n“This mixing state of the aerosol components affects ari and aci and its representation in models is associate with large uncertainties (Zhuo et al., 2018; Zheng et al., 2021; Kodros et al., 2018). Generally, an aerosol populations tends to become more and more internally mixed with atmospheric residence time, even within tens of kilometers or after few hours of transport (Ervens et al., 2010). At the same time, studies suggest that the mixing state of atmospheric aerosols is neither fully represented by the assumption or parameterization of an external mixture nor internal mixture (Sharma et al., 2018; Body et al., 2018). Our parameterization of κ and κ is based on a wide variety of atmospheric conditions org inorg at different locations and, therefore, represents an atmospherically relevant distribution of prevalent aerosol mixing states. At the same time, special aerosol populations, such as freshly emitted and externally mixed particles, might deviate from the average retrieval.”\n\n[R2.5] One implication may underestimate the significance of some studies on aerosol hygroscopicity. On page 8 lines 14-16 the authors write, “In turn, this also implies that an experimental determination of the κ of individual compounds within the thousands of different organics – with many of them being unidentified – is not essential to reduce uncertainties in the effective radiative forcing of aerosol particles.” I agree that it is not essential to further examine thousands of different organics. However, the variation of the κorg has been represented using the atomic O:C ratio that reflects the oxidation level of the organics.6, 7 Maybe the authors could mention this research direction for future study since this could probably fill the gap between data of Vogel et al. (and maybe Cerully et al.) and your fitted line in Fig. S6 in the future?\n\n[A2.5] We added the following statement on page 9, following the referee’s suggestion:\n\n“The variability of κ within the organic aerosol fraction might be efficiently represented by average chemical properties such as the oxygen-to-carbon ration (Jimenez et al., 2009; Cerulli et al., 2015).”\n\n[R2.6] On page 6 line 3: In the section of “Climate model sensitivity to changes in κorg and κinorg”, the authors describe the great details of absolution and relative changes in radiative forcing, and the sensitivity of radiative forcing to κorg and κinorg. Readers may want to see more in-depth discussion and implications. For example, on page 6 line 15: “Further note that the model yields an RFari of -0.11Wm-2 (Table 1), which is about half of the value of -0.22W m-2 given in the recent report of the Intergovernmental Panel on Climate Change (IPCC) (2).” It is a good comparison here but what does this imply and is it a big difference? Another example on page 8 line 5: “Note here the much larger uncertainty in ERFaer”. Where does the large uncertainty come from, and will it influence the conclusion? Lastly, I am also wondering if there are some available sensitivity studies by applying some different models, and if these results were comparable to results here?\n\n[A2.6] We modified the original statement:\n\n“Further note that the model yields an RFari of -0.11Wm-2 (Table 1), which is about half of the value of -0.22W m-2 given in the recent report of the Intergovernmental Panel on Climate Change (IPCC) (2).”\n\nas follows and also added some more explanation and context. Note also that we changed the RFari value according to the latest IPCC report.\n\n“Further note the ∆RFari and ∆ERFaer from ECHAM-HAM can be considered rather as lower limit values and corresponding results from other climate models might be higher. Myhre et al. (45) showed in a model comparison study that ECHAM-HAM yields a global mean anthropogenic RF (all-sky) of -0.15 W m−2, in comparison to the 16-model mean of −0.27 ± 0.15 W m−2 (± one standard deviation). Along these lines, the RFari of ~ -0.11 W m−2 derived here from ECHAM-HAM (Table 1) is much less than the value of -0.3 W m−2 given in the recent report of the Intergovernmental Panel on Climate Change (IPCC) (2).”\n\nTypos and Formats\n\n[R2.7] Page 3 lines 19-20: “These campaign-specific results show a larger range in κorg ranging from 0.06 to 0.19 than for κinorg, ranging from 0.63 to 0.71…” The ranges of κorg and κinorg summarized here are not consistent with the original data in Table S2. Please correct or clarify it correspondingly.\n\n[A2.7] True. Obviously, the numbers in the text were not finally updated in the course of several revisions of Table S2. We have corrected the statement as follows:\n\n“These campaign-specific results show large ranges in κ ranging from 0.04 to 0.25 than for κ , org inorg ranging from 0.46 to 0.71…”\n\n[R2.8] Page 11 lines 15-17: The work by Cerully et al. (55) is referred to SI Fig.S6, “All campaign data sets from Fig. 1C shown here in gray, in combination with data from Vogel et al. (32) in blue and Cerully et al. (55) in red.” The red markers are missing in this figure.\n\n[A2.8] Thank you – by mistake indeed an older version of the figure was included. We replaced it by the latest version of the figure shown below:\n\n[R2.9] For the Figure 1C on page 4, can the authors at least refer these markers to Fig.S5 so that we know which site each of them represents? On page 5 lines 8-17, we may also need to refer the discussions to Fig. S5.\n\n[A2.9] Colors and shapes of the markers are identical in Fig. 1A, 1C and S5. To underline this, we added the following statement to the caption of Fig. 1: “The colors and shapes of the markers in panels (A) and (C) as well as in Fig. S5 are identical to relate the data sets to the corresponding sites.”\n\nMoreover, we added the following sentence to page line 8ff. as suggested by the referee:\n\n“The individual data sets are shown in Fig. S5.”\n\n[R2.10] In SI Table S2, the retrieved κorg is 0.19 at PRD station in Rose et al. But for the same PRD station, the retrieved κorg is 0.06 in this study in Table S3. Can the authors explain the reason why they are quite different since some readers may be interested in this?\n\n[A2.10] Correct, the original retrieval from Rose et al., 2011 in Table S2 and the retrieval with the method of this study in Table S3 are not identical. This can be explained by the different methods used for the retrieval: The most important differences are that (i) the data sets were binned on the ε axis in org this study and (ii) that a bivariate linear fit was used here (see experimental section). To clarify this aspect, the following statement was added to the caption of Table S3:\n\n“Note that the retrieved κ and κ in this table were obtained with the approach as outlined in the org inorg experimental section and deviate from the retrievals in the original studies as summarized Table S2. The main differences are the binning on the ε axis and the application of the linear bivariate fit applied org here.”\n\n[R2.11] Page 5 lines 8: The description “robustly and broadly” is a qualitative statement and readers may wonder how statistically representative the relationship is. Therefore, is it reasonable here to do some significance tests and see if it’s statistically significant?\n\n[A2.11] As outlined in the method section, various variants of the analysis and retrieval gave pretty much the same results, which was a strong indication for us that the overall approach is robust indeed.\n\n[R2.12] Page 6 line 9: “The model parameterizes the overall κ through Eq. 3 based on compound-specific κ values for sea salt, black carbon, mineral dust, organic carbon, and sulfate aerosols (details in supplementary materials).” No data information is available in SI. What are the “details” mean here?\n\n[A2.12] In the course of the submission, the experimental section was moved back and forth between the SI and the appendix of the manuscript. The “details” including references for further reading are in fact now in the experimental sections and not in the SI, as the referee pointed out correctly here. Thanks for providing this hint. We modified the corresponding statement as follows: “The model parameterizes the overall κ through Eq. 3 based on compound-specific κ values for sea salt, black carbon, mineral dust, organic carbon, and sulfate aerosols (details in experimental section).”\n\nReferences\n\n1. Kodros, J. K.; Hanna, S. J.; Bertram, A. K.; Leaitch, W. R.; Schulz, H.; Herber, A. B.; Zanatta, M.; Burkart, J.; Willis, M. D.; Abbatt, J. P. D.; Pierce, J. R., Size-resolved mixing state of black carbon in the Canadian high Arctic and implications for simulated direct radiative effect. Atmos. Chem. Phys. 2018, 18 (15), 11345-11361.\n2. Sharma, N.; China, S.; Bhandari, J.; Gorkowski, K.; Dubey, M.; Zaveri, R. A.; Mazzoleni, C., Physical Properties of Aerosol Internally Mixed With Soot Particles in a Biogenically Dominated Environment in California. Geophys. Res. Lett. 2018, 45 (20), 11473-11482.\n3. Zheng, Z. H.; West, M.; Zhao, L.; Ma, P. L.; Liu, X. H.; Riemer, N., Quantifying the structural uncertainty of the aerosol mixing state representation in a modal model. Atmos. Chem. Phys. 2021, 21 (23), 17727-17741.\n4. Zhou, C.; Zhang, H.; Zhao, S. Y.; Li, J. N., On Effective Radiative Forcing of Partial Internally and Externally Mixed Aerosols and Their Effects on Global Climate. J. Geophys. Res-Atmos. 2018, 123 (1), 401-423.\n5. Bondy, A. L.; Bonanno, D.; Moffet, R. C.; Wang, B. B.; Laskin, A.; Ault, A. P., The diverse chemical mixing state of aerosol particles in the southeastern United States. Atmos. Chem. Phys. 2018, 18 (16), 12595-12612.\n6. Jimenez, J. L.; Canagaratna, M. R.; Donahue, N. M.; Prevot, A. S.; Zhang, Q.; Kroll, J. H.; DeCarlo, P. F.; Allan, J. D.; Coe, H.; Ng, N. L.; Aiken, A. C.; Docherty, K. S.; Ulbrich, I. M.; Grieshop, A. P.; Robinson, A. L.; Duplissy, J.; Smith, J. D.; Wilson, K. R.; Lanz, V. A.; Hueglin, C.; Sun, Y. L.; Tian, J.; Laaksonen, A.; Raatikainen, T.; Rautiainen, J.; Vaattovaara, P.; Ehn, M.; Kulmala, M.; Tomlinson, J. M.; Collins, D. R.; Cubison, M. J.; Dunlea, E. J.; Huffman, J. A.; Onasch, T. B.; Alfarra, M. R.; Williams, P. I.; Bower, K.; Kondo, Y.; Schneider, J.; Drewnick, F.; Borrmann, S.; Weimer, S.; Demerjian, K.; Salcedo, D.; Cottrell, L.; Griffin, R.; Takami, A.; Miyoshi, T.; Hatakeyama, S.; Shimono, A.; Sun, J. Y.; Zhang, Y. M.; Dzepina, K.; Kimmel, J. R.; Sueper, D.; Jayne, J. T.; Herndon, S. C.; Trimborn, A. M.; Williams, L. R.; Wood, E. C.; Middlebrook, A. M.; Kolb, C. E.; Baltensperger, U.; Worsnop, D. R., Evolution of organic aerosols in the atmosphere. Science 2009, 326 (5959), 1525-9.\n7. Cerully, K. M.; Bougiatioti, A.; Hite, J. R.; Guo, H.; Xu, L.; Ng, N. L.; Weber, R.; Nenes, A., On the link between hygroscopicity, volatility, and oxidation state of ambient and water-soluble aerosols in the southeastern United States. Atmos. Chem. Phys. 2015, 15 (15), 8679-8694.\n\nREVIEWERS' COMMENTS\n\nReviewer #1 (Remarks to the Author):\n\nThe authors have done a thorough job responding to the reviews; thank you for considering them carefully. I recommend publication. The only further suggestion I would make is as follows.\n\n“Previous studies documented for organic compounds that the hygroscopicity measured above water saturation, as deduced from observed CCN activity, is higher than that observed in the subsaturated regime, as deduced from light scattering or hygroscopic tandem differential mobility analyser (HTDMA) data (Zheng et al., 2020; Mikhailov et al., 2021). This means that the κorg derived here from CCN activity is likely an upper estimate when used for direct forcing calculations. Albeit, Table 1 suggests that the Δκ between super- and subsaturated retrievals barely changes the global mean direct effects, it is still worth noting as it might affect conclusions on local effects as indicated by Fig. 2D.”\n\nZheng et al., Long-range transported North American wildfire aerosols observed in marine boundary layer of eastern North Atlantic, Environment International, 139, 2020.\n\nMikhailov et al., Water uptake of subpollen aerosol particles: hygroscopic growth, cloud condensation nuclei activation, and liquid–liquid phase separation, Atm. Chem. Phys, 21, 2021.\n\nThese are interesting and appropriate papers to make this point. I had in mind earlier lab studies that explored nonidealities of secondary organic aerosol components which was observed early on in the study of SOA hygroscopicity. There are a number of such studies that can be added; here is one suggestion for a paper studying this issue that specifically mentions the “gap” in the article title:\n\nM.D. Petters, H. Wex, C.M. Carrico, E. Hallbauer, A.Massling, G.R. McMeeking, L. Poulain, Z. Wu, S.M.Kreidenweis, F. Stratmann: Towards closing the gap between hygroscopic growth and activation for secondary organic aerosol – Part 2: Theoretical approaches. Atmos. Chem. Phys., 9 (2009), pp. 3999-4009, 10.5194/acp-9-3999-2009\n\nOne additional note: Petters and Kreidenweis (2007) is listed as both reference 7 and 78.\n\nKind regards, Sonia Kreidenweis\n\nResponses to the second round of review of the manuscript “Global organic and inorganic aerosol hygroscopicity and its effect on radiative forcing”, by Pöhlker et al., submitted for publication in Nature Communications\n\nDear editor, we would like to thank you and referee 1 again for the valuable comments and useful suggestions to improve our manuscript. Below, you will find our responses to the individual comments of the referees along with a description of changes that we did in the manuscript. We have used the following color code:\n• Black: the referee’s comments.\n• Blue: the authors’ responses.\n• Red: Quotes from the original manuscript.\n• Red & italic: Text modifications in the manuscript related to the referee comments.\n\nResponses to Referee #1 (Sonia Kreidenweis)\n\nThe authors have done a thorough job responding to the reviews; thank you for considering them carefully. I recommend publication.\n\nWe thank Sonia Kreidenweis for the thorough second round of reviewing our manuscript and the positive evaluation.\n\n[R1.1] The only further suggestion I would make is as follows.\n\n“Previous studies documented for organic compounds that the hygroscopicity measured above water saturation, as deduced from observed CCN activity, is higher than that observed in the subsaturated regime, as deduced from light scattering or hygroscopic tandem differential mobility analyser (HTDMA) data (Zheng et al., 2020; Mikhailov et al., 2021). This means that the κorg derived here from CCN activity is likely an upper estimate when used for direct forcing calculations. Albeit, Table 1 suggests that the Δκ between super- and subsaturated retrievals barely changes the global mean direct effects, it is still worth noting as it might affect conclusions on local effects as indicated by Fig. 2D.”\n\nZheng et al., Long-range transported North American wildfire aerosols observed in marine boundary layer of eastern North Atlantic, Environment International, 139, 2020.\n\nMikhailov et al., Water uptake of subpollen aerosol particles: hygroscopic growth, cloud condensation nuclei activation, and liquid–liquid phase separation, Atm. Chem. Phys, 21, 2021.\n\nThese are interesting and appropriate papers to make this point. I had in mind earlier lab studies that explored nonidealities of secondary organic aerosol components which was observed early on in the study of SOA hygroscopicity. There are a number of such studies that can be added; here is one suggestion for a paper studying this issue that specifically mentions the “gap” in the article title:\n\nM.D. Petters, H. Wex, C.M. Carrico, E. Hallbauer, A.Massling, G.R. McMeeking, L. Poulain, Z. Wu, S.M.Kreidenweis, F. Stratmann: Towards closing the gap between hygroscopic growth and activation for secondary organic aerosol – Part 2: Theoretical approaches. Atmos. Chem. Phys., 9 (2009), pp. 3999-4009, 10.5194/acp-9-3999-2009\n\n1\n\n[A1.1] Thank you for your thoughts here. We have added the reference you suggested (Petters et al., 2009) and kept the two references that we selected already in the course of the first revision (Zheng et al., 2020; Mikhailov et al., 2021).\n\n[R1.2] One additional note: Petters and Kreidenweis (2007) is listed as both reference 7 and 78.\n\n[A1.2] Thank you for pointing this out. It has been corrected in the revised manuscript file.\n\n2"}]

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