SUPPLEMENTARY INFORMATION

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1 SUPPLEMENTARY INFORMATION DOI: /NGEO1809 Cloud droplet number enhanced by co-condensation of organic vapours supplementary information David Topping, Paul Connolly and Gordon McFiggans S1. Model description The Aerosol- Cloud- Precipitation Interactions Model (ACPIM) model 27 was extended to account for the co- condensation of 10 logarithmically spaced volatility bins as usually represented in the basis set approach 31. The model solves a set of 4 coupled ordinary differential equations for the water vapour mass mixing ratio, rv; its total pressure, P; temperature, T and height, z of the parcel as it rises through an atmosphere in hydrostatic balance. Furthermore there are an additional n+10(1+n) coupled equations describing the mass of liquid water in each of the n aerosol size bins; the mass of each of the 10 organic components in each n size bins and the vapour mixing ratio of the 10 organics. The first 4 coupled ODEs are, i) conservation of water vapour mass: ddrr! dddd = NN ddmm!! dddd where rv is the water vapour mixing ratio, Ni is the number mixing ratio of aerosol in bin i and mi is the corresponding liquid water mass. ii) the hydrostatic relation: dddd dddd = PP RR! TT gggg where Ra is the specific gas constant for air, g is the gravitational field strength and w is the vertical wind speed. iii) the first law of thermodynamics for an air parcel 32 :!" =!!!!"!!!!!!"!!!!"!!!" where cp is the specific heat capacity of air and Lv is the latent heat of fusion. iv) and the rate of change of height of the parcel: dddd dddd = ww where z is the height of the parcel. Each of the water mass bins has an ODE describing its time rate of change through diffusion of vapour mass and heat 32 : NATURE GEOSCIENCE 1

2 dm! dt = 2πD! D! T, P S S!",! e!"# (T)ρ!,! D! T, P L! S!",! e!"# (T)ρ! L! M! k! T T RT 1 + ρ!rt M! where the i subscript refers to each bin, Di is the diameter of bin i, Dv is the diffusivity of air, modified for the transition regime 32, ka is the thermal conductivity of air, also modified for the transition regime 32, esat is the saturation vapour pressure of water vapour (calculated using regressions from Buck research), ρt,i is the density of the aerosol particle including all components, ρw and Mw are the density and molecular weight of water, R is the Universal gas constant, S is the saturation ratio of water vapour and Seq is the equilibrium vapour pressure, calculated from Köhler theory. Similar equations are used to describe the condensation of each of the organic vapours, with the appropriate gas phase diffusivity, vapour pressures and equilibrium relations 8 for the organics accounting for depletion of semi- volatile organics from the gas phase. For organic compounds, gas phase diffusivity D g (cm 2 s - 1 ) was calculated as follows 33 : D g = 1.9(MW ) 2/3 where MW is the molar mass (g mol - 1 ). This is adjusted for mass accommodation effects via transition regime condensation theory 32 D! = D! D D !! + 2D! Dα 2πMW 1000RT where α is the accommodation coefficient for the organic vapour, taken to be unity in the base case simulations in this study. The temperature dependence of vapour pressures was calculated using the Clausius- Clapeyron equation with an enthalpy of vapourisation 13 ΔHvap of 150 kj mol - 1. The final 10 ODEs conserve the organic mass loading in each volatility bin, j: dr!!",! dt = N! dm!"#,!,! dt where rorg,j is the mixing ratio of the jth volatility component and morg,i,j is the mass of organic of type j in each of the i size bins.

3 For each model run an iterative step was implemented to initially calculate the total amount of organic material in each volatility bin required to produce a dry aerosol distribution with a specific ratio of condensed organic mass to core mass. 70 size bins were used in all simulations. This number was deemed the minimum required to capture smooth changes in cloud droplet number due to condensation of semi- volatile organic mass over specific areas of the size distribution. At the lowest updraft velocity (0.1 ms - 1 ), increasing the number of bins to a maximum of 250 introduced a change of ~5% in cloud droplet number in the highest semi- volatile loading scenarios and highest number concentrations. S2. Model Scenarios 9 size distributions were taken to cover the range of distribution permutations previously used for cloud model sensitivities 10, displayed in the first two columns of table S1, with each of 3 total number concentrations, shown in the third column. As stated in the main body of text, an iterative method was used to calculate the total amount of organic material in each volatility bin required to produce a dry aerosol distribution with a specific ratio of condensed organic mass to core mass. This was varied between 20 to 80% of the total mass in 20% steps. Three particle cores were assumed, each helping to determine the CCN effectiveness of the particle: i) (NH4)2SO4, with a molecular weight of 132 g mol - 1 and density of 1769 kg m - 3, and ii) involatile soluble or iii) involatile insoluble organic, each with a molar mass of 320 g mol - 1 and density of 1400 kg m - 3 previously used 8. The entire volatility profile is multiplied by a scalar until there is enough total mass to get the desired mass fraction in the condensed phase using a Newton- Raphson iterative scheme. This represents 324 different aerosol initialisations. 30 different updraught velocities were used for each initialisation, varying from 0.1 to 3 ms - 1 in steps of 0.1ms - 1 representing stratocumulus to trade wind cumulus clouds. Each run was started at a pressure of Pa and temperature of K. In total 9720 simulations were conducted. The total OA volatility distribution 13 was used in all cases with an average molar mass 27 of condensing components of 200 g.mol - 1. In these simulations, the condensing organic was assumed to be completely soluble and non- dissociating. We consider the impacts of non- ideality in section S3 below. Median Diameter, Dm, nm Geometric standard deviation, σ Total Number, Na, cm - 3 particle organic µgm - 3, 0.8 mass fraction, 0% RH total mass, (ppt) organic µgm - 3 particle organic % RH, µgm (79) (1660) (7581) Table S1: The range of size distribution parameters, the corresponding initial particulate (in the 80% mass fraction case) and total organic loadings at 0% RH and the resulting organic loading just below cloudbase under the conditions of Figure 2.

4 The parameter space provides 27 size distributions with 4 initial organic mass fractions, each with 3 types of residual mass core leading to 324 simulations at each of 30 updraught speeds. Within our simulations, we used a bin structure with the distribution being truncated at D=1.12 µm to avoid an unrealistic number of large particles, which can cause confounding effects on droplet formation. This truncation is only important in terms of either number or mass for the distributions at the largest modal size (Dm=200 nm) and breadth (σ=2.2) Note that effective radius will depend on the cloud depth and both droplet number and effective radius depend on the initial temperature and RH. The effect of entrainment is not considered. S.3 Evaluating the sensitivity to the distribution of organic component volatility A number of sensitivity simulations were conducted to investigate the impact of the variability in ambient volatility distributions. The distributions were taken from the Cappa and Jimenez study (reference 13) as in reference 8. The distribution of volatility of the overall organic aerosol is that reported as the Total OA distribution. This was split according to the conventional aerosol mass spectrometer definitions into factors attributable to Hydrocarbon- like OA, HOA, Biomass Burning OA, BBOA and two distinct forms of Oxygenated OA, OOA, the so- called Semi- Volatile OOA, SV- OOA and Low Volatility OOA, LV- OOA. For intermediate size distributions and updraught velocity cases, it was found that there was an increase in droplet number of between 24% and 40% depending on the volatility profile, unless it was purely LV- OOA and then there was seldom a significant increase. This is clearly because there is little additional condensable vapour to draw out of the vapour phase onto the growing droplet. Figure S1 below shows the variability in the amount of condensed material according to its volatility for the case presented in main text Figures 1 and 2. Note that the absolute mass loading corresponds to the model input particle size distribution and is lower than the mass reported by Cappa and Jimenez. The components are iteratively repartitioned to provide the illustrated volatility distributions. Figure S2 illustrates the droplet number evolution for the same volatility distributions.

5 Figure S1: The predicted mass of condensed phase components at each volatility with changing RH in a simulation using the same conditions as Figures 1 and 2 but varying the volatility distribution to match those reported in Cappa and Jimenez (2010). Co- condensation will be clearly important for any volatility distribution where there is vapour available for condensation.

6 Figure S2: Droplet number evolution in the parcel model simulation under the same conditions as Figures 1 and 2 in the main text but with different distributions of volatility of components (using the same colour scheme as S1 above (that used in Cappa and Jimenez (2010), reference 13). The HOA and BBOA distributions largely overlay one another, as do the SV- OOA and OOA. The LV- OOA droplet evolution is indistinguishable from the case with no co- condensation. The Total OA, which comprises all other distributions in their appropriate fractional contributions, is that which has been used throughout the main text. S.4 Assessing the potential effects of non-ideality All of the simulations were run assuming ideal solution thermodynamics. As stated in the main text, it might be expected that the higher volatility compounds exhibit lower water affinity than those with lower volatility, increasing their equilibrium vapour pressures above the growing droplet. The compounds contributing to the organic vapours in each volatility bin will be formed from oxidation of biogenic and anthopogenic VOCs and it is expected that their distribution of functionality and molar mass will be reasonably represented by those predicted by a near- explicit model of VOC degradation. To test the impacts of non- ideality from a reasonable distribution of functionality of components in each volatility bin, 2727 oxidised intermediates predicted from the Master Chemical Mechanism 28 simulations previously used 8 were mapped into their volatility bins using vapour pressure estimation from a recently developed technique 29. Molecular concentrations in each bin were scaled to match the same mass loadings used in the scenario displayed in Figure 2 in the main text. Activity coefficients were calculated using the UNIFAC 30 method. The results are displayed in figure S3. Non- ideality decreased the predicted mass loadings, with a maximum of 40.8% of the total remaining in the condensed phase in the highest volatility bin (Log C*=3). In 30 randomly selected model

7 simulations, total mass loading reductions across all volatility bins at % RH averaged 29.2%, and was never close to being sufficient to entirely suppress enhancement of droplet activation, meaning that there would always still be a significant increase in Nd. At cloud base concentrations, to prevent all semi- volatile condensation, activity coefficients would need to vary from 3.7x10 4 for a log10c * of - 1 and 1x10 3 for a log10c * of 3 with corresponding mole fractions of ~ and ~ respectively. Such activity coefficients are never predicted for any of the components. It is recognised that UNIFAC has limitations in calculating activity coefficients in dilute aqueous conditions and it may be more appropriate to use data from emerging techniques more capable of faithfully representing non- ideality under such conditions 34 when they become available for the breadth of functional groups expected in the atmosphere. Figure S3: Illustration of the difference between ideal and non- ideal simulation for the case illustrated in main text Figure 2. As explained in the text, this has been conducted by mapping 2727 MCM components onto the volatility distribution and then calculating non- ideality by evaluating the activity coefficients for each component with changing RH. It can be seen that there is a reduction in the additional partitioning of component mass with increasing RH, and that this is greater for more volatile components. However, in all cases co- condensation still increases condensed mass and Nd. It should be noted that the distribution of volatilities is truncated at C * =1000 µg.m - 3, whereas cloud liquid water content can be 3 or more orders of magnitude greater than this value. There may be very much more ambient organic material available at saturation concentrations, C *, of between 1 mg.m - 3 and 1 g.m - 3. The effects of co- condensation could be considered a lower limit for this reason, although the degree

8 to which activity coefficients for components in this range would allow significant condensation / dissolution is unknown. S.5 Solubility of the condensed organics The model formulation follows Raoult s Law such that the mole fraction of condensed components determines the vapour pressure over the drop and the difference between the ambient partial pressure and this vapour pressure drives the condensation. The effective solubility constants of components throughout the simulations can be calculated based on the predicted vapour mixing ratios and the concentrations in the droplets for comparison with expected Henry s Law constant values. The effective solubility predictions should be viewed in the context of the oxygenated functionality and carbon number of organic components expected in each C * range 31. For example, organic acids and diacids with carbon numbers ranging from 3 to 12 are found in the volatility range of log10c * between - 1 to ~3, with additional oxygenated functionality as volatility decreases. According to the extensive compilation of Henry s Law constants 35, mono- and dicarboxylic acids have Henry s Law constants (KH) between ~ M atm - 1. For example, malic acid, with a predicted vapour pressure of 10-9 atm (and hence log10c * ~1), has KH of 2.0 x M atm - 1. Similarly, citric acid (vapour pressure atm, log10c * of - 4) has a value of 3.0 x M atm - 1, tartaric acid (vapour pressure atm, log10c * of - 2) has a KH value of 1.0 x M atm - 1. Glyceraldehyde, with a higher vapour pressure of 10-5 atm (log10c* of 5, above the volatility range important in our model simulations) has KH of 2.0 x M atm - 1 ). Henrys Law values for polyols vary between M/atm 35 ; for example, 1,2,3- butanetriol (vapour pressure 10-7, log10c * 3) has KH of 3.0 x M atm - 1 and erythritol (1,2,3,4- tetrahydroxy butane, vapour pressure 10-10, log10c* ~0) has a value of 2.0 x M atm - 1. In the left hand panel of Figure 5 in a recent investigation of condensed orgnic components from MCM predictions 36, it can be seen that the O:C ratio and molecular weight distribution of components predicted to condense must correspond to multifunctional, heavily oxygenated molecules. Such highly polar molecules will likely have even higher KH values than the di- acids and polyols. Higher volatility compounds whose contribution to co- condensation are largely excluded in the model runs in the current study (log10c* 4) include alcohols, ketones and aldehydes with KH values of the order , ~10 1 and M atm - 1 respectively 31. Those compounds with KH values reported as less than or equal to 10 3 M atm - 1 include alkanes, alkenes, alkynes and ketones 35, none of which are generally expected to contribute significantly to condensed phase organic mass and all of which have vapour pressures that make their saturation concentration logc * much greater than 3 and hence not important for our parcel model simulations. The following are the effective KH values for each volatility bin at % RH as calculated from the non- ideality sensitivity analyses presented in S4. It can be seen that these values are fully consistent with the literature values of KH for this range of volatility of components.

9 log10c * KH,ideal, eff KH,nonideal,eff Average O:C ratio x x x x x x x x x x x x x x x x x x x x Table S2: Effective solubility of organic components in each volatility bin corresponding to the equilibrium of vapour and particulate concentrations at % RH under the ideal and non- ideal simulations illustrated in Figure S3. The O:C ratio is calculated from the molecular composition of the MCM compounds in each bin. The high solubility of these highly polar, relatively low volatility components is the reason why they are almost completely scavenged in our simulations. It can be seen from Figure S3 (and amended table S1 above) that a fraction of those components in the higher volatility bins remain unscavenged even at % RH and must await the activation into droplets above supersaturation before remaining vapours are scavenged. A limitation to the solubility as manifested by the apparent non- ideality and an increase in the component activity coefficients is responsible for the decrease in the scavenged fraction in the higher C * bins (though this will not be sufficient to prevent scavenging as the droplets become substantially more dilute above supersaturation). It can be seen from Figure 2 in the main text and Figures S1 and S3 here that the vapours contributing most to the co- condensation (those with the greatest increases in additional condensed mass with increasing RH) are those in volatility bins corresponding to - 1< log10c * < 3. From Table S2 it can be seen that they will have an effective solubility around 4 x10 5 < KH < 4 x 10 7 and O:C ratios between and All these values are completely reasonable for compounds measured or predicted to have reasonable concentrations in the atmosphere, and present largely in the vapour phase, at least under drier conditions. Co- condensation does not require any of the very low volatility components of log10c * < - 1 ever to be in the organic vapour pool. They will always be in the condensed organic pool as is illustrated by the fact they are always coloured green in Figure 2 and S3. Again, it should be noted that the magnitude of the effect of co- condensation that we claim is likely a lower limit since there are potentially many more higher volatility components (e.g. glyceraldehyde) that are sufficiently soluble (though fractionally less well- scavenged) and can play a role in the process.

10 As the droplet grows, the increase in liquid water leads to each compound becoming increasingly diluted (significantly below the effective KH shown in Table S2 above). The vapour pressure above the droplet is consequently lowered causing an increased tendency to condense. Simultaneously the co- condensing vapour becomes depleted as it moves into the droplets, causing a decreased tendency to condense. In our simulations it is always found that the former effect is greater than the latter. Therefore dilution of components in growing droplets invariably overwhelms depletion of their vapour, increasing the condensed mass of increasingly volatile material and causing substantial enhancement in both cloud condensation nuclei and droplets under all reasonable conditions investigated. S.6 Effects of changing the width of the size distribution Figures S4 and S5 show the predicted number of cloud droplets as a function of updraught velocity for model runs initialised with 300 cm - 3 particles, a median diameter of 60nm and standard deviation of 1.3 and 1.7 respectively. The legend highlights the dry involatile mass fraction of a soluble organic using different coloured lines, dashed/solid lines representing assumed co- condensation and no co- condensation respectively. The number of activated droplets at all updraught velocities is smaller for the wider distribution. In both cases the difference in predicted number is maximum between an updraft velocity of ~0.5 to 1 m s - 1. Figure S4: Number of predicted activated droplets as a function of updraught velocity for a size distribution with median diameter of 60nm, standard deviation of 1.3 and total concentration of 300 particles per cc. Each coloured line represents a dry mass fraction of semi- volatile soluble organic mass, as displayed in the legend.

11 Figure S5: Number of predicted activated droplets as a function of updraught velocity for a size distribution with median diameter of 60nm, standard deviation of 1.7 and total concentration of 300 particles per cc. Each coloured line represents a dry mass fraction of semi- volatile soluble organic mass, as displayed in the legend. S.7 Effects of changing the properties of an involatile core Figure S6 displays the predicted increase in cloud droplet number on changing the property of the involatile core for a simulation with 900 cm - 3 particles, 40% dry involatile core mass, median diameter of 150nm, standard deviation of 1.7 as a function of updraft velocity. The largest increases are found for a distribution with an insoluble involatile core as both the amount of soluble material increases, as does the average hygroscopicity of the total solute.

12 Figure S6: Percentage increase in droplet number as a function of updraft velocity for a simulation with 900 cm - 3 particles, 40% dry involatile core mass with varying composition. The distribution median diameter is 150nm. Solid lines represent a standard deviation of 1.7, the upper and lower bounds representing 1.3 and 2.2 respectively. S.8 On the mass accommodation coefficient of condensing organic vapours Consistent with a recent study of the contribution of organic condensation to particle growth 17 the accommodation coefficient of all condensing organic species has been assume to be unity in all of base case simulations. It is recognised that there is uncertainty in this assumption and the arguments surrounding the accommodation coefficient of organic molecules on atmospheric aerosol particles are complex. There are very few direct measurements on dilute aqueous droplets under RH conditions relevant to the current study and none of vapours of such low vapour pressures as are important in our simulations and with the high polarity expected of such high O:C ratios. Molecular dynamics modelling of mass accommodation of organics to liquid water surfaces tend to yield values approaching unity, in disagreement with the lower experimentally determined values. The assumption of unity is a reasonable base case, but the accommodation coefficients of organic semi- volatile compounds should be another area for further work, for both the purposes of cloud activation and for nanoparticle growth 17.

13 A number of sensitivity simulations have been conducted, establishing that the sensitivity is dependent on the assumed degree of (dis- )equilibrium at model initialisation and distance below cloudbase at which it is assumed that this condition pertains. If full equilibration of all components just below cloudbase is assumed (as is the case for water in many parcel model studies previously published), there is negligible sensitivity to organic accommodation coefficient, αi. There is a decrease in the sensitivity to αi with an increase in the RH at which it is assumed that the parcel is initially equilibrated, with low sensitivity at 90% and negligible sensitivity at 95% and higher. (In a simulation using the conditions corresponding to Figure 2 in the paper, Nd increases by 34% at α = 1 and 32% at α = 0.01 equilibrating at 90%, 32% at 1 and 16% at 0.01 at 80%, by 29% at 1 and 13% at 0.01 at 70%). If, however, all organic material were to be assumed in the vapour phase just prior to lifting the parcel to cloudbase, then there would be a strong dependence on α with more than 95% damping of the effect of co- condensation with reduction of accommodation coefficient to However, this condition is unreasonable since it assumes that all organic components are fully out of equilibrium. If the organic components are given a reasonable time to tend towards equilibrium, then the sensitivity is limited and variable across simulations depending on the degree of equilibration by cloudbase. Further work coupling a model under dry and moist conditions to the geographical variability of surface fluxes of organic molecules undergoing atmospheric oxidation is resommended, but is outside the scope of the current work. S.9 The effect of the co-condensational enhancement in droplet number on the global radiative budget The change in cloud albedo, for a change in droplet number of 40% (20%, 10%), i.e. N/N0=1.4 (1.2, 1.1) is given by 18 : ΔAc = x ln(n/n0) = (0.014, ), i.e. 2.5% (1.4%, 0.71%) The solar irradiance (Wm - 2 ) is related to planetary albedo, Ap, by: F = 0.25 x F0 x (1- Ap), where F0 = 1370 Wm - 2 From the above, a change in albedo leads to a radiative effect: ΔF = x ΔAp If the fraction of clouds affected is just that over land (i.e. around 0.3) and the global cloud fraction is about 0.7, the change in cloud albedo is related to change in planetary albedo roughly by: ΔAp = ΔAc x 0.3 x0.7 Therefore the effect associated with such a change is: ΔF = x (0.014, ) x 0.3 x 0.7 = (- 0.98, ) Wm - 2 Note that we are not contesting that all of this effect is a forcing, since a substantial amount of semi- volatile material may be of biogenic origin. However, the effect of co- condensation is systematically to increase droplet number and the impact on the radiative budget is one of systematic cooling. Irrespective of the source of the cooling, the forcing or effect needs to be established, its variability quantified and the effect incorporated into models if they are to have any fidelity at reproducing

14 process level quantitative bottom up understanding of the system. Note also that the amount of organic material in the vapour phase of anthropogenic origin that can be scavenged during co- condensation will not necessarily be substantially smaller than the total amount as there is no reason for it to follow the distribution of organic aerosol. Of course, the geographical distribution of semi- volatile compounds is subject to uncertainty and may well be most prevalent over land. However, droplet concentrations are neither universally nor homogeneously lower over land. Regions of high biological activity with substantial emissions of biogenic VOCs are not necessarily accompanied by high particle number, Na, or resulting droplet number, Nd and may encompass substantial forested areas of low albedo. Furthermore, the cloud cover is geographically and temporally very heterogeneous, and spans a wide range of updraught conditions. The calculations presented should be taken as broad order- of- magnitude estimates to demonstrate the very large potential significance. Our reasonable estimates in these calculations and systematic changes in the energy budget on the order of the size of the cloud albedo are clearly significant. A detailed analysis of the spatial and temporal distribution of the impacts must await further work, since the required observational constraint and model frameworks necessary for such a study do not yet exist. References: 31. Donahue, N. M., Epstein, S. A., Pandis, S. N., and Robinson, A. L.: A two- dimensional volatility basis set: 1. organic- aerosol mixing thermodynamics, Atmos. Chem. Phys., 11, , doi: /acp (2011). 32. Pruppacher, H. R. and Klett, J. D., Microphysics of Clouds and Precipitation, Springer (1996). 33. Lim, H. J., Carlton, A. G. And Turpin, B. J., Isoprene Forms Secondary Organic Aerosol through Cloud Processing Model Simulations, Environ. Sci. Technol., 39, 12, , doi: /es048039h (2005). 34. Suda, S. R., M. D. Petters, A. Matsunaga, R. C. Sullivan, P. J. Ziemann, and S. M. Kreidenweis, Hygroscopicity frequency distributions of secondary organic aerosols, J. Geophys. Res., 117, D04207, doi: /2011jd (2012). 35. R. Sander, R., Compilation of Henry's Law Constants for Inorganic and Organic Species of Potential Importance in Environmental Chemistry (Version 3) law.org (1999). 36. Barley, M. H., D. Topping, D. Lowe, S. Utembe and G. McFiggans, The sensitivity of secondary organic aerosol (SOA) component partitioning to the predictions of component properties, Part 3: Investigation of condensed compounds generated by a near- explicit model of VOC oxidation, Atmos. Chem. Phys., 11, , doi: /acp , 2011.