Introduction

It has long been considered that increasing the abundance of cloud condensation nuclei (CCN) in optically thin clouds would lead to increased reflectance at cloud top (the 1st indirect aerosol radiative effect)1, and extended lifetime due to delays in precipitation onset (the 2nd indirect aerosol radiative effect)2. Both effects lead to an increase in planetary albedo, thereby partly offsetting warming caused by an accumulation of greenhouse gases in the atmosphere. Because of their high susceptibility, and the high sunlight absorption of the underlying oceanic surface, marine clouds are thought to be particularly important contributors to the aerosol-cloud-radiation cooling effect—for example, a 20–35% increase in low-level cloud amount could offset a doubling of CO23,4,5. The potential role of marine clouds in regulating climate led to suggestions of various feedback cycles involving both primary (i.e. bubble-mediated sea-spray) marine aerosol production6 and secondary (gas-to-particle) marine aerosol production7. For primary production of sea-salt, it was suggested that zonal wind speeds would increase with rising global temperatures, leading to increased sea-salt fluxes to the atmosphere6; while plankton activity was suggested to increase with rising temperatures, leading to increased emissions of biogenic sulfur gases from the ocean surface, increasing sulfate aerosol formation, ultimately increasing the availability of CCN7.

In general, an increased number concentration of CCN within a cloud-topped boundary layer leads to increased cloud droplet number concentration (CDNC), and assuming the cloud liquid content is unchanged, to increased cloud albedo. Exploitation of this in geoengineering proposals involves regional-scale addition of sea-salt particles, in the range 0.8–4 µm diameter8,9,10, to mitigate global warming. However, such connections would require a monotonic relationship between sub-cloud CCN and CDNC which may not always be the case11,12.

Primary sea-salt and secondary sulfate aerosol can also become enriched in organics under conditions of high biological activity13, leading to quite complicated changes in the cloud droplet activation properties. This is due to the diverse effects that organics can have on water uptake, which can inhibit or augment droplet activation at a given supersaturation depending on the nature of the inorganic–organic chemical mixture14,15.

Approaches to quantify the less complex scenario of the relative contribution of sulfate and sea-salt to CCN have typically concluded that non-sea-salt sulfate (\({\mathrm{nss}}{\hbox{-}}{\mathrm{SO}}_4^{2 - }\)) dominates marine boundary layer CCN at higher supersaturations while sea-salt dominates at low supersaturations16,17,18,19. In this study, we aim to not only quantify the first order effect of sea-salt addition (or subtraction) to a sulfate-rich CCN population, but also to elucidate any possible higher order effects such as modification of the supersaturation which can indirectly impact on the sulfate CCN concentration.

In doing so, we apply a relatively novel technique to a suite of measurements and associated analysis of marine aerosol physico-chemical and CCN characteristics in the clean Southern Ocean/sub-Antarctic marine environment to quantify the number of sea-salt and sulfate activated cloud droplets (as opposed to CCN spectra). CCN measurements are central to the analysis, as the data gathered are used to generate critical supersaturation (Sc) versus critical dry diameter of activation (Dc) curves (or Sc–Dc curves) of the ambient marine air. Our data analysis, centred on the Sc–Dc curves, builds on the well-justified assumption that, in the absence of clouds, the initial size distribution of submicron secondary marine aerosol is monomodal prior to forming a cloud in boundary layer circulation (i.e. what we call a cloud cycle) and only becomes bimodal after the first cloud cycle20. This is the case because \({\mathrm{nss}}{\hbox{-}}{\mathrm{SO}}_4^{2 - }\) aerosol formation via aqueous phase oxidation of dissolved SO2 in cloud drops is kinetically favoured over SO2 oxidation in haze droplets or in the gas phase or via homogenous production pathways20. This rapid oxidation pathway selectively increases the solute mass, and hence dry size, of the activated nuclei leading to a bimodal size distribution, separated by an intermodal minimum, with one mode representing non-activated particles and the other representing (previously) activated CCN. After the first cloud formation, successive non-precipitating cloud cycles further add solute mass to the active nuclei, acting to widen the intermodal separation20,21. Effectively, the number-size distribution holds key information on the number concentration of cloud droplets in a given cloud and combined with the CCN Sc–Dc curve analysis enables us to determine the mean cloud peak supersaturation (Speak). Once the Speak is determined, the Dc for each aerosol species can be approximated from a theoretical model of CCN activation and then the number concentration of activated cloud droplets from each species is determined (see methods), ultimately allowing quantification of the relative importance of \({\mathrm{nss}}{\hbox{-}}{\mathrm{SO}}_4^{2 - }\) and sea-salt to cloud droplet activation.

Results

Southern Ocean aerosol measurements

The general properties of the submicron aerosol representative of the Austral summertime Southern Ocean region were reported in an earlier study19 where aerosol properties were classified in terms of air mass origin and subsequent advection. The area was dominated by maritime polar (mP) and marine modified continental Antarctic (cAA) air masses (Supplementary Fig. 1). The mP submicron aerosol was bimodal comprising a dominant Aitken mode with modal dry mobility diameter around 43 nm and an accumulation mode with modal dry mobility diameter of the order of 160 nm. The cAA aerosol also was bimodal with an Aitken mode also around 43 nm and a dominant accumulation mode centred around 120 nm. The air mass average number concentrations were 387 cm−3 and 263 cm−3 for the mP and cAA, respectively. The average refractory black carbon concentration was 1 × 10−4 µg m−3 and 2 × 10−4 µg m−3 for mP and cAA aerosol, respectively, indicating the pristine nature of the air masses encountered.

Both air masses contained approximately the same average \({\mathrm{nss}}{\hbox{-}}{\mathrm{SO}}_4^{2 - }\) concentration, 0.4 µg m−3 and 0.37 µg m−3, respectively, while the mP aerosol comprised 10 times more sea-salt than the cAA aerosol (0.3 µg m−3 in mP and 0.03 µg m−3 in cAA). Ammonium was on average higher in the mP air (0.09 µg m−3) compared to cAA air masses (0.04 µg m−3) and organic matter ranged from 0.07 µg m−3 in mP air to 0.02 µg m−3 in cAA air (Supplementary Table 1). In essence, we had a simple marine aerosol system which comprised two basic inorganic chemical species—a partly neutralised \({\mathrm{nss}}{\hbox{-}}{\mathrm{SO}}_4^{2 - }\) aerosol and a sea-salt aerosol. Neither of the average air mass cases had sufficient contributions of organics to make any difference in water uptake processes (i.e. hygroscopic growth or cloud droplet activation). If we assume that the unspeciated organics, making up a volume fraction of 7% of the mP case and 3% of the average cAA case, are primary and the organic enrichment in sea-spray is negligible since you would need volume fractions greater than 55% to see noticeable effects on water uptake processes22. If we assume that the unspeciated organics are of secondary origin (combining the volume fraction with the chemically speciated methanesulfonic acid) then we see a volume fraction of 18% for both air masses, which is still very low to see water uptake effects14. To discern the sea-salt and \({\mathrm{nss}}{\hbox{-}}{\mathrm{SO}}_4^{2 - }\) size distributions, we applied a scaled sea-salt flux distribution23 to measured aerosol particle size distributions, where the scaled sea-salt flux distribution was guided by bulk submicron chemical composition derived from the HR-ToF-AMS.

As presented in a related study19, we can regard the number concentration of cloud droplets, or the number concentration of activated CCN, as the number of particles larger than the intermodal minimum, which has been shown to be reasonable from direct measurements of in-cloud and out-of-cloud aerosol21,24. In doing so, we find that only 45% of the total measured particles were apparently activated in mP air masses while 71% were apparently activated into cloud droplets in cAA air masses, leading to a similar average CDNC in both air masses (176 cm−3 versus 187 cm−3, respectively). The major difference in aerosol chemistry between the two cases is the presence of sea-salt being significantly greater in the mP air.

S c–D c curve analysis of Southern Ocean data

To elucidate this significant difference in activation potential (e.g. particle size-dependent hygroscopicity and activation kinetics) of aerosol in the different air masses, we utilise measurements of CCN activation through Sc–Dc activation curves for the ambient cases (see methods) and we derive the characteristic aerosol critical supersaturation. This procedure is applied using the intermodal minimum as the Dc of the mixed aerosol population and deriving Speak from the ambient Sc–Dc activation curves (see methods). Once Speak is known, the Dc for the sea-salt size distribution and \({\mathrm{nss}}{\hbox{-}}{\mathrm{SO}}_4^{2 - }\) size distribution, and the concentration of sea-salt based CDNC and \({\mathrm{nss}}{\hbox{-}}{\mathrm{SO}}_4^{2 - }\) CDNC could be extracted. Each aerosol species will activate at a slightly different Dc based on its chemical properties and Speak. To determine the number of sea-salt which activated (CDNCSS) and \({\mathrm{nss}}{\hbox{-}}{\mathrm{SO}}_4^{2 - }\) which activated (CDNCSUL), we summed up particles larger than the associated Dc for theoretical sea-salt and sulfate activation at Speak calculated from the Aerosol Inorganic-Organic Mixtures Functional groups Activity Coefficients (AIOMFAC) model25.

For the air mass average scenarios (Supplementary Fig. 2), the cAA aerosol comprised a total \({\mathrm{nss}}{\hbox{-}}{\mathrm{SO}}_4^{2 - }\) particle population of 256 cm−3, six sea-salt particles cm−3, a Speak of 0.38% and a Dc of 59 nm, resulting in an activated cloud droplet concentration of 187 cm−3. Conversely, the mP aerosol comprised a total \({\mathrm{nss}}{\hbox{-}}{\mathrm{SO}}_4^{2 - }\) particle population of 362 cm−3, 25 sea-salt particles cm−3, a Speak of 0.24%, and a Dc of 71 nm, resulting in an activated cloud droplet concentration of 176 cm−3. These results, along with each individual case making up the average, are compiled in Table 1. The data from all cases were statistically compared to clarify any connection between the critical parameters leading to the suppression of \({\mathrm{nss}}{\hbox{-}}{\mathrm{SO}}_4^{2 - }\) activation by sea-salt activation. We found that there was a high anti-correlation (Pearson correlation coefficient r = −0.91, p < 0.01) between the activation of sea-salt and Speak, followed in turn by a high anti-correlation (r = −0.96, p < 0.01) between Dc and Speak, ultimately leading to a high anti-correlation (r = −0.96, p < 0.01) between the percentage sulfate activated and Dc (Fig. 1a). Despite inborn uncertainties from the calculation technique (see methods), the air mass data indicate a relationship between higher concentrations of sea-salt nuclei in a particle population rich in sulfate nuclei and the reduction of peak supersaturation.

Table 1 Calculated best central estimate values from ambient measurements are listed by air mass type (cAA or mP) chronologically and include the air mass averages (avg).
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Fig. 1: Comparison of cloud properties showing linear relatiosnhips in both observed data and subsequent parcel modelling.
figure 1

a Linear representation of the link between (Left) the cloud peak supersaturation (Speak, %) and number concentration of sea-salt particles which activated into cloud droplets; (Middle) critical dry diameters (Dc) and Speak; and (Right) the percentage of sulfate particles which activated into cloud droplets and Dc. The three linear representation give Pearson’s r-values as indicated at the top of the graphs (all are significant for p < 0.01). Each panel shows individual mP cases as grey circles and cAA cases as black circles, where error bars represent the uncertainty calculated for Speak, Dc, and nss-SO4 activated (see Methods). The open triangle (mP) and open square (cAA) shows the averaged case examples. b Parcel model simulations of experimental cases (red markers) with best fit line from model (red line) and experimental (black line) data.

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Microphysical modelling

The experimental data suggest sea-salt strongly controls the activation of \({\mathrm{nss}}{\hbox{-}}{\mathrm{SO}}_4^{2 - }\) nuclei whereby the activated CDNC from \({\mathrm{nss}}{\hbox{-}}{\mathrm{SO}}_4^{2 - }\) nuclei can be reduced. Yet, the derivations of Speak and relative contributions of sea-salt and sulfate particles to total CDNC rely on a mixture of particle properties, assumptions, activation parameterisations, and the AIOMFAC model. To evaluate this mixed methodology and whether the observation-derived experimental data could be reproduced in a theoretical framework, we simulated each case using a simple adiabatic cloud parcel model with explicit microphysics (see methods). While we did not have the complete set of input data to replicate the environmental conditions exactly, we found that for realistic updrafts and assuming an initial monomodal \({\mathrm{nss}}{\hbox{-}}{\mathrm{SO}}_4^{2 - }\) size distribution with a modal diameter of 46–76 nm, and a total number concentration equal to the sum of the sulfate contributions to the Aitken and accumulation modes (Supplementary Fig. 3), we could replicate the cloud-processed size distribution along with the suppression effect of sea-salt on supersaturation and \({\mathrm{nss}}{\hbox{-}}{\mathrm{SO}}_{4}^{2 - }\) activation, albeit with marginally more scatter in comparison to the experimental data (Fig. 1b).

Over the range of \({\mathrm{nss}}{\hbox{-}}{\mathrm{SO}}_4^{2 - }\) concentrations we encountered (100–600 cm−3), we found that with the addition of sea-salt nuclei to the lower sulfate concentration, with a vertical wind speed of 0.1 m s−1, total CDNC fell from 40 to 26 cm−3 while at the highest \({\mathrm{nss}}{\hbox{-}}{\mathrm{SO}}_4^{2 - }\) concentrations, total CDNC decreased from 160 cm−3 to about 28 cm−3 (Fig. 2). It should be noted that the model sensitivities also predict an inflection point for total CDNC at 50 \({\mathrm{nss}}{\hbox{-}}{\mathrm{SO}}_4^{2 - }\) particles cm−3 for 0.1 m s−1, where adding sea-salt actually increased CDNC. For the highest simulated updraft of 0.5 m s−1, the addition of sea-salt increased total CDNC from 80 to 130 cm−3 at the lower observed \({\mathrm{nss}}{\hbox{-}}{\mathrm{SO}}_4^{2 - }\), and decreased CDNC from 340 to 290 cm−3 at the higher observed \({\mathrm{nss}}{\hbox{-}}{\mathrm{SO}}_4^{2 - }\). The inflection point for CDNC at this updraft was 350 cm−3 \({\mathrm{nss}}{\hbox{-}}{\mathrm{SO}}_4^{2 - }\) particles (Fig. 2). The simulations reveal a strong and disproportionate control of sea-salt on the activation of \({\mathrm{nss}}{\hbox{-}}{\mathrm{SO}}_4^{2 - }\) nuclei whereby the activated CDNC from \({\mathrm{nss}}{\hbox{-}}{\mathrm{SO}}_4^{2 - }\) nuclei can be reduced, for example, in one scenario from 300 to 100 cm−3, through the addition of 30 cm−3 sea-salt nuclei.

Fig. 2: Sensitivity analysis of the cloud parcel model predictions to changing sea-salt number concentration (SS) and updraft velocity (w), depending on nss-SO4 concentration (Nsulfate).
figure 2

Left axis shows CDNC (cm−3) in dashed lines while the right axis shows cloud peak supersaturation (Speak%) in solid lines. All panels display sensitivity as a function of Nsulfate in log-scale. All simulations were initialised at a parcel temperature of 268.15 K, 98.5% relative humidity, and 920 hPa. Different sea-salt particle number concentrations (SS) are indicated on the graph. Line shade indicates changes in SS (from 1 to 160 sea-salt particles cm−3) for w = 0.1 m s−1 (a), w = 0.3 m s−1 (b), and for w = 0.5 m s−1 (c). On all panels (a–c) the blue shaded region marks the range of Nsulfate measured in the eight steady-state cases from the Southern Ocean study.

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We calculated the change in albedo from the change in CDNC over our simulations (Fig. 3). The change is calculated in reference to the baseline cloud albedo for w = 0.1 m s−1 and a sea-salt concentration of 1 cm−3. When w < 0.3 m s−1, adding sea-salt nuclei reduces the overall cloud albedo by as much as 30% for moderate \({\mathrm{nss}}{\hbox{-}}{\mathrm{SO}}_4^{2 - }\) particle concentrations in the range observed (100–600 cm−3). However, at higher w, increasing sea-salt nuclei leads to similar increases in albedo when \({\mathrm{nss}}{\hbox{-}}{\mathrm{SO}}_4^{2 - }\) particle concentrations are lower (~100 cm−3) and leads to little change when \({\mathrm{nss}}{\hbox{-}}{\mathrm{SO}}_4^{2 - }\) particle concentrations are higher (~600 cm−3). These microphysical effects propagate into changes in albedo by as much as 30%, for moderate contributions of sea-salt.

Fig. 3: Changes in cloud albedo (dA) as a function of updraft velocity (w) and sea-salt aerosol concentration.
figure 3

The percent dA is calculated relative to the base case of w = 0.1 m s−1 and Nsea-salt = 1 cm−3 (A = 0.31 for Nss-SO4 = 100 cm−3 and A = 0.41 for Nss-SO4 = 600 cm−3). If the albedo increases the dA% change is positive (blue), if albedo decreases the dA% is negative (red), as indicated by the diverging colour scale. The grey contour line shows dA = 0%. a A fixed nss-SO4 monomodal aerosol population of 100 cm−3 is simulated. b A fixed nss-SO4 monomodal aerosol population of 600 cm−3 is simulated.

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This study identifies an important microphysical effect of sea-salt during the cloud formation process in which sea-salt CCN can increase or decrease CDNC in marine boundary layer clouds depending on prevailing conditions and the abundance of secondary marine aerosol. This highlights that the role of sea-spray in aerosol-cloud systems is more complex than originally thought and that sea-spray is a fundamentally important component of the marine aerosol climate system. In particular, the most significant impact of sea-salt CCN is not the direct contribution it makes to the CDNC but, indirectly, in how it can determine \({\mathrm{nss}}{\hbox{-}}{\mathrm{SO}}_4^{2 - }\) CCN activation.

Methods

Aerosol measurements

Submicron aerosol was measured during a campaign to the Southern Ocean from January–February 2015, with a suite of ship-borne in situ instrumentation. Non-refractory aerosol chemistry at sizes less than 1000 nm diameter was measured with an Aerodyne high-resolution time-of-flight aerosol mass spectrometer (HR-ToF-AMS); a TSI, Inc. scanning mobility particle sizer (SMPS) for aerosol particle dry mobility sizes from 20 to 500 nm; a Droplet Measurement Technologies, Inc. single particle soot photometer (SP2) measuring black carbon, and a Droplet Measurement Technologies, Inc. manufactured CCN chamber (CCNC)26 measuring size-segregated CCN number concentration at varying supersaturation. The CCNC ran in a particle size-segregated set-up (see Paramonov et al.27 and Rose et al.28) which utilised a differential mobility analyser (DMA) to separate out 10 different dry particle mobility diameters (Dm), log-spaced equally, ranging from 26 to 490 nm. The DMA utilised 2 L min−1, which then was separated isokinetically between a butanol-based condensation particle counter (CPC) and further isokinetic split between the CCNC and a 0.5 L min−1 carrier flow (Supplementary Fig. 4). The CCNC then measured CCN concentrations at 0.08, 0.29, 0.47, 0.82, 1.48% supersaturation, which were resolved upon calibration as outlined by Rose et al.28. Standard HR-ToF-AMS transmission efficiency is 100% for particles in the aerodynamic diameter range 70–500 nm, dropping gradually for smaller and large particles, with ~50% transmission efficiency at ~30 nm and 1000 nm29,30. More detailed information on instrumentation and calibration can be found in Fossum et al.19.

S c–D c activation curves

Critical dry diameters (Dc) for each critical supersaturation (Sc) were resolved by plotting the fraction of activated CCN number to total condensation nuclei (CN) number concentration (NCCN/NCN) against the dry mobility diameter (Dm) and Dc was determined from the Dm at which NCCN/NCN = 0.5. Taking each case’s values for Sc and plotting them against Dc gives a critical dry diameter activation curve which should be linear in log–log space for a given chemical composition (following assumptions made in Petters and Kreidenweis31). The CCN activation efficiency curves used in this analysis result from the best linear fit to the log10(Sc) vs. log10(Dc) data. Speak is evaluated at the intermodal minimum using the ambient Sc–Dc activation curves. The uncertainty of the CCN counter is ±0.02% for Speak values. As the ambient CCN curve is based on the average size-dependent physico-chemical aerosol population properties, the Dc for different chemical species at Speak may be different from the ambient. The model predictions for CCN activation curves of selected solutes in aqueous droplets were carried out by a combination of the AIOMFAC model25,32 and application of the Köhler equation33. The uncertainty in Speak is propagated to the chemical species-specific Dc, but because the non-linear relationship between Sc and Dc the uncertainty varies depending on both parameters. Dc was found to range from 38 to 85 nm between different chemical species with an uncertainty ranging from ±0.7 to 9.4 nm.

Separation of sea-salt from \({\mathrm{nss}}{\hbox{-}}{\mathrm{SO}}_4^{2 - }\)

For the study dataset, sea-salt is considered here to be chemically represented by the theoretically derived Sc–Dc curve of NaCl, and \({\mathrm{nss}}{\hbox{-}}{\mathrm{SO}}_4^{2 - }\) is chemically represented in accordance with the bulk molar degree of neutralisation. This simplification is reasonable based on the small fractions of organic mass (excluding methanesulfonic acid) in either average air mass case compared with the inorganic components, which may otherwise affect the hygroscopic properties of the aerosol. Using the number-size distributions of the aerosol, and the Dc of sea-salt and \({\mathrm{nss}}{\hbox{-}}{\mathrm{SO}}_4^{2 - }\), respectively, the number contribution of the different aerosol types which would be considered activated into cloud droplets can be calculated using Speak.

First, the SMPS data are constrained by fitting a sea-salt distribution from a North East Atlantic derived sea-spray source function23. This parameterisation is used for the Southern Ocean dataset in the absence of any multimodal sea-salt distribution parametrised from Southern Ocean data. Using a single spectral shape from a wind speed of 6.3 m s−1, which compared well with the measurements (average ship observed wind speed of the PEGASO cruise ~7.5 m s−1), the distribution is scaled to better match observed sea-salt mass from the HR-ToF-AMS. This mass is assumed to represent a nascent pre-cloud cycling sea-salt distribution. The scaled sea-salt distributions are subtracted from the overall number-size distributions with the remainder being assumed as the \({\mathrm{nss}}{\hbox{-}}{\mathrm{SO}}_4^{2 - }\) number contribution. Using the Dc for either sea-salt or \({\mathrm{nss}}{\hbox{-}}{\mathrm{SO}}_4^{2 - }\), the number-size distributions are summed up for mobility diameters > Dc. The total activated number is similarly the sum of the number-size distribution for sizes > intermodal minimum. The percent contribution is determined as the fraction of activated sea-salt or \({\mathrm{nss}}{\hbox{-}}{\mathrm{SO}}_4^{2 - }\) particles to total activated number. Outside of the intermodal minimum being a culmination of multiple cloud microprocesses, there is a ±5% instrumentation error on the intermodal minimum value, which owes to the combination of a ±10% uncertainty in the SMPS size-binning and subsequent lognormal fitting of the ambient data. As the contribution calculation stems from the intermodal minimum calculation and Speak value, the maximum deviation in Dc or Speak from either uncertainty would only result in a ±8% contribution change.

Model description

The 1-D Lagrangian parcel model used in this study calculates cloud particle activation using a hygroscopicity parameter, κ, from κ-Köhler theory31 to describe water activity of the aqueous droplet. The model uses a combination of Lagrangian microphysical equations for the formulation of droplet growth in a rising adiabatic parcel34, which accounts for the activation of particles while other coefficients involved in the diffusivity and thermal conductivity of water vapour follow the methods of Abdul-Razzak and Ghan35. This model is written in Python, and is available as open source code called Pyrcel (http://github.com/darothen/pyrcel)36. All simulations through the model were run for the same initial parameters of parcel initial temperature (T = 273.15 K for mP and T = 268.15 K for cAA), pressure (P = 920 hPa) and relative humidity (RH = 98.5%). The κ parameter for \({\mathrm{nss}}{\hbox{-}}{\mathrm{SO}}_4^{2 - }\) was based on the molar degree of neutralisation (DONmol) of each case, and for sea-salt was 1.2. In the model, multimodal sea-spray distributions were used as input, the submicron modes derived from the source function found in Ovadnevaite et al.23 and the supermicron mode described from a wind speed parameterisation37, both described in Supplementary Table 2. Input for a \({\mathrm{nss}}{\hbox{-}}{\mathrm{SO}}_4^{2 - }\) mode was reverse-engineered as Aitken monomodal distributions which would theoretically be produced in the marine environment from a single source (see supplementary material for a more detailed description of process and theory). These were different in each case with the reverse-engineered Aitken mode having a count median diameter ranging from 46 to 76 nm.

Model sensitivity was tested for a range of environmental conditions including updraft velocity, cloud base temperature and pressure, and the location and amplitude of the initial lognormal \({\mathrm{nss}}{\hbox{-}}{\mathrm{SO}}_4^{2 - }\) and sea-salt particle number-size distributions (see supplementary material). The sensitivity study was evaluated by isolating and manipulating key variables to reveal single effects (see Fig. 2, and Supplementary Figs 6–8), and then testing compounding effects. Modelled cases for the different air mass types used case representative environmental conditions to achieve closure between activated and calculated CDNC and Speak.