CCN concentrations can be predicted using κ-Köhler theory together with PNSD measurements (Eqs. 3 and 4 in ), once the bulk hygroscopicity parameter (κchem) has been derived. Below we describe the three schemes used to calculate κchem:  

Scheme 1: Chemical composition measurements from the ACSM and the BC mass concentration are considered, so Eq. () can be expressed in terms of three main components: organics (OA), inorganics (IA), and black carbon (BC) (Eq. ). This approximation has been shown to provide a reliable estimate of the effective aerosol hygroscopicity e.g.,.3κchem=κOAϵOA+∑iκIAiϵIAi+κBCϵBCThe contribution of inorganic aerosols to κchem includes several inorganic salts present in the atmosphere, such as ammonium nitrate, ammonium sulfate, ammonium bisulfate and sulfuric acid. The volume fractions of these salts are determined using the simplified ion pairing scheme from . The densities and κ values used for each component are summarized in Table S6 in the Supplement.

The prediction of CCN concentrations from aerosol optical properties has been explored in several studies e.g.,. In addition to exploring the ability of AOPs to estimate CCN concentrations, the main application of this approach is to improve satellite retrievals e.g.,. In (hereafter referred to as S2019), a new empirical parameterization was developed by analyzing in situ measurements at six stations representing different environments. S2019 investigated the relationships between CCN concentrations at different SS and AOPs, and derived the following parameterization that explicitly depends on the SAE, BSF, BSF_min (1st percentile of BSF data) and σsp of PM₁₀ particles: 4NCCN,S2019(SS)≈(286±46)SAE⋅ln⁡SS0.093±0.006(BSF-BSFmin⁡)+(5.2±3.3)⋅σsp.

This parameterization is designed to be applicable to any site, regardless of its environmental conditions, and for any SS < 1.1 % and provides a basis for estimating NCCN directly from optical measurements .

In this study, we first test the generality of Eq. () and assess whether its performance holds across a wider range of aerosol types. Then we apply the S2019 methodology to our 7 sites plus the 6 sites utilized by S2019 to develop a new equation based on 13 sites to see if it improves the predictions of NCCN. The derivation is detailed in the Supplement (Shen methodology section) and leads to the following equation: 5NCCN,new(SS)≈(320±78)SAE⋅ln⁡SS0.089±0.011(BSF-BSFmin⁡)+(8.7±9.3)⋅σsp.

For the seven sites with available AOPs included in this study, the BSF_min⁡ is estimated as 0.11±0.01. Accounting for the uncertainties in the regression coefficients, the propagated relative uncertainties in the predicted CCN concentrations are 81 %, 34 %, 27 %, 26 %, 25 % and 25 % at supersaturations 0.1 %, 0.2 %, 0.4 %, 0.6 %, 0.8 % and 1.0 %, respectively. Applying the original S2019 parameterization (Eq. ) to the same dataset yields uncertainties from 16 % to 52 %. The wider error range in the new fit is driven primarily by the larger standard deviation of Rmin, defined as the first percentile of NCCN/σsp (see Supplement for details), which is ±9.3 cm⁻³ Mm compared to ±3.3 cm⁻³ Mm in S2019. It is important to highlight several methodological differences between our approach and that of . Although both studies include measurements from the MAO site, in our analysis this site is treated as independent from that in S2019 due to differences in time periods and data constraints: we used data from 2014–2015 and applied a relative humidity (RH) filter (RH < 40 %), while S2019 only used 2014 data without RH restrictions. Furthermore, instead of applying a threshold of σsp>10 Mm⁻¹ as in S2019, our study used a less restrictive filtering approach by excluding only data (σsp, BSF and SAE) when σsp values were below 0.5 Mm⁻¹ and above the 99.5th percentile, allowing a broader range of scattering conditions to be considered. Differences in the treatment of CCN data may also contribute to the variability between the resulting parameterizations.

The Twomey equation describes the relationship between supersaturation (SS) and CCN concentration (NCCN) via a power law with parameters C and k: 6NCCN(SS)=C⋅SSk. This relationship is depicted graphically in Fig. S7 (solid lines) for some of the sites considered here. While Fig. S7 shows the overall fits to the data for each site, C and k can also be found for each individual SS scan at each site. Previous studies have found strong correlations between C, k and various aerosol properties . Here, machine-learning is applied to predict these parameters from AOPs.

Random forest (RF) is a machine learning method that relates target variables (here, C and k) to predictors or “features” . Its main tuning parameters are (a) the number of trees, (b) the number of features considered at each decision node, and (c) the minimum number of observations required in a terminal or “leaf” node (also known as minimum leaf size), which controls the depth and complexity of each tree. The RF model might give better predictions with more trees and more explanatory variables considered, but that also increases the computational cost. Here, we use combinations of AOP variables (σsp, σap, BSF, SAE, SSA, and AAE) as predictors to train the model. The RF algorithm is trained on one portion of the data and then the results of the training are applied to the non-training or test data to validate the prediction. In this work, two different validation strategies are considered. First, our primary validation uses a stratified 70/30 split: for each site, 70 % of scans are randomly chosen for training and the remaining 30 % for testing. These per-site subsets are then pooled across all sites to form single training and test sets. Second, as an additional check, we perform leave-one-site-out (LOSO) cross-validation – iteratively holding out one site for testing and training on the others – to assess how including or excluding any given station affects model performance and to verify that the 70/30 approach yields valid results across all locations. The predictors are not scaled or normalized before processing.

We implemented RF in MATLAB with TreeBagger function considering 500 trees, using the default minimum leaf size value (1) and sampling all predictors at each split. Performance was assessed via out-of-bag (OOB) error, and feature importance via OOB-permutation . The model was run once to find the features relevant for C and then again, on the same data, to find the features relevant for k. Normalized importance scores reveal the variables that most consistently predict C and k. These predicted C and k values are then plugged into the Twomey power-law (Eq. ) to estimate CCN concentrations at any given SS.

The aerosol sub-micrometer chemical composition measured with the ACSM is available at four of the nine stations (see Tables S4 and S5 for details). The operating temperature of the ACSM (600 °C) is not high enough to vaporize refractory components of the aerosol particles, thus only the non-refractory components can be analyzed. As a result, components such as elemental carbon, crustal material, and sea salt cannot be detected . To complement the ACSM chemistry, BC concentrations are derived from the PSAP absorption coefficient measurements. Figure  presents pie charts that illustrate the relative contribution of the species considered (organics, SO42-, NO3-, NH4+, Cl⁻, BC) to PM₁ at each site, along with the total mean mass concentration.

The mean concentration of PM₁ in the four sites ranges from 0.54 to 5.56 µg m⁻³, with varying contributions of the different components, reflecting the distinct aerosol characteristics of each location during the measurement period. Continental sites, COR and SGP, exhibit the highest concentrations (4.01 and 5.56 µg m⁻³, respectively). The mean value measured at SGP is slightly lower than that measured during 2010–2011 at the site (7 µg m⁻³) while for COR, the same value is reported in for the same campaign. In contrast, the lowest mass concentration is observed at the marine site ENA with a mean value of 0.54 µg m⁻³. The mountain site GUC exhibits an intermediate concentration of 1.57 µg m⁻³. These mean values are consistent with previous studies reporting PM₁ levels below 1 µg m⁻³ in remote and pristine marine environments over the Pacific, Atlantic, and polar oceans , as well as with observations from high-altitude mountain sites where lower aerosol mass concentrations are typically found due to reduced anthropogenic influence e.g.,. It is important to note that the aerosol chemical composition exhibits strong seasonal variability, and the values presented here reflect specific measurement periods rather than long-term, annual averages, except at SGP, where long-term measurements are available.

For non-marine sites, the most abundant aerosol component is organic aerosol (OA), with the relative contribution ranging from 50 % at COR to 73 % at GUC. The OA concentration is highest at SGP (2.30 µg m⁻³), followed by COR (2 µg m⁻³). At the marine site ENA, sulfate and organic have the same concentration values (0.19 µg m⁻³), representing 35 % each of the total PM₁ mass. The presence of sulfate at this site is likely mainly associated with sea salt particles , consistent with its location in the marine environment. For COR, SGP, and GUC, sulfate is the primary inorganic component, with contributions of 31 % at COR, 17 % in SGP, and 12 % in GUC. The high contribution of SO42- in COR has been linked to SO₂ emissions from small fires occurring outside Patagonia and the Atacama Desert .

The ammonium contribution ranges from 6 % at the GUC mountain site (0.10 µg m⁻³) to 16 % at the ENA marine site (0.009 µg m⁻³). At the continental sites, COR and SGP, ammonium accounts for 9% of the PM₁ mass concentration (0.36 and 0.50 µg m⁻³, respectively). Differences in ammonium contributions reflect both emission sources and total aerosol load. In continental environments, higher ammonium concentrations are driven by local and regional anthropogenic sources, including agriculture (especially livestock and fertilizer use), road traffic, industrial activities, landfills, coal combustion, and biomass burning . In contrast, the low total PM₁ mass observed at the marine site ENA results in a relatively high ammonium mass fraction despite low absolute concentrations. The ocean is one source for this ammonium e.g.,. Regional transport and secondary formation processes further enhance ammonium levels through the production of compounds such as ammonium sulfate and nitrate .

At most stations, nitrate plays a minor role (contribution less than 6 %) except for the continental stations (SGP; 11 % and COR; 7 %). SGP shows the higher mean NO3- concentration (0.6 µg m⁻³), followed by COR (0.3 µg m⁻³). The higher contribution of nitrate at continental sites is associated with anthropogenic emission sources such as fossil fuel combustion, biofuel combustion, and agricultural fertilization .

Among BC concentrations, the highest contributions are observed at ENA (9 %; 0.05 µg m⁻³), likely influenced by local human activity near the station, which is located within half a kilometer of the local airport . At the mountain site GUC, BC concentrations remain low (0.42 µg m⁻³), yet it accounts for 5 % of PM₁ mass. At continental sites, BC contributes less than 2 % with concentrations of 0.11 µg m⁻³ at SGP and 0.08 µg m⁻³ at COR.

The bulk chemical composition is used to estimate the overall κchem for each site, as explained in Sect. . In this study, κchem is derived based on three variations of Eq. (): (i) including BC (Scheme 1); (ii) excluding BC (Scheme 2); and (iii) assuming a fixed κchem of 0.3 for all aerosols (Scheme 3). Figure a shows the resulting κchem values for each scheme at sites with available chemical composition measurements. Scheme 3, which assumes a constant value κchem regardless of site characteristics, is represented as a horizontal line at all stations. Among all sites and for both schemes 1 and 2, the marine station (ENA) has the highest κchem values (around 0.45), followed by the continental sites (COR and SGP, approximately 0.3), and the mountain site (GUC, around 0.23). In this context, applying a fixed value of κchem=0.3 (Scheme 3) tends to underestimate aerosol hygroscopicity in the marine environment and overestimate it at the mountain sites, while for the continental stations it provides a reasonably accurate approximation. The inclusion of BC in Scheme 1 results in slightly lower κchem values compared to Scheme 2 across all sites, since BC is assumed to be completely hydrophobic (κBC=0), thereby reducing the volume-weighted contribution of hygroscopic species. It is also worth noting that at marine sites, κchem may be underestimated due to the inability of the ACSM to detect refractory sea salt, which can significantly contribute to aerosol hygroscopicity in those regions .

In general, κCCN is lower than κchem for all sites (see Fig. a and Table ). Note that these two parameters cannot be directly compared since κCCN only accounts for activated particles in the CCNC and its calculation depends primarily on the dry aerosol size distribution and CCN concentrations as a function of SS, while κchem represents a bulk, mass-weighted hygroscopicity of all particles measured by the ACSM in the 40–1000 nm size range . As a result, if particles with diameters close to Dcrit are less (more) hygroscopic than the larger particles dominating submicron mass, κCCN is expected to be smaller (larger) than κchem.

Figure b shows the variation in the chemical composition derived hygroscopicity parameter (κchem) from Scheme 1 as a function of the binned and averaged ratio of organic to total aerosol mass concentration (OA / [OA + IA]) for the four locations with ACSM measurements. The data were binned into 30 logarithmically spaced intervals between 0.01 and 10. The standard deviation is represented for each averaged value. Figure S8 in the Supplement provides the corresponding analysis using Scheme 2. For both schemes, a clear decreasing trend in κchem with increasing organic fraction is observed at all sites, reflecting that a higher contribution of organic aerosols reduces the overall hygroscopicity of the aerosol population. This behavior is consistent with the typically lower hygroscopicity of organic compounds relative to inorganic salts . At low (OA / [OA + IA]) ratios (<0.1) κchem becomes more noisy due to the lower number of data points, but appears to plateau between 0.5 and 0.7. When OA / [OA + IA] < 0.1, the volume fractions ϵi of sulfate, ammonium, and nitrate dominate, as these are the main inorganic species at all sites (as shown in Fig. ). Consequently, these species govern the sum in Eq. (), and κchem plateaus at their volume-fraction-weighted average value (approximately 0.5–0.7; see Table S6).

This pattern is further supported by the results presented in Figs.  and a. GUC, the site with the highest organic fraction (73 %), exhibits the lowest κchem,Sch1 value among all the sites (∼0.2). Similarly, the other two continental sites, SGP and COR, have intermediate OA fractions (61 % and 50 %, respectively) and correspondingly low κchem,Sch1 values (∼0.25 and ∼0.30). In contrast, the marine site ENA, with a lower organic fraction of 35 %, presents a more balanced chemical composition – 35 % organics, 35 % sulfate, and 16 % ammonium – and a higher κchem,Sch1 (∼0.45). These results suggest that the organic fraction is a key driver of particle hygroscopicity, modulating the ability of the aerosol to take up water, thereby impacting the overall particle hygroscopicity . In general, increasing organic fraction leads to a reduction in κchem, while a higher contribution of inorganic species – particularly sulfate and ammonium - increases overall hygroscopicity .

Using the calculated κchem values, NCCN is estimated using κ-Köhler theory (Sect. ). The predictions are made considering the three κchem schemes. Figure  compares the predicted and measured CCN concentrations at all SS for the four sites where chemical composition measurements are available.

Among the three schemes, the coefficient of determination (R2) is virtually identical (0.82 or 0.83), indicating a similarly strong correlation between predicted and observed CCN concentrations for all schemes. Scheme 1 (Fig. a) shows the best overall agreement with observations, with a slope of 1.09 and the lowest median relative bias (13 %), indicating a slight overall overprediction. Scheme 2 (Fig. b), which is best interpreted as a sensitivity test that indicates the impact of BC rather than as a different predictive approach, shows a slightly higher slope of 1.15 and a median relative bias of 15 %, reflecting a slightly higher overprediction compared to observations. However, the overall performance remains comparable to Scheme 1, with similar predictive capability despite not considering BC. Scheme 3 (Fig. c), which uses a fixed κchem, exhibits the highest slope (1.22) and the highest median relative bias (24 %), pointing to a consistent tendency to overpredict NCCN. It must be considered that CCN concentrations predicted from κchem are based on the bulk, mass-weighted hygroscopicity of all particles measured by the ACSM as mentioned in Sect. 3.2.2. Because the CCNC measures the number of particles activated at the critical supersaturation (Dcrit), and κCCN is inferred from number concentrations, the measured CCN concentration primarily reflects the hygroscopicity of particles near Dcrit. Consequently, if particles around Dcrit are less (or more) hygroscopic than the larger particles dominating the submicron mass, the predicted CCN concentration based on κchem may overestimate (or underestimate) the measured CCN concentration.

Figure S9 in the Supplement provides further insight into the performance of each scheme across different stations by showing the R2 and median relative bias (MRB) values per site. Table S7 lists the number of data points available per site for each scheme. Continental stations (SGP, COR, GUC) exhibit a good predictive skill with a slight CCN concentration overestimation across schemes, while the marine site ENA shows larger sensitivity to hygroscopicity assumptions, largely due to the inability of the ACSM to detect sea-salt aerosol. Despite these limitations, the results are consistent with previous studies e.g., confirming that composition-derived κchem values improve CCN predictions, while a constant bulk κchem=0.3 provides a realistic first-order estimate of CCN number concentrations in diverse environments.

Aerosol optical measurements are available at 7 of the 9 sites (not available for SBS-CP and SBS-SPL). Figure  provides an overview of key aerosol optical parameters for all sites, including σsp and σap, and four derived parameters: BSF, SAE, AAE and SSA. All measurements used in this analysis correspond to PM₁₀ aerosol size cut hourly data and are reported at 550 nm, or for the blue/red wavelength pair for SAE and AAE. As filtering criteria, for the calculation of the derived parameters, measurements with σsp<0.5 Mm⁻¹ were not considered and unphysical values were also excluded, i.e., SSA and BSF outside 0–1. In addition, negative SAE and AAE values were also excluded. On average, the combined constraints eliminated about 4 % of the data across all stations, although at MOS up to 17 % of the measurements were discarded. The filter responsible for most exclusions varied depending on the station, while the SSA constraint was generally the least restrictive, removing the fewest data points. It is important to note that the values presented here correspond to specific measurement periods rather than year-round averages, except for SGP and GUC, where more than 1 year of AOP observations are available and allow for a more representative characterization.

The scattering coefficient (Fig. a) shows notable variability across sites, reflecting differences in aerosol loading. The highest median σsp is observed at the marine site ENA (e.g., 20.7 Mm⁻¹), which contrasts with the low PM₁ concentration at this site. This is likely due to high concentrations of supermicron sea salt particles commonly found in marine-influenced environments . This site is followed by MAO, SGP, and COR continental stations, with median values of 15.9, 13.9, and 8.9 Mm⁻¹, respectively. In contrast, the mountain site GUC and the polar locations (MOS and ANX) show the lowest median scattering coefficients (e.g., 4.7, 5.2, and 5.7 Mm⁻¹, respectively), consistent with their remote and cleaner atmospheric conditions. These findings align with those reported by , where values below 10 Mm⁻¹ were observed for polar environments and mountain sites.

The absorption coefficient (Fig. b) has a different pattern at the sites than the scattering coefficient. The highest median σap is observed at the continental site MAO (1.63 Mm⁻¹), suggesting a strong presence of absorbing particles, likely from biomass burning and anthropogenic emissions . This is followed by the other continental stations, COR and SGP, with median values of 0.55 and 0.65 Mm⁻¹, respectively. Marine and polar sites exhibit significantly lower values, with ENA, MOS and ANX showing median concentrations of 0.17, 0.27, and 0.09 Mm⁻¹. The mountain site GUC reports a moderate absorption level of 0.28 Mm⁻¹, in line with previous findings for high-altitude, remote locations, where aerosol absorption tends to be limited due to the absence of nearby combustion sources .

The back-scattered fraction (Fig. c), which is a proxy for particle size in the aerosol population, shows the highest median values at continental and mountain sites. The highest BSF is observed at COR (0.16), followed by SGP, GUC, and MAO, all with median values of 0.14. These elevated BSF values indicate a greater contribution from smaller particles. Marine and polar sites (ENA, ANX, and MOS) show smaller median BSF values in the range 0.10–0.13. This highlights the different source regimes - sea spray and remote transport in the marine boundary layer, and aged background aerosol in polar regions.

The scattering Ångström exponent (Fig. d) provides complementary information to BSF, as it is more sensitive to particles in the upper accumulation and coarse modes . The highest SAE values are observed at continental and mountain sites such as SGP (2.01), GUC (1.67), and COR (1.37), consistent with the prevalence of fine-mode aerosols from anthropogenic and biomass burning sources. At COR, frequent dust transport during the austral spring may explain its relatively lower SAE compared to other continental sites . In contrast, lower SAE values at marine and polar sites – ENA (0.36), ANX (0.62), and MOS (1.27) – suggest a stronger influence of coarse-mode particles such as sea spray or aged background aerosol.

The absorption Ångström exponent (Fig. e), which describes the wavelength dependence of aerosol light absorption and provides insight into aerosol composition, shows relatively consistent median values across most sites, ranging between 1.1 and 1.3, but with the higher percentiles ranging up to 2–2.5. The median values reflect locations with absorption primarily due to BC based on the AAE / SAE matrix, while the higher AAE values indicate occasional incursions of absorbing aerosols related to dust or biomass burning organics . In contrast, the polar site MOS exhibits a notably lower median AAE of 0.67. AAE values below 1 have been previously reported at remote Arctic and marine sites , although such low AAE values may also be partially influenced by measurement artifacts in the presence of coarse-mode aerosols .

Finally, the single scattering albedo (Fig. f), which indicates the relative contribution of absorbing particles to aerosol extinction coefficient, shows high values across most sites (>0.9), suggesting the dominance of scattering aerosols. ANX, MOS, and ENA, which are all marine influenced, have median SSA > 0.95, while GUC, SGP and COR have median SSA values closer to 0.9. The lowest median SSA is found at MAO (0.80), indicating a relatively more absorbing aerosol mixture at this site consistent with anthropogenic and biomass sources.

Following the S2019 methodology described in Sect. , Fig.  compares predicted CCN concentrations using (a) the original S2019 equation (NCCN,S2019) and (b) the new version of the S2019 equation derived using the original data of S2019 and the data from the stations in this study (NCCN,new), against measured CCN concentrations (NCCN meas) for the seven sites with optical properties in this study and for all SS. The number of data points for each site used in the comparison – identical for both equations – is provided in Table S7 in the Supplement. The comparison shows an increase in the regression slope from 0.72 in plot (a) to 0.86 in plot (b), indicating a better agreement between predicted and measured NCCN when using the new equation. The coefficient of determination (R2) remains unchanged (0.61), suggesting that the overall model performance is comparable in terms of explained variance. The median relative bias decreases in absolute value from -27 % in (a) to -8 % in (b) as the number of sites increases, indicating a reduced underestimation in the predictions. Meanwhile, the similar length of the MRB whiskers in both cases suggests that the variability remains comparable, even when a broader range of stations and aerosol conditions are included. However, the interquartile range decreases from 81 to 69, indicating reduced variability in errors. This reduction in MRB, together with the smaller IQR, reflects an improvement in prediction accuracy, with fewer extreme deviations and a more balanced distribution of errors. Consequently, the new equation provides CCN predictions that are more reliable and closely aligned with the measured CCN concentrations across the full range of conditions.

Figure S10 in the Supplement provides additional insight into the performance of both equations across different stations by displaying the site-specific R2 and MRB (median relative bias) values. As observed in Fig. , the coefficients of determination remain largely unchanged between the two equations. For continental (COR, SGP, MAO) and mountain (GUC) sites, CCN concentrations tend to be slightly underpredicted with MRB < 0 (Fig. S10a), whereas overpredictions are more common at marine (ENA) and polar (MOS, ANX) sites (MRB > 0; Fig. S10a). The new equation (Fig. S10b) generally increases the predicted NCCN values, leading to an overall improvement in prediction accuracy. Figure S11 shows the slope and relative bias for each measured SS between the predicted and the measured CCN concentrations considering the new equation. Excluding the lowest SS (0.1 %), both the slope and the median relative bias remain relatively stable across all SS values, indicating that the predictive equation performs consistently well regardless of SS. The larger deviation observed at 0.1 % SS may be attributed to the logarithmic function used to capture the dependence of NCCN on SS. These results confirm that the original S2019 equation performs well across a wide range of conditions, even when evaluated with an extended dataset. However, the new equation proposed in this work provides a more accurate and balanced estimation of NCCN, particularly by reducing systematic underestimation and improving agreement across the full concentration range.

To further explore the potential of aerosol optical properties to predict CCN concentrations, a random forest model was implemented to estimate the C and k parameters of the Twomey equation. As input variables for the RF model, the same set of AOPs as in the S2019 equation (Sect. ) is considered: σsp, BSF and SAE. All RF models considered in this work were trained with 500 regression trees, a number selected based on a convergence analysis of out-of-bag RMSE and R2, which indicated stable model performance for both C and k parameters. Detailed model performance metrics for both training and test datasets including R2, RMSE, MAE, and hyperparameter settings (number of trees, maximum depth) are provided in the Supplement (Random forest performance section). The close agreement between training and test metrics for both C and k indicates stable model behavior and no evidence of overfitting. Once the model is run, the predicted parameters are used to compute CCN concentrations across a range of SS. The performance of the model is evaluated by comparing these predictions based on RF with measured CCN values, allowing a direct comparison with the results of the S2019 parameterizations.

Figures  and S12 present the results of the RF model. Figure a and b display the relative importance of each input variable in predicting the C and k parameters, respectively, while Fig. S12 compares the observed and RF-predicted C and k parameters. For the C parameter, σsp contributes the most, followed by BSF and SAE, highlighting the dominant role of the total particle loading in determining the potential CCN concentration. In contrast, BSF is the most important variable in k prediction, followed by SAE and σsp, suggesting that the physicochemical properties of the particles, more strongly reflected by BSF and SAE, are more relevant to capture the chemical sensitivity embedded in k. These results are consistent with previous studies that have shown that C is primarily influenced by aerosol number concentration and total mass loading, while k reflects aerosol hygroscopicity and size distribution . Typically, high C values are found under polluted conditions with high particle number concentrations, whereas low k values are associated with particles exhibiting higher hygroscopicity and larger sizes . Thus, independent prediction of these two parameters offers valuable information on the abundance and physicochemical properties of aerosols that influence CCN activation.

Figure c shows the comparison of the predicted CCN concentrations, calculated using the RF-derived C and k values, and measured CCN concentrations across all supersaturations. The result shows a slope of 0.90 and a R2 of 0.62, indicating good agreement between predictions and measurements. The inset boxplot shows the distribution of relative bias, with a median value of approximately 19 %, indicating an overall overestimation.

RF models can take advantage of additional informative features without a significant loss in predictive performance so, as the next step, the RF model is extended by including the full set of AOPs as predictors: σsp, BSF, SAE, σap, AAE and SSA. Although some of these variables are strongly correlated (see Fig. S13), RF models are known to be robust to multicollinearity . A full compilation of training and test metrics, as well as RF configuration details for this extended model is provided in the Supplement (Random Forest performance section). The improvement in R2 and error metrics is consistently observed for both training and test datasets, indicating that the improved performance reflects increased predictive information rather than model overfitting. Figure c compares the predicted CCN concentrations – calculated using RF-derived C and k values from the full AOP set – with the observed values. The extended model achieves a slope of 0.91 and an R2 of 0.69, slightly improving upon the performance of the RF model using only the three Shen-based variables (slope = 0.90, R2=0.62). The median relative bias also decreases slightly from 19 % (three-variable case) to 15 % (full AOP set), with comparable interquartile ranges (-92 to 180 vs. -88 to 145). To assess the RF models' performance across different SS levels, Fig. S14 presents the slope and median relative bias for both schemes. Results are consistent across the SS range, with slopes ranging from 0.80 to 0.99 and median relative biases between 8 % and 32 %, indicating that the predictive capability of the RF models is independent of SS. Finally, Fig. S15 in the Supplement shows site-specific R2 values comparing predicted and measured CCN concentrations for both RF schemes, the S2019 AOPs (Fig. S15a) and the full AOP set (Fig. S15b). While the overall performance is similar, the inclusion of all AOPs – despite some strong inter-variable correlations (Fig. S13) – slightly improves both the coefficient of determination and the bias across all sites, supporting a more accurate prediction of CCN concentrations.

To better understand the source of these improvements in CCN prediction, we next analyze the relative importance of the input variables used to estimate the C and k parameters when using the full AOPs set. Figure a and b display the relative importance of each input variable in predicting the C and k parameters, respectively, while plots in Fig. S16 compare the observed and RF-predicted C and k parameters. AAE is identified as the most important input for the prediction of k (Fig. b), followed by SAE and BSF, suggesting that the chemical sensitivity embedded in k is better captured when accounting for absorption-related properties. For the prediction of the C parameter, BSF is the most important variable (Fig. a), followed by SAE and AAE, while σsp is of relatively lower importance. This result contrasts with the previous model (Fig. a), where σsp dominated, highlighting that including absorption-related parameters redistribute the contribution across variables. As previously mentioned, some of these variables are strongly correlated (Fig. S13) and the model tends to distribute the importance among correlated variables affecting overall predictive performance (Genuer et al., 2010).

To further analyze how different AOPs contribute to the prediction of the C and k parameters, Fig.  presents heatmaps of variable importance for models using different combinations of AOP inputs for C (Fig. a) and k (Fig. b). In these heatmaps, each row corresponds to a model run (the first row includes all AOPs; subsequent rows exclude one AOP at a time), and each column represents one of the six AOPs. Analyzing these heatmaps reveals that BSF remains the most important predictor of C, except when σsp, σap, or BSF itself are excluded from the model. In these cases, the model shifts its reliance to a closely related variable: AAE becomes the dominant predictor when BSF is removed, while σap and σsp substitute for each other when one is absent. This behavior likely reflects the partial redundancy and strong interdependence among BSF, AAE, σsp, and σap. Indeed, their relationships are supported by the Spearman correlation coefficients (Fig. S13 in the Supplement): BSF and σsp are negatively correlated (ρs=-0.41), σsp and σap show a strong positive correlation (ρs=0.68), and BSF and AAE are moderately correlated (ρs=0.36). While these correlations help explain why certain variables gain importance when others are removed, it is important to note that RF variable importance also depends on how much each variable contributes to reducing prediction error across the ensemble, not solely on pairwise correlations . For the prediction of k (Fig. b), the AAE is the most important predictor under the full model. Removing AAE shifts the top rank to BSF, again reflecting their correlation. This result highlights the RF model's ability to reallocate predictive importance among partially redundant features, relying on combinations of variables that together best capture the relevant information rather than depending on any single variable.

RF model results could be influenced by the differences in the availability of data at each measurement site, providing better results for those sites where datasets are longer. Therefore, to evaluate the influence of each location on model generalization when considering all AOPs, a LOSO cross-validation approach is applied as explained in Sect. . This analysis is intended to evaluate spatial robustness and site representativeness, rather than to provide an alternative global performance metric to the train-test and OOB evaluations discussed above. Figure S17 in the Supplement shows the variable importance for each site in the LOSO iteration. In each subplot, the name of the site excluded is indicated. The importance of predictors remains consistent across sites: AAE and SAE typically dominate the prediction of k, while BSF, SAE and AAE are more important for predicting C. This consistency confirms that no single site influences feature selection within the model. Notably, when SGP – the site with the largest number of observations – is excluded, some shifts in variable importance are observed. However, these changes are not large enough to affect the overall importance, suggesting that the 70/30 approach used in the main analysis is not biased by the dominance of SGP data. Figure S18 in the Supplement shows the comparison between predicted and observed CCN concentrations at each excluded site. Slopes range from 0.38 in ENA to 1.87 in MOS, and R2 values from 0.03 to 0.56. Although predictive performance remains good for most sites, the model shows reduced accuracy at marine and polar locations (e.g., ENA, MOS, ANX). This is likely due to the fact that the training data are dominated by continental stations, limiting the model’s ability to capture the distinct AOP characteristics of marine and polar environments.

A recently published study by used an ensemble of multiple machine learning tools to investigate the ability of AOPs to predict CCN concentrations at 4 sites which are common to this study (SGP, GUC, ENA and MOS). As input variables, uses σsp, BSF, SAE and SSA at the different wavelengths. The R2 values obtained ranged between 0.2 to 0.63, depending on the predictive model construction. Their ensemble model was trained specifically for each site and for SS = 0.4 %, aiming at optimizing their predictive potential to the unique atmospheric conditions of each site. In our case, we decided to apply the RF model to the whole range of SS and to all sites together in order to provide a general model that performs reasonably well at most atmospheric conditions.