Optimizing CCN predictions through inferred modal aerosol composition – a boreal forest case study

Supplement of Atmos. Chem. Phys., 25, 17275–17300, 2025 https://doi.org/10.5194/acp-25-17275-2025-supplement © Author(s) 2025. CC BY 4.0 License. Supplement of Optimizing CCN predictions through inferred modal aerosol composition – a boreal forest case study Rahul Ranjan et al. Correspondence to: Rahul Ranjan ([email protected]) and Ilona Riipinen ([email protected]) The copyright of individual parts of the supplement might differ from the article licence. 1 1 2 Figure S1 (a) Lognormal size distributions calculated from the fit parameters obtained after applying the algorithm by Hussein 3 et al. (2005) on observed size distributions. The solid lines represent the median values, while the shading indicates the 4 percentiles. (b) Fitted versus observed total particle number concentration. 5 6 7 Figure S2 Number of data points for each season. 8 9 10 11 Figure S3 Monthly variation of activation diameter (Dact) for different supersaturation levels (SS) derived from aerosol number 12 size distributions and observed CCN concentration. The plots display the median values (solid lines) and the corresponding 13 2 25th to 75th percentile range (error bars). Each panel represents a different supersaturation level ranging from 0.1% to 1.0%. 14 The x-axis shows the months of the year, while the y-axis indicates Dact. Error bars represent the variability within each month. 15 16 17 Table S1. Median activation diameters (Dact) in nanometers by season: 18 Seasons Dact at SS = 0.1% Dact at SS = 0.2% Dact at SS = 0.3% Dact at SS = 0.5% Dact at SS = 1.0% Spring 206 127 100 80 54 Summer 224 135 105 82 57 Autumn 224 137 109 84 56 Winter 206 129 104 82 55 19 20 S1. Calculation of mass fraction of organic nitrate 21 22 We have used the fragmentation pattern of nitrate in the ACSM to determine whether the detected nitrate 23 is from ammonium nitrate or organic nitrate. The idea is based on Farmer et al. (2010) and in a nutshell, ammonium 24 nitrate will yield a higher fraction of NO! " as opposed to NO# " compared to organic nitrate. NO! " and NO# " are the 25 main peaks where nitrate will be distributed in. the fraction of nitrate that would be from organic nitrates ( 𝑓$% ). 26 The formula as mentioned in Farmer et al., 2010 is: 27 28 𝑓$% = ( 𝑅&'( −𝑅)% ) ×(1+𝑅$%) ( 𝑅$% −𝑅)% ) ×(1+𝑅&'(), (S1) 29 - 𝑓$% is the fraction of nitrate that is from organic nitrates 30 - 𝑅&'( is the NO# " : NO! " from ACSM measurements (nitrate fractions of m/z 30 and m/z 46) 31 - 𝑅)% is the NO# " : NO! " that the AN calibration would yield 32 - 𝑅$% is the NO# " : NO! " for pure organic nitrate 33 34 Here, it is assumed that 𝑅)% = 2 since this would limit the number of negative values for 𝑓$% , when 𝑅$% = 10. 35 The 𝑅$% = 10 is to be expected from the NO3 oxidation of 𝛂 -pinene, which is assumed as a major source of ON 36 at SMEAR II. Finally, using Eq. S1 with the 𝑅)% and 𝑅$% constants for 2016 onwards, a conservative guess for 37 the time series for 𝑓$% can be derived (Fig. S4). As 𝑓$% exhibits a clear, and rather consistent seasonality, a seasonal 38 mask could be retrieved using day-of-the year -based 3-month running median (Fig. S4). This day-of-the-year 39 based mask is used further to estimate how much of the measured nitrate was present as ON and AN (the 40 ammonium nitrate mass fraction fAN = 1 – fON). 41 42 3 43 Figure S4 Mask determining how much of the NO3 ion is organic nitrate, and how much ammonium nitrate. 44 45 46 Figure S5 Predicted ammonium ion (concentration necessary to achieve ion balance within the particles) and observed mass 47 concentration of ammonium ion. 48 49 S2. Demonstration of how scaling works 50 51 In this section, we describe the method (also referenced in Sect. 2.2.3 of the main article) used to scale 52 the fitted size distribution to match the observations. This ensures that the total particle concentration, as well as 53 the number of particles in each bin of the reconstructed size distribution (derived from fitted bimodal lognormal 54 parameters), remains consistent with the observed size distribution (see Fig. S6). As a result, whether we use the 55 original observed size distribution or the fitted bimodal size distribution when applying bulk chemical 56 composition, the predicted CCN spectra remain the same. During scaling process, for each bin, the observed 57 concentration is compared to the sum of the two fitted modes. If only one mode contributes, its concentration is 58 4 adjusted directly to match the observed value. When both modes contribute, the difference between observed and 59 fitted totals is distributed proportionally based on each mode's relative contribution. 60 To better understand the process, scaling is explained in the steps as follows: 61 We have (in cm-3): 62 𝑁&'(,+ : Observed concentration in bin i 63 𝑁,+-,)+-,+ : Fitted concentration for Aitken mode in bin i 64 𝑁,+-,.//,+ : Fitted concentration for accumulation mode in bin i 65 𝑁(/.012,)+-,+ : Scaled concentration for Aitken mode in bin i 66 𝑁(/.012,.//,+ : Scaled concentration for accumulation in bin i 67 The scaling follows these steps: 68 Step 1: Scaling in the size distribution where only the Aitken mode has particles ( 𝑁,+-,.//,+/ = 0) 69 𝑁(/.012,)+-,+ =𝑁,+-,)+-,+ +(𝑁&'(,+ −𝑁,+-,)+-,+) (S2) 𝑁(/.012,.//,+ =0 (S3) Step 2: Scaling in the size distribution where only the accumulation mode has particles ( 𝑁,+-,)+-,+/ = 0) 70 71 𝑁(/.012,.//,+ =𝑁,+-,.//,+ +(𝑁&'(,+ −𝑁,+-,.//,+) (S4) 𝑁(/.012,)+-,+ =0 72 Step 3: Scaling where both modes have contributions to the number of particles ( 𝑁,+-,)+-,+/ ≠ 0, 𝑁,+-,.//,+ ≠ 0); 73 Compute the fractional contributions of each mode 74 fractional contribution of Aitken mode, 𝒳13=/ 𝑁,+-,)+-,+/ 𝑁,+-,)+-,+ /+𝑁,+-,.//,+ (S5) fractional contribution of accumulation mode, 𝒳23=/ 𝑁,+-,.//,+ 𝑁,+-,)+-,+ /+𝑁,+-,.//,+ (S6) 5 scaling factor, 𝒳3=𝑁&'(,+ −(𝑁,+-,)+-,+ +𝑁,+-,.//,+) / (S7) apply scaling, 𝑁(/.012,)+-,+ =/𝑁,+-,)+-,+ +/𝒳3.𝒳13 (S8) 75 𝑁(/.012,.//,+ =/𝑁,+-,.//,+ +/𝒳3.𝒳23 (S9) 76 77 78 Figure S6 An example of the size distribution scaling procedure. Bimodal fitting is done first and then the scaling aligns the 79 reconstructed lognormal size distributions (black line in the left panel i.e. sum of fitted modes) with the observed distribution 80 across binned diameters (Dp). 81 82 S3. Conservation of mass 83 84 In both the Nelder–Mead and DREAM-MCMC optimizations, the total aerosol mass is conserved across 85 all chemical species (organics, inorganics, and eBC). Additionally, the eBC mass is fixed in both the Aitken and 86 accumulation modes. This constraint reduces the optimization problem: we only vary the mass of one species 87 (e.g., organics in the Aitken mode), while the remaining components are derived from conservation laws. For a 88 given time step in the time series, let, 𝑚)+- -&- and 𝑚.// -&- are the total masses in Aitken and accumulation mode, 89 respectively, obtained from bimodal size distribution and mass fractions. Similarly, let 𝑚45,)+- and 𝑚45,.// are the 90 fixed eBC masses, then for each 𝑚&67,)+- the optimization algorithm explore: 91 92 𝑚+8&67,)+- =/𝑚)+- -&- −(𝑚&67,)+- +𝑚45,)+-) 𝑚&67,.// =/𝑚&67 -&- −𝑚&67,)+- 𝑚+8&67,.// =/𝑚.// -&- −(𝑚&67,.// + 𝑚45,.//) (S10) (S11) (S12) 93 S4. Bayesian inference and MCMC 94 95 6 Bayesian inference is a rigorous method for quantifying uncertainty in model parameters (see also see 96 Gelman et al., 2013), using probability statements. Unknown parameters are treated as random variables with 97 some joint posterior probability distribution, which can be written using Bayes law as: 98 99 𝑝(𝜃|𝑌)=/𝑝(𝜃)𝐿(𝑌|θ) 𝑝(𝑌) (S13) 100 where 𝑝 ( 𝜃 ) is the prior distribution which encompasses what is known about the parameters prior to observing 101 any data, 𝐿(𝑌|θ) is the likelihood function which measures how well the model fits observed data, and 102 103 𝑝(𝑌)=/;𝑝(𝜃)𝑝(𝑌|θ)dθ (S14) 104 is the marginal distribution of Y, which represents the probability of observing Y given all possible parameter 105 values 𝜃 . The result of conditioning the prior distribution with some observations is the posterior probability 106 distribution 𝑝 ( 𝜃 | 𝑌), which represents the updated probability of the model parameters. Bayesian inference is 107 therefore a process of creating a probability model and iteratively updating that model based on some observations, 108 resulting in a best estimate of the parameters and knowledge about their uncertainty, sensitivity, and correlation 109 (in the case where 𝜃 is vector-valued). 110 111 Monte Carlo Markov Chain (MCMC) simulations are a methodology for sampling from posterior distributions. 112 Generally, they involve repeatedly and sequentially sampling 𝜃 such that each new draw depends only on the 113 previous sample and therefore forms a Markov chain, and correcting those draws so that the chain converges to 114 the target distribution. Many different algorithms have been proposed for generating and correcting chain samples. 115 Here we use the DiffeRential Evolution Adaptive Metropolis Markov Chain Monte Carlo (DREAM-MCMC) 116 algorithm (Vrugt et al. 2009). This algorithm runs multiple chains simultaneously and adaptively updates the 117 proposal distribution using a randomized subset of the chains’ joint history. It also supports large proposal jumps 118 and outlier rejection during the initial burn-in phase, which accelerate convergence. This type of self-adaptive 119 evolutionary strategy is particularly well suited to heavy-tailed or multi-modal posteriors, such as in this study 120 where different combinations of aerosol chemical composition and size distributions parameters could result in 121 similar CCN spectra. 122 123 S5. Chain evolution in DREAM-MCMC 124 As mentioned in sect. 2.2.3.1, we ran five DREAM-MCMC chains with 40,000 sampling steps each for 125 each CCN observation window. Figure S7 shows that for both windows there is an overprediction of the CCN 126 spectra when bulk composition is used, which is mostly corrected with the DREAM-MCMC optimized 127 parameters, showing that when size-segregated composition is combined with variability in the lognormal size 128 distribution parameters, most of the discrepancy between observed and predicted CCN can be resolved. Figures 129 S8 and S9 show examples of the chain evolution and the resulting posterior distributions for two distinct cases. 130 7 131 Figure S7. Observed and optimized CCN spectra. The black line shows the observed spectra, the blue line represents the 132 optimized spectra using the Nelder–Mead method with only size-segregated chemical composition as the optimized parameter, 133 and the red line represents the DREAM-MCMC optimization where both size-segregated composition and size distribution 134 parameters are optimized. Panel (a) corresponds to 2019-05-11 05:00:00, and panel (b) corresponds to 2019-10-15 07:00:00. 135 136 The first example (Figure S7a and Figure S8) corresponds to a spring-time window, specifically 2019-05-11 137 05:00:00. There is a higher total CCNc, and the DREAM-MCMC improves the closure at all super-saturations. 138 All 5 chains converge well with 𝑅 =-hat values very close to 1 for all parameters. The posterior distributions are 139 relatively compact with the chain evolution indicating stable convergence, with broader distributions for morg,Ait 140 (in this note denoted as Morg1) and NAit (in this note denoted as N1). There is a significant shift in the median of the 141 posterior distribution of Morg1 compared to the initial guess, whereas the posteriors of the size distribution 142 parameters are centred on values very close to the median of the observations, suggesting that an increased mass 143 fraction of organics in the Aitken mode is the key to better CCN closure for this time-step. However, the posterior 144 distribution for Morg1 is relatively wide, indicating less sensitivity to the exact value compared to the very tight 145 posterior distributions for D1, N1, and D2 (the diameters and number concentrations corresponding to Aitken and 146 accumulation modes), which suggest that the closure is very sensitive to those three parameters. 147 In the second example (Figure S7b and Figure S9) the situation is more complex. This corresponds to a fall 148 window, specifically 2019-10-15 07:00:00, where the total CCNc is lower. While DREAM-MCMC significantly 149 improves the closure, it struggles more compared to the previous case, over-predicting at 0.1% SS and 150 underpredicting at 0.2% and 0.3%. The chains show slower mixing and broader posteriors for several parameters, 151 particularly Morg1, N1 and D2. In this case medians of the posterior distributions are significantly shifted from the 152 initial guesses for all parameters. The 𝑅 =-hat values using all 5 chains are below 1.5 for all parameters but are 153 larger for N1 and D1 (approx. 1.3 for both), indicating poorer mixing. Wider posteriors indicate possibly weak 154 identifiability, meaning that multiple parameter combinations can yield similarly good agreement with the 155 observed CCN spectra, pointing to stronger parameter correlations in the posterior. Here, Morg1 is more poorly 156 constrained than in the first case, but the number concentration parameters (N1 and N2) still play a more dominant 157 role in reducing the CCN prediction. 158 159 8 160 Figure S8. Chain evolution (right) and posterior distributions of the optimized parameters (left) from the DREAM-MCMC 161 run. Each plot shows five parallel chains with 40,000 sampling steps. The vertical dashed line in the right panels marks the 162 end of the burn-in period, and the posterior distributions on the left are taken from the final samples after burn-in which are 163 used for posterior inference. Results correspond to observation 4200 (2019-05-11 05:00:00). 164 15 268 Figure S17. Seasonal variability of 𝜅 for Aitken and accumulation mode particles derived using Nelder–Mead optimization 269 (left) and DREAM–MCMC inversion (right). Boxes represent interquartile ranges, whiskers the 5th–95th percentiles, and 270 horizontal lines the medians. 271 272 273 Table S3. Median of optimized mass fractions of various chemical species in Aitken mode in different seasons 274 Spring Summer Autumn Winter Organics 0.89 0.92 0.87 0.83 Inorganics 0.0017 0.0001 0.0001 0.0001 eBC 0.10 0.075 0.13 0.17 275 Table S4. Median of optimized mass fractions of various chemical species in accumulation mode in different 276 seasons 277 Spring Summer Autumn Winter Organics 0.54 0.71 0.57 0.46 Inorganics 0.37 0.23 0.32 0.40 eBC 0.09 0.06 0.10 0.14 278 Table S5. Mean of optimized mass fractions of various chemical species in Aitken mode in different seasons 279 Spring Summer Autumn Winter Organics 0.70 0.75 0.72 0.69 Inorganics 0.20 0.19 0.16 0.16 eBC 0.1 0.06 0.11 0.15 280 Table S6. Mean of optimized mass fractions of various chemical species in Accumulation mode in different 281 seasons 282 Spring Summer Autumn Winter Organics 0.54 0.65 0.55 0.44 16 Inorganics 0.37 0.28 0.33 0.41 eBC 0.09 0.06 0.11 0.15 283 Table S7. Median mass fractions by group and optimization method. 284 285 Groups Organics (Aitken) Inorganics (Aitken) BC (Aitken) Organics (Acc) Inorganics (Acc) BC (Acc) κAitken > κaccumulation (MCMC) 0.11 0.78 0.11 0.69 0.23 0.08 κAitken > κaccumulation (Nelder-Mead) 0.0004 0.87 0.12 0.68 0.23 0.087 κaccumulation > κAitken (MCMC) 0.87 0.04 0.09 0.54 0.37 0.088 κaccumulation > κAitken (Nelder-Mead) 0.91 0.0001 0.09 0.09 0.58 0.087 286 Table S8. Median κ and fraction of data points by group and optimization method. 287 288 Groups Median κAitken Median κaccumulation Fraction of data κAitken > κaccumulation (MCMC) 0.47 0.21 0.54 κAitken > κaccumulation (Nelder-Mead) 0.50 0.20 0.23 κaccumulation > κAitken (MCMC) 0.13 0.27 0.46 κaccumulation > κAitken (Nelder-Mead) 0.11 0.26 0.77 289 290 S10. Insights on effect of the assumption of fixed eBC mass in both modes 291 292 The CCN spectra obtained using bulk chemical composition generally depicts overprediction from the 293 observations, with the largest bias at both lowest supersaturation (0.1%) and the highest supersaturation (1.0%). 294 A way to reduce this overprediction is to have a size-segregated composition that makes the Aitken mode as low 295 in hygroscopicity as possible. As a conservative approach, when eBC is fixed only in accumulation mode (leaving 296 no eBC mass in Aitken mode), the 5 year averaged (median) NRMSE remains almost similar at 0.28 (a little on 297 higher side), while Aitken kappa is a bit higher as an non-hygrosocopic element i.e. eBC is now completely is 298 accumulation mode. In another approach, we allowed eBC to vary as an additional optimization parameter along 299 with organics in the Aitken mode instead of keeping its mass fraction fixed in both modes. As expected, this 300 adjustment lowers the NRMSE from 0.28 to 0.23, while the optimized 𝜅 remains nearly unchanged, but a little on 301 lower side than the setup we use (see Table S10). Interesting to note that, this setup suggest that there should be 302 70% eBC in Aitken mode which seems unrealistic. Complementary results from DREAM-MCMC optimization 303 (optimizing modal BC mass fraction while considering variability of lognormal parameters of size distribution 304 during CCN cycle, see Table S11) of the same problem suggests similar results with around on an average 41% 305 BC in Aitken mode – again a very high number considering the expected aerosol sources at the cite. 306 307 17 308 Table S9. Median of optimized mass fractions of various chemical species in Aitken and accumulation mode 309 when all eBC are kept in accumulation mode – results from Nelder-Mead 310 Organics (Aitken) Inorganics (Aitken) eBC (Aitken) Organics (accumulation) Inorganics (accumulation) eBC (accumulation) 0.99 0.01 0.00 0.59 0.43 0.10 311 Table S10. Median of optimized κ in different seasons when all eBC are kept in accumulation mode– results from 312 Nelder-Mead 313 Spring Summer Autumn Winter κAitken 0.12 0.12 0.12 0.12 κaccumulation 0.27 0.21 0.24 0.29 314 Table S11. Median of optimized mass fractions of various chemical species in Aitken and accumulation mode 315 when eBC is also an optimized parameter 316 Organics (Aitken) Inorganics (Aitken) eBC (Aitken) Organics (accumulation) Inorganics (accumulation) eBC (accumulation) NelderMead 0.26 0.046 0.70 0.62 0.31 0.07 MCMC 0.32 0.27 0.41 0.63 0.30 0.07 317 S11. Optimizing organic properties 318 319 We conducted additional inverse-closure sensitivity studies to assess how the assumed organic aerosol 320 properties influence the optimized parameters. Three types of inverse-closure tests were performed: 321 a) Using bulk-composition but optimizing only the organic density, 𝜌&67 and organic hygroscopicity 322 parameter, 𝜅&67 323 b) Optimizing 𝜌&67 and 𝜅&67/ while also accounting for variability of size distribution lognormal parameters 324 during CCN cycles 325 c) Optimizing morg,Ait, 𝜌&67 and 𝜅&67/ but not accounting for variability of size distribution lognormal 326 parameters during CCN cycles 327 In all tests, 𝜅&67 was varied between 0.05 and 0.15, while 𝜌&67 ranged from 1000 to 3000 kg m⁻³. Method (a) 328 resulted in a lower NRMSE but yielded a median optimized organic density of 1000 kg m⁻³, which appears 329 unrealistic. Method (b) produced a slightly higher NRMSE (0.085 compared to 0.079 from 𝜅P5P5 ) but provided 330 a more realistic optimized organic density of 2179 kg m⁻³, exhibiting clear seasonal variability, with a minimum 331 of approximately 1750 kg m⁻³ in summer. This value is notably higher than the 1500 kg m⁻³ assumed in the 332 original inverse-closure approach. Both methods produced optimized 𝜅&67 values between 0.05 and 0.07, 333 depending on the season. Overall, we obtained a reasonable estimate of optimized 𝜅&67 however, due to certain 334 18 unknown factors, the optimized 𝜌&67 values remain physically implausible. In contrast, method (c) produced highly 335 consistent and realistic results, as summarized in the table below. 336 Table S12: Median of optimized quantities in different seasons when morg,Ait, r org and κorg are considered the for 337 optimization while not accounting for variability of size distribution lognormal parameters 338 𝜿𝐀𝐢𝐭𝐤𝐞𝐧 𝜿𝒂𝒄𝒄𝒖𝒎𝒖𝒍𝒂𝒕𝒊𝒐𝒏 𝜿𝐨𝐫𝐠 𝐀𝐢𝐭𝐤𝐞𝐧 𝜿𝐨𝐫𝐠 𝐚𝐜𝐜𝐮𝐦𝐮𝐥𝐚𝐭𝐢𝐨𝐧 𝝆𝐨𝐫𝐠/ (kg m⁻³) Spring 0.16 0.24 0.07 0.07 1228.56 Summer 0.15 0.18 0.07 0.07 1304.12 Autumn 0.13 0.23 0.07 0.08 1307.69 Winter 0.11 0.26 0.06 0.07 1224.46 339 340