The Master Chemical Mechanism (MCM v3.3.1; available at http://mcm.york.ac.uk, last access: 28 August 2026) is a near-explicit chemical mechanism that describes the gas-phase oxidation of 143 volatile organic compounds (VOCs) to carbon dioxide (CO₂) and water (H₂O). In MCM v3.3.1, the rate coefficients and associated reaction mechanisms for alkene ozonolysis reactions follow the recommendations of Jenkin et al. (1997, 2015) and Saunders et al. (2003). Although this mechanism provides a detailed representation of CI formation, loss, and subsequent chemical evolution, several key rate coefficients and parameters differ substantially from the latest IUPAC recommendations (Cox et al., 2020). In addition, several important processes are not explicitly represented, including the specific fates of CIs, the unimolecular decomposition of sCIs, the reactions of sCIs with water dimers ((H₂O)₂), and the distinct reactivities of sCI stereoisomers. To address these limitations, we updated the gas-phase alkene + O₃ chemistry in MCM v3.3.1 primarily in accordance with current IUPAC recommendations. The updates include the alkene ozonolysis rate coefficients (kO3+alkene), OH yields (Yi,OH), sCI yields (Yi,sCI), and sCI bimolecular reaction rate coefficients (kb), as well as accounting for sCI unimolecular decomposition pathways and adding sCI + (H₂O)₂ reactions. Where IUPAC provides temperature-dependent kinetic expressions, these were adopted; in addition, a temperature-dependent rate expression was incorporated for the CH₂OO + SO₂ reaction, based on Onel et al. (2021). Specifically, the branching ratios for the unimolecular decomposition or isomerization pathways of CIs and sCIs were constrained using reported OH yields and the yields of other relevant products. For sCIs exhibiting stereoisomerism, including CH₃CHOO, C₂H₅CHOO, and the C₄ intermediates formed during isoprene ozonolysis, the Z-stereoisomers were assumed to undergo predominantly rapid unimolecular decomposition under tropospheric conditions, such that their contribution to bimolecular reactions was considered negligible (Newland et al., 2015). Accordingly, in the updated mechanism, hereafter denoted MCM v3.3.1g, stereoisomeric sCIs participating in bimolecular reactions are represented explicitly by their E-stereoisomers. The unimolecular decomposition pathways of sCIs were considered together with the decomposition or isomerization channels of their corresponding chemically activated CIs. The kinetic parameters and product yields for the alkene ozonolysis reactions before and after the updates are summarized in Tables S1 and S2 in the Supplement. The complete set of updated reaction equations, together with the corresponding rate coefficients and explicit branching ratios, is provided in Table S3. These updates were applied to C₁–C₄ Criegee intermediates, which are widely recognized to play a critical role in tropospheric chemistry.

The concentration of (H₂O)₂ is determined by assuming rapid thermal equilibrium between water monomers and dimers. Given this fast atmospheric exchange, the dimer concentration is considered to be in thermodynamic equilibrium with the monomer, as expressed in Eq. (1): 1KeqD=H2O2H2O2, where KeqD is the temperature-dependent equilibrium constant for dimer formation (Scribano et al., 2006). Following the methodology of Lade et al. (2024), the reaction of sCIs with water dimers is parameterized using an effective third-order rate coefficient, keff (cm⁶ molec.⁻² s⁻¹), and the rate of sCI loss via reaction with water dimers, rsCI+(H2O)2, is given by Eq. (2): 2rsCI+(H2O)2=kb,dimersCIH2O2=kb,dimerKeqDsCIH2O2=keffsCIH2O2, where keff is defined as the product of the bimolecular rate coefficient for the sCI + (H₂O)₂ reaction (kb,dimer, cm³ molec.⁻¹ s⁻¹) and KeqD. To calculate KeqD accurately, thermochemical data were retrieved from the Active Thermochemical Tables (ATcT). Standard Gibbs free energies of formation (ΔfGT°) for both the water monomer and dimer were extracted from Tables 1 and 3 in Ruscic (2013). These discrete data points were then used to calculate the reaction Gibbs free energy (ΔrGT°) over the temperature range of 200–360 K, which spans typical tropospheric conditions. The temperature dependence of KeqD was subsequently obtained via a linear regression of ln⁡KeqD as a function of 1T, yielding the following empirical van't Hoff–type parameterization in Eq. (3): 3KeqDT=Aexp⁡BT, where the coefficients A and B represent the intercept and slope, respectively, derived from the fitting procedure, with A=1.15×10-23 cm³ molec.⁻¹ and B=1549.32 K.

An interpretable machine learning (ML) framework was developed in this study to systematically evaluate the role of sCIs in SO₂ oxidation, encompassing model development, validation, and interpretation. The learning algorithm used throughout was Extreme Gradient Boosting (XGBoost) (Chen and Guestrin, 2016), which constructs an additive ensemble of regression trees by iteratively minimizing a regularized loss function, with each successive tree fitted to the negative gradients (i.e., pseudo-residuals) of the current ensemble's predictions. This formulation enables nonlinear responses and predictor interactions to be represented far more flexibly than a single regression tree. Regularization, subsampling, cross-validation, and early stopping were applied to suppress overfitting, and hyperparameters were tuned via random search or Bayesian optimization. The same sampling–training–testing workflow was applied to every model in this study. Two classes of XGBoost models were constructed (using the XGBoost Python package, version 2.1.3; https://github.com/dmlc/xgboost, last access: 28 August 2026): surrogate models trained on AtChem-simulated chemical evolution, and an observation-based model trained on ambient measurements. Four complementary interpretation methods were used to explain the XGBoost model outputs: SHAP (SHapley Additive exPlanations), Sobol sensitivity analysis, partial dependence plots (PDPs), and individual conditional expectation (ICE) plots.

sCIs are short-lived reactive intermediates generated from the ozonolysis of alkenes. Their contribution to gas-phase SO₂ oxidation is governed jointly by their atmospheric steady-state concentration and their bimolecular rate coefficient with SO₂. The steady-state concentration is itself determined by the initial ozonolysis rate coefficient, the total sCI yield, and the structure-dependent reactivities of individual sCI species toward other competing sinks – most notably H₂O, (H₂O)₂, and NO₂ – which collectively regulate the fraction of sCIs available to react with SO₂. We therefore introduce the sCI-mediated SO₂ oxidation rate, LSO2,sCIs, as the target variable, which simultaneously accounts for sCI production and the effective SO₂ oxidation capacity. Figure 1a and b show that, in both MCM v3.3.1 and MCM v3.3.1g, alkene and O₃ concentrations are positively correlated with LSO2,sCIs, whereas RH and NO_x exhibit marked negative correlations. This pattern is consistent with alkenes and O₃ driving sCI production, while H₂O/(H₂O)₂ and NO₂ act as competing sinks that reduce the fraction of sCIs available to react with SO₂. Notably, updating the mechanism substantially increases the magnitude of the absolute SHAP (|SHAP|) values across all features (Fig. 1c), with the average |SHAP| value ranging from 211.9 to 11 177.3 molec. cm⁻³ s⁻¹ in MCM v3.3.1, versus 694.0 to 30 429.5 molec. cm⁻³ s⁻¹ in MCM v3.3.1g. This indicates that the updated mechanism yields a substantially stronger sensitivity of LSO2,sCIs to perturbations in environmental and precursor variables, such that the same change in a given feature produces a larger response in LSO2,sCIs. Importantly, the update does not amplify the influence of all features to the same degree; rather, it also reshapes the relative importance attributed to individual alkenes (Fig. 1d). In MCM v3.3.1, the alkene relative importance follows the order: trans-but-2-ene (TBUT2ENE, 21.5 %) > cis-but-2-ene (CBUT2ENE, 17.6 %) > isoprene (C₅H₈, 9.5 %) > 2-methylpropene (MEPROPENE, 4.3 %) > ethene (C₂H₄, 0.7 %) > propene/but-1-ene (C₃C₄, 0.5 %). In MCM v3.3.1g, isoprene becomes the most important alkene feature (23.8 %), followed by trans-but-2-ene (11.0 %), cis-but-2-ene (9.7 %), and 2-methylpropene (6.0 %), while ethene (0.9 %) and propene/but-1-ene (0.7 %) remain minor contributors. The approximately sixfold increase in the average isoprene |SHAP| value, rising from 3773.1 to 24 500.7 molec. cm⁻³ s⁻¹ after the mechanism update, is markedly larger than the corresponding shift observed for any other alkene. Indeed, prior studies have shown that regions with intense biogenic emissions tend to exhibit elevated sCI-mediated SO₂ oxidation rates, an effect attributed primarily to sCIs derived from isoprene (Hata et al., 2023; Kukui et al., 2021). It should be noted, however, that the relative importance ranking obtained here reflects each alkene's attributed contribution when all alkenes are perturbed over an identical concentration range (0.1–20 ppb); by contrast, isoprene's prominence in previous field and modeling studies may partly reflect its typically higher ambient concentration relative to other alkenes, rather than solely an intrinsically higher sCI reactivity. Within the present perturbation ranges (O₃: 2–90 ppb; each alkene: 0.1–20 ppb; RH: 10 %–80 %), RH emerges as the most influential feature overall, exceeding the attributed importance of every alkene (Fig. 1d). This is consistent with prior kinetic evidence that H₂O/(H₂O)₂ dominates the bimolecular loss of sCIs, such that most sCIs have limited capacity to survive under high humidity (Cox et al., 2020; Lade et al., 2024).

The changes in mean absolute SHAP interaction values before and after the update (Fig. 2) further clarify the mechanistic origin of the differential amplification magnitudes in alkene attribution. In MCM v3.3.1g, the elevated SHAP interaction values involving RH with both O₃ and the individual alkenes indicate that MCM v3.3.1 substantially underestimated the competitive scavenging of sCIs by H₂O/(H₂O)₂, thereby masking the strong regulatory role of humidity in sCI-mediated SO₂ oxidation. In parallel, the interaction effects between O₃ and the individual alkenes are also enhanced in MCM v3.3.1g, indicating that MCM v3.3.1 likewise underestimated the sCI + SO₂ oxidation capacity. Critically, the relative degree of underestimation in these two competing removal pathways differs across alkene systems. For isoprene, the RH–C₅H₈ interaction increased from 928.0 to 5094.0 molec. cm⁻³ s⁻¹ (a 5.5-fold increase), whereas the O₃–C₅H₈ interaction increased from 697.3 to 4435.3 molec. cm⁻³ s⁻¹ (a 6.4-fold increase). This indicates that MCM v3.3.1 underestimated the reactivity of its derived sCIs toward SO₂ to a greater extent than their reactivity toward H₂O/(H₂O)₂; a comparable pattern is observed for 2-methylpropene. For the remaining alkenes, by contrast, the underestimation of the sCI+H₂O/(H₂O)₂ pathway predominates.

Based on the MCM v3.3.1g results, isoprene contributes more than twice as much as cis-/trans-but-2-ene, 3.8 times as much as 2-methylpropene, and roughly thirty times more than ethene and propene/but-1-ene in terms of their attributed influence on LSO2,sCIs (Fig. 1c). At 298.15 K, the ozonolysis rate coefficients span more than two orders of magnitude (Table S1), following the order: trans-but-2-ene (2.0×10-16 cm³ molec.⁻¹ s⁻¹) > cis-but-2-ene (1.3×10-16 cm³ molec.⁻¹ s⁻¹) > isoprene (1.28×10-17 cm³ molec.⁻¹ s⁻¹) ≈ 2-methylpropene (1.15×10-17 cm³ molec.⁻¹ s⁻¹) ≈ propene (1.05×10-17 cm³ molec.⁻¹ s⁻¹) ≈ but-1-ene (1.00×10-17 cm³ molec.⁻¹ s⁻¹) > ethene (1.56×10-18 cm³ molec.⁻¹ s⁻¹). Total sCI yields follow the sequence (Tables S1 and S3): isoprene (0.66; 0.55 CH₂OO +0.08 (CH=CH₂)(CH₃)COO +0.03 (C(CH₃)=CH₂)CHOO) > ethene (0.42; CH₂OO) > propene (0.28; 0.20 CH₂OO +0.08 CH₃CHOO) > but-1-ene (0.23; 0.15 CH₂OO +0.08 C₂H₅CHOO) ≈ trans-but-2-ene (0.22; CH₃CHOO) ≈ cis-but-2-ene (0.20; CH₃CHOO) ≈ 2-methylpropene (0.20; 0.13 CH₂OO +0.07 (CH₃)₂COO). Beyond overall yield, sCI speciation varies considerably: aside from cis- and trans-but-2-ene, CH₂OO is the dominant sCI across all remaining alkene systems. Critically, the bimolecular reactivities of sCIs are strongly structure-dependent. With respect to SO₂ oxidation, CH₃CHOO, C₂H₅CHOO, (CH₃)₂COO, and (C(CH₃)=CH₂)CHOO exhibit rate coefficients three to four times higher than those of CH₂OO and (CH=CH₂)(CH₃)COO. The reactivity order toward H₂O/(H₂O)₂ is markedly different, however, broadly following CH₃CHOO ≈ C₂H₅CHOO > CH₂OO > (CH=CH₂)(CH₃)COO ≈ (CH₃)₂COO ≫ (C(CH₃)=CH₂)CHOO. These contrasts in sCI fate, including ozonolysis kinetics, effective sCI yield (i.e., the fraction of sCIs that persist to undergo bimolecular reactions), and the relative importance of sCI+SO₂ vs. sCI+H₂O/(H₂O)₂ pathways, collectively shape the relationship between alkenes and LSO2,sCIs. Hence, the capacity of different alkene ozonolysis systems to oxidize SO₂ cannot be reduced to ozonolysis kinetics and sCI yield alone; the competitive removal of sCIs by H₂O/(H₂O)₂ should also be considered (Fig. 2b). A previous H₂SO₄ proxy study similarly noted that the apparent rate constant describing the alkene ozonolysis source spans nearly three orders of magnitude in the real atmosphere, reflecting the underlying complexity of sCI chemistry (Yang et al., 2021).

Figure3 further shows the effects of various alkenes on LSO2,sCIs at different RH under MCM v3.3.1g, illustrating the regulatory role of the sCI+H₂O/(H₂O)₂ pathway. Consistent with the average |SHAP| ranking, isoprene, trans-but-2-ene, cis-but-2-ene, and 2-methylpropene all exhibit substantially positive impacts of varying degrees as their concentrations increase, whereas ethene and propene/but-1-ene display near-zero or weakly positive dependence across the investigated concentration range. The substantial vertical dispersion at fixed alkene concentrations, observed for all alkenes, indicates that identical alkene abundances can yield markedly different impacts on LSO2,sCIs, signifying the non-linear responses arising from interaction effects. For most alkenes (excluding propene/but-1-ene), this vertical spread increases with concentration, indicating that higher alkene concentrations expand the range of possible LSO2,sCIs values, while the realized magnitude remains strongly contingent on ambient conditions. Propene/but-1-ene, by contrast, shows large vertical dispersion across the full concentration range without a significant concentration dependence, suggesting that variability in its SHAP values is driven almost entirely by interaction effects. Ethene similarly shows a significant degree of dispersion in its SHAP values at low concentrations. Taken together, the relationship between alkene concentration and LSO2,sCIs is nonlinear for all alkenes; however, the degree of nonlinearity differs among alkenes, reflecting differences in the relative strength of their interactions with other feature variables.

We use RH coloring in Fig. 3 to visualize the strength of humidity's interactive effects. Across all alkenes, higher RH consistently suppresses the contributions of alkenes to LSO2,sCIs. The degree of suppression, however, varies markedly with alkene identity, and can be rationalized directly from the kinetic properties of their produced sCIs. Under high-humidity conditions, the contribution of propene/but-1-ene to the variation of LSO2,sCIs is weak. This is attributable to the relatively low rate coefficients for the reactions of propene/but-1-ene with O₃, which result in significantly lower sCI production than that from ethene and isoprene. The primary sCIs generated from propene/but-1-ene ozonolysis are CH₂OO, CH₃CHOO, and C₂H₅CHOO, all of which react rapidly with H₂O/(H₂O)₂. Additionally, CH₂OO, which constitutes the largest proportion, has relatively low reactivity toward SO₂. Consequently, the limited sCIs produced from these two alkenes make a further restricted contribution to sCI-mediated SO₂ oxidation. Ethene, despite having the slowest ozonolysis rate coefficient, produces CH₂OO with a substantially higher yield (0.42) than propene or but-1-ene, partially compensating for its sluggish kinetics. However, since CH₂OO is efficiently scavenged by H₂O/(H₂O)₂, ethene's contribution remains small and sensitive to humidity, consistent with the mixed positive and negative SHAP values observed at low concentrations in Fig. 3a. In contrast, cis-but-2-ene and trans-but-2-ene benefit from both the highest ozonolysis rate coefficients among the investigated alkenes and the exclusive production of CH₃CHOO, which reacts rapidly with SO₂. These advantages translate into strong positive contributions to LSO2,sCIs; however, because CH₃CHOO is also highly reactive toward H₂O/(H₂O)₂, the realized contribution is strongly RH-dependent, as evidenced by the pronounced RH stratification in the dependence plots. 2-methylpropene generates both CH₂OO and (CH₃)₂COO. (CH₃)₂COO reacts rapidly with SO₂ but comparatively slowly toward H₂O/(H₂O)₂, resulting in weak competition from H₂O/(H₂O)₂. This explains why 2-methylpropene shows the smallest vertical dispersion growth with concentration among the more influential alkenes, and why its relationship with LSO2,sCIs is more nearly linear, since (CH₃)₂COO maintains its reactivity toward SO₂ even under elevated humidity. Isoprene exhibits the strongest positive contribution to LSO2,sCIs across the full humidity range, arising from the favorable combination of relatively fast ozonolysis, the highest total sCI yield (0.66), and a diverse sCI speciation that includes not only CH₂OO but also (CH=CH₂)(CH₃)COO and (C(CH₃)=CH₂)CHOO. (C(CH₃)=CH₂)CHOO reacts rapidly with SO₂ while undergoing only slow scavenging by H₂O/(H₂O)₂, sustaining efficient SO₂ oxidation even at high RH. The interaction between isoprene and RH is thus primarily attributable to the CH₂OO fraction, whereas (CH=CH₂)(CH₃)COO and (C(CH₃)=CH₂)CHOO enable isoprene to remain a dominant driver of LSO2,sCIs across a wider humidity range. Taken together, when the investigated alkenes are perturbed over the same concentration ranges, ethene and propene/but-1-ene exert negligible direct control on LSO2,sCIs relative to the remaining alkenes. Isoprene and the C₄ alkenes, cis-/trans-but-2-ene and 2-methylpropene, represent the dominant alkene precursors, but their effective impacts are jointly shaped by RH. This finding underscores the need for surrogate modeling to resolve these complex, nonlinear atmospheric reactions into a clear relationship between precursors and LSO2,sCIs. Such modeling enables the identification of key alkene precursors, quantification of the dependence of their contributions on ambient environmental conditions, and elucidation of the key reactions governing their roles in sCI-mediated SO₂ oxidation.

The surrogate model developed in Sect. 3.1 quantifies how key factors govern LSO2,sCIs, the absolute rate of SO₂ oxidation by sCIs. A large LSO2,sCIs, however, does not necessarily imply that sCIs are important for SO₂ oxidation, because their importance also depends on the strength of the parallel OH-driven oxidation pathway. OH and sCIs share certain precursors, but their formation pathways are not entirely identical: alkene ozonolysis simultaneously produces both, so alkenes and O₃ drive both pathways, yet OH is additionally sustained through routes that do not involve sCIs, including RO_x–NO_x radical cycling and the direct photolysis of O₃, HONO, and other species. OH is therefore governed by a broader set of factors, including NO_x, NO₂ %, and the wider VOC composition, several of which exert little or no direct influence on sCI chemistry. As a result, the two oxidation pathways do not respond in tandem to environmental perturbations. Variations in the relative importance of sCIs therefore shape the sensitivity of LSO2 to its controlling factors. To systematically diagnose the atmospheric conditions under which sCIs play a significant role in SO₂ oxidation, and to elucidate how this role modulates the precursor sensitivity of LSO2, we constructed dedicated surrogate models for μsCIs and LSO2. Their feature sets capture the key controls on both pathways (see Sect. 2.3), and the models were trained on a large ensemble of constrained AtChem simulations spanning atmospheric conditions representative of anthropogenically and biogenically influenced environments. Because photolysis exerts decisive control over OH production, daytime (08:00–18:00 LT) and nighttime (22:00–05:00 LT) conditions were analyzed separately.

Sobol sensitivity analysis was applied to identify the dominant atmospheric controls on μsCIs and to quantify the extent to which each feature exerts its influence independently or through interaction with other features during the daytime period (Fig. 4a). Here, the first-order index S1 measures the independent main-effect contribution of a single feature, whereas the total-order index ST additionally encompasses all higher-order interactions involving that feature; a markedly larger ST relative to S1 therefore indicates that a feature operates predominantly through coupling with other features rather than through its own variation alone. The analysis identifies ARI, O₃, alkene %, and VOCs as the dominant controls on μsCIs, with independent contributions ranked as ARI (S1=0.17) > alkene % (S1=0.16) > O₃ (S1=0.15) > VOCs (S1=0.13). RH ranks immediately behind (S1=0.09), while NO_x and NO₂ % register the weakest direct contributions (S1=0.03 and 0.04, respectively). The low-ARI tier (ARI =0) is dominated by ethene and propene, representative of typical urban anthropogenic emissions (Zhao et al., 2020); the mid-ARI tier (ARI =1) features an elevated proportion of but-2-ene, characteristic of industrial source environments or marine ecosystems (Giorio et al., 2022); and the high-ARI tier (ARI =2) is driven primarily by isoprene, representative of biogenic (Rhew et al., 2017) or petrochemical-influenced conditions (Guo et al., 2022). The alkene mixture proportions at each ARI level are detailed in Fig. S1. Comparing S1 and ST across all features reveals a clear differentiation in how each feature exerts its influence. For RH, ST≈S1 (ST=0.11), indicating negligible interaction effects; RH influences μsCIs almost entirely through its independent main effect. For ARI (ST=0.27), alkene % (ST=0.26), O₃(ST=0.22), and VOCs (ST=0.23), ST substantially exceeds S1, indicating that although their independent main effects dominate, non-negligible interaction effects are also present. Among these, ARI exhibits both the largest S1 and ST, reinforcing that alkene speciation not only exerts the strongest independent control on μsCIs but also acts as a key moderator of the effects of O₃, alkene %, and VOCs. The contrast is most pronounced for NO_x and NO₂ %: their S1 values account for less than half of their respective ST values (NO_x: ST=0.09; NO₂ %: ST=0.09), indicating that their influence on μsCIs is overwhelmingly mediated through interactions with other features rather than through direct action. This strong interaction dependence reflects the fact that the influence of NO_x and NO₂ % on μsCIs is conditional on the values of other features.

The directional effects of these features are further illustrated by the 2D PDPs (Fig. 4b–i). Hereafter, feature levels denote normalized values rather than the actual concentrations; corresponding time-varying concentrations are shown in Fig. S1. Among the features that directly govern LSO2,sCIs, ARI, O₃, VOCs, and alkene % exhibit mutually reinforcing positive effects on μsCIs, suggesting that conditions favorable for alkene ozonolysis simultaneously enhance the relative competitiveness of the sCI pathway. RH negatively affects μsCIs by suppressing the sCI+SO₂ pathway through enhanced sCI loss to H₂O/(H₂O)₂. Despite NO₂ being a known sCI scavenger, NO₂ % exhibits a synergistic co-enhancement with O₃ and VOCs on μsCIs. These synergistic effects are expected to arise from the influence of NO₂ % on OH, through its role in governing how NO_x is partitioned between radical termination and cycling (Sillman and He, 2002). A higher NO₂ fraction, at fixed total NO_x, is expected to reduce the NO available for HO₂/RO2→OH conversion, thereby suppressing the SO₂+OH oxidation channel more strongly than it scavenges sCIs, particularly under high-O₃ and high-VOCs conditions. Correspondingly, the higher the NO₂ %, the more strongly μsCIs increase with rising O₃ and VOCs. NO_x, by contrast, exerts predominantly suppressive interactions with O₃ and VOCs: μsCIs peaks at the lowest NO_x levels and declines sharply as NO_x increases only slightly from its minimum, before leveling off or increasing slightly at higher concentrations, such that μsCIs at the highest NO_x level remains well below the peak observed at the lowest NO_x level. The sensitivity of μsCIs to O₃ and VOCs is modulated by NO_x levels. At the lowest NO_xlevel, increases in O₃ and VOCs produce the largest increments in μsCIs. Across the remainder of the NO_x range, raising O₃ or VOCs from their minimum to maximum levels increases μsCIs by only 0.03–0.04. The effect of NO_x on μsCIs arises primarily from its control over the steady-state OH concentration: at extremely low NO_x level, radical recycling efficiency is greatly diminished, leading to suppressed OH; at excessively high NO_x levels, OH is likewise suppressed, but through accelerated termination reactions between radicals and NO_x. Under both conditions, the attenuation of OH-mediated SO₂ oxidation shifts a greater share of the total oxidation burden to sCIs, resulting in elevated μsCIs.

Taken together, daytime μsCIs tends to be elevated under atmospheric conditions characterized by high O₃ concentrations, abundant VOCs, a large alkene fraction, and relatively low RH. With respect to NO_x, μsCIs is only appreciably enhanced under extremely low NO_x levels; across the remainder of the NO_x range, its influence on μsCIs is comparatively weak. This finding is consistent with previous studies reporting that sCI chemistry plays a more prominent role in SO₂ oxidation in biogenic-rich forested and rural environments (Kim et al., 2015) than in polluted urban settings (Dada et al., 2020). Among the identified controls, O₃, VOCs, alkene %, and ARI, which collectively characterize conditions favorable for sCI formation, not only directly promote LSO2,sCIs but also exhibit pronounced synergistic positive effects on μsCIs. This pattern implies that, as these variables increase, OH increases less strongly than sCI production and may even decrease modestly. Consequently, although O₃ and alkenes jointly initiate the chemical processes leading to the formation of both OH and sCIs, their effects on the OH-mediated and sCI-mediated SO₂ oxidation pathways differ in both magnitude and direction. Under most daytime conditions, the OH pathway dominates SO₂ oxidation, such that the sensitivity of LSO2 to precursor species is primarily shaped by how those precursors affect OH. However, as shown by the NO_x dependence of μsCIs, the response of OH to precursor perturbations is itself condition-dependent, exhibiting a non-monotonic relationship with NO_x. This gives rise to distinct OH response patterns under high- and low-μsCIs conditions and, by extension, distinct sensitivities of LSO2 to its precursors. To quantify the magnitude of these differences, the dataset was partitioned into high- and low-μsCIs subsets based on the median daytime μsCIs value (1.1 %), and the relationship between each feature and LSO2 was characterized separately for each subset.

Figure 5 illustrates how total gas-phase SO₂ oxidation rate varies with O₃, VOCs, and alkene % across the high- and low-μsCIs regimes. The mean ICE curves show that LSO2 increases monotonically with all three features under both regimes; however, the response is systematically amplified under high-μsCIs conditions, with the mean curve exhibiting a steeper and more sustained increase across the full feature range. Beyond the mean response, the spread of individual ICE curves provides insight into response heterogeneity, namely, the extent to which the effect of a given feature on LSO2 varies across different atmospheric conditions. Notably, negative LSO2 responses to increases in VOCs and alkene % are observed under extremely low NO_x level. To quantify this directional heterogeneity, we computed the fraction of individual ICE curves exhibiting a net negative slope between the minimum and maximum feature values, termed the “neg-slope fraction”. For O₃, positive associations with LSO2 are nearly universal in both regimes, with a neg-slope fraction of 0 % under the high-μsCIs regime and 9 % under the low-μsCIs regime. For alkene %, the neg-slope fraction increases from 7 % under the high-μsCIs regime to 21 % under the low-μsCIs regime. A similar pattern is evident for VOCs, with the neg-slope fraction rising from 21 % under high-μsCIs to 35 % under low-μsCIs regimes. This regime contrast warrants further examination. At an extremely low NO_x level, high μsCIs is associated with abundant alkene concentrations. Although higher alkene concentrations may promote radical termination and thereby suppress OH and reduce LSO2, the high-μsCIs subset nevertheless exhibits a smaller neg-slope fraction than the low-μsCIs subset. This suggests that the alkene ozonolysis pathway offsets part of the OH suppression caused by enhanced radical termination, thereby dampening the negative LSO2 response. At moderate-to-high NO_x levels, positive LSO2 responses to increases in VOCs, alkene %, and O₃ dominate and are considerably stronger under the high-μsCIs regime than under the low-μsCIs regime. This amplified sensitivity likely reflects the fact that high-μsCIs regime is associated with abundant alkenes, which simultaneously promote OH propagation through RO_x cycling pathway and drive alkene ozonolysis.

In summary, LSO2 exhibits both positive and negative responses to VOCs and alkene % across the full scenario space, with the key distinction being that under the high-μsCIs regime, negative responses are less frequent and positive responses are stronger. To clarify the mechanistic basis of this contrast, we examined the OH and sCI budgets for two representative scenarios at normalized NO_x levels of 0 and 0.5 (Fig. 6a, b). This analysis was used to explain why negative LSO2 responses to increases in VOCs and alkene % are more frequent in the low-μsCIs regime. OH production is partitioned into initiation (∑OH_new), which encompasses all primary OH production via photolysis and alkene ozonolysis (Sheehy et al., 2010), and propagation (OH_propag), defined as the rate of HO2→OH conversion. At an extremely low NO_x level (NO_x, norm = 0), the ozonolysis pathway accounts for 39.65 % of ∑OH_new (see Sect. S5 for detailed calculations), and the ratio OH_propag/∑OH_new is 3.67, indicating that radical propagation contributes approximately 3.7 times as much OH as primary initiation. At a moderate NO_x level (NO_x, norm =0.5), the ozonolysis share of ∑OH_new decreases to 29.28 %, whereas the OH_propag/∑OH_new ratio rises to 6.96, reflecting substantially enhanced radical cycling efficiency, as evidenced by the HO2→OH conversion rate reaching 7.04×108 molec. cm⁻³ s⁻¹. At an extremely low NO_x level, the RO_x recycling is severely suppressed, thus primary OH initiation contributes a correspondingly larger fraction to the total OH budget, and the ozonolysis pathway in turn accounts for a larger share of OH production. Under this condition, the contribution of alkene ozonolysis to OH production can partly offset the suppressive effect of enhanced radical termination on OH, which explains why the neg-slope fraction for LSO2 is smaller in the high-μsCIs subset than in the low-μsCIs subset. At a moderate NO_x level, OH is sustained predominantly through radical cycling rather than through photolysis or ozonolysis, and the increase in NO_x additionally enhances HONO photolysis, further diminishing the relative contribution of ozonolysis to OH generation. Under these conditions, perturbations in VOCs and alkene % influence LSO2 primarily through their modulation of OH propagation. Because high-μsCIs conditions at this NO_x level are associated with abundant alkenes, both the RO_x cycling and ozonolysis pathways are strongly activated, and LSO2 therefore exhibits a pronounced positive response to increases in precursor concentrations.

The nighttime Sobol sensitivity indices (Fig. 7a) reveal controls on μsCIs that differ markedly from those identified during the day. ARI, RH, and NO_x emerge as the dominant controls, with independent contributions ranked as ARI (S1=0.21) > RH (S1=0.19) > NO_x (S1=0.17). VOCs (S1=0.13), alkene % (S1=0.11), and O₃ (S1=0.08) rank immediately behind, while NO₂ % exerts a negligible direct influence (S1=0.002). Comparing S1 and ST across all features, ST only slightly exceeds S1 for most features, indicating that independent main effects dominate and interaction effects are limited, with the total-order ranking following ARI (ST=0.25) > RH (ST=0.22) > NO_x (ST=0.20) > VOCs (ST=0.17) > alkene % (ST=0.14) > O₃ (ST=0.10). NO₂ % retains the smallest ST (ST=0.02), reinforcing that its regulatory effect on μsCIs at night is negligible. The close agreement between ST and S1 across most features at night stands in sharp contrast to the daytime results, where ST substantially exceeded S1 for several key features. This collapse of interaction effects reflects a fundamental mechanistic shift: in the absence of photolysis, the primary OH initiation pathway is alkene ozonolysis, which is simultaneously the sole sCI formation pathway. Perturbations to precursors therefore affect both oxidation pathways in the same direction and with similar magnitude, suppressing the conditional interactions that characterize the daytime sensitivity structure. This finding is broadly consistent with previous studies demonstrating that Criegee intermediate chemistry constitutes a non-negligible OH source under dark or low-light conditions (Khan et al., 2018). The rise of RH from a minor factor during the day to the second-ranked control at night reflects the substantially lower OH concentrations characteristic of nocturnal conditions, which elevate the relative contribution of sCIs to gas-phase SO₂ oxidation (Kukui et al., 2021) and thereby amplify the suppressive effect of H₂O/(H₂O)₂ on μsCIs. The contrasting behavior of NO_x and NO₂ % between day and night also warrants attention. At night, photolytic regeneration of NO from NO₂ is effectively absent; instead, NO within NO_x is oxidized to NO₂ through reactions with O₃ and peroxy radicals, leading to progressive NO₂ accumulation. This enhances the termination reaction between NO₂ and OH, suppressing steady-state OH and indirectly elevating μsCIs. As a result, nighttime μsCIs is governed primarily by total NO_x abundance rather than by the NO/NO₂ partitioning, which explains why NO₂ % exerts a negligible effect at night.

The directional effects of these features are further elucidated by the 2D PDPs (Fig. 7b–i). ARI, O₃, VOCs, and alkene % exhibit mutually reinforcing positive effects on μsCIs, consistent with their roles as sCI precursors: conditions favorable for LSO2,sCIs simultaneously enhance the relative competitiveness of the sCI oxidation pathway. RH exerts a pronounced negative effect on μsCIs. With respect to NO_x, μsCIs reaches a locally elevated value (approximately 0.1) at the lowest NO_x level, then drops sharply as NO_x increases only slightly from its minimum, before rising significantly and monotonically across the remainder of the range to reach its global maximum (approximately 0.16) at the highest NO_x level, such that a strong positive relationship between NO_x and μsCIs prevails across most of the range. This near-monotonic behavior reflects the role of NO_x in modulating steady-state OH through radical termination, as described above.

Taken together, nighttime μsCIs tends to be elevated under atmospheric conditions characterized by high O₃ concentrations, abundant VOCs, a large alkene fraction, and relatively low RH. With respect to NO_x, the highest μsCIs values occur under elevated NO_x levels, although a smaller enhancement is also evident under extremely low NO_x conditions. This is consistent with a previous study reporting that elevated NO_x levels in power plant environments at night are highly conducive to a large sCI contribution fraction (Meidan et al., 2019). Furthermore, ARI, O₃, VOCs, and alkene %, which collectively characterize conditions favorable for sCI formation, not only strongly promote LSO2,sCIs but also exert pronounced synergistic effects on μsCIs. This pattern indicates that O₃ and alkenes do not affect the OH- and sCI-mediated SO₂ oxidation pathways to the same extent. Notably, unlike during the day, when OH is sustained primarily by radical propagation, nocturnal OH production is more strongly linked to primary initiation, alkene ozonolysis, because the absence of photolysis limits OH production from photolytic sources and radical recycling. Alkene ozonolysis is also the sole formation pathway for sCIs. Therefore, differences in the sensitivity of LSO2 across μsCIs regimes are expected to reflect differences in the strength of the alkene ozonolysis pathway. To examine these differences, the dataset was partitioned into high- and low-μsCIs subsets based on the median nighttime μsCIs value (8.0 %), and the relationship between each feature and LSO2 was characterized separately for each subset.

Figure 8 shows how LSO2 responds to precursor perturbations across the high-μsCIs and low-μsCIs regimes at night. The mean ICE curves reveal that LSO2 increases monotonically with all three features under both regimes; however, the response is systematically enhanced under the high-μsCIs regime, with the mean curve exhibiting a steeper and more sustained increase across the full feature range. Beyond the mean response, the spread of individual ICE curves provides insight into response heterogeneity across different atmospheric conditions. For O₃, near-universal positive associations with LSO2 are observed in both regimes, with neg-slope fractions of 1 % and 3 % under the high- and low-μsCIs regimes, respectively, indicating that O₃ consistently promotes LSO2 regardless of the μsCIs regime. For alkene %, the neg-slope fraction increases from 1 % under the high-μsCIs regime to 10 % under the low-μsCIs regime. The contrast is most pronounced for VOCs, for which the neg-slope fraction rises from 5 % under the high-μsCIs regime to 29 % under the low-μsCIs regime, with the excess negative responses in the low-μsCIs regime arising predominantly from high-NO_x scenarios.

To elucidate the role of alkene ozonolysis in driving these response differences, we examined the OH and sCI budgets for two representative high-NO_x scenarios corresponding to the low-μsCIs (μsCIs=0.008) and high-μsCIs (μsCIs=0.14) regimes, respectively (Fig. 9a, b). Under the low-μsCIs scenario, alkene ozonolysis accounts for 30.18 % of ∑OH_new, which is 5.56×105 molec. cm⁻³ s⁻¹. In contrast, under the high-μsCIs scenario, alkene ozonolysis contributes 94.24 % of ∑OH_new, which reaches 2.29×107 molec. cm⁻³ s⁻¹. These results show that, when alkene ozonolysis is efficient at night, it acts not only as the sole formation pathway for sCIs but also as the dominant OH initiation pathway. When alkene ozonolysis is weak, the ratio OH_propag/∑OH_new is 16.23, indicating that OH is sustained predominantly through radical cycling. In this regime, OH initiation is supplied primarily by photolysis in the early morning hours, with a smaller contribution from ozonolysis. Reducing total VOCs does not affect the photolytic OH initiation source, but decreases the OH–to–RO₂ flux and thus weakens OH loss through VOC oxidation. Provided that radical recycling efficiency changes little, this reduction in OH reactivity can slightly increase steady-state OH and LSO2,OH. Because the alkene-derived sCI flux is negligible in this regime, ΔLSO2,sCIs is close to zero. The OH-mediated response can therefore dominate, producing a net increase in LSO2 as VOCs decrease (a negative slope). Conversely, when alkene ozonolysis is strong, it simultaneously serves as the dominant OH initiation source and the principal sCI formation pathway. The ratio OH_propag/∑OH_new decreases to 2.68, far below that under weak ozonolysis, indicating a much greater relative contribution of initiation to OH. Under these conditions, VOC perturbations influence the OH- and sCI-mediated SO₂ oxidation pathways in the same direction, thereby reducing the occurrence of negative LSO2 responses. Between the two scenarios, the rates of ozonolysis-driven sCI and OH formation increase by factors of 127.5 and 123.3, respectively. Accordingly, the rate at which sCIs form H₂SO₄ increases by a factor of 133, whereas the rate at which OH forms H₂SO₄ increases by only a factor of six. This difference arises because OH reacts with alkenes and is incorporated into the RO_x cycle, such that part of the additional OH production supports radical cycling rather than directly increasing steady-state OH. The contrasting neg-slope fractions for VOCs and alkene % can thus be explained by their distinct chemical roles. Reducing alkene % simultaneously weakens a primary OH initiation source and the sCI formation pathway, such that LSO2 declines almost universally. By contrast, reducing total VOCs primarily lowers OH reactivity rather than suppressing OH initiation under alkene-poor conditions corresponding to the low-μsCIs regime. The resulting increase in OH-mediated oxidation can outweigh the negligible change in the sCI pathway, producing a negative LSO2 response (neg-slope =29%).

To validate the predictive capability of the surrogate model developed in Sect. 3.2 for μsCIs, and to evaluate how the sensitivity of SO₂ oxidation to its precursors depends on the relative contributions of sCIs in ambient air, we selected a summer episode in Wuhai City as a real-atmosphere validation case. Figure 10 presents the constrained simulation results derived from AtChem–MCM v3.3.1, including time series of sulfuric acid concentrations (H₂SO₄–AtChem) and the daytime- and nighttime-averaged fractional contributions of sCIs to total SO₂ oxidation (μsCIs–AtChem) over the period 1 June to 15 July 2021. The corresponding pollutant mixing ratios and meteorological parameters are shown in Fig. S3. SO42- denotes the ambient particulate sulfate mass concentrations measured concurrently by online ion chromatography. The term “μsCIs–surrogate model” represents the daytime- and nighttime-averaged μsCIs predictions generated by the surrogate model described in Sect. 3.2. The strong agreement (R2=0.75) between the surrogate predictions (μsCIs–surrogate model) and the explicit AtChem simulations (μsCIs–AtChem) demonstrates the robust predictive performance of the constructed machine learning surrogate for μsCIs.

To evaluate whether ambient SO42- concentrations serve as a reliable proxy for gas-phase H₂SO₄ production during the target episode, an XGBoost model was trained on a comprehensive long-term observational dataset spanning 9 October 2019 to 30 June 2022 (summary statistics of all variables are provided in Table S4), with hourly SO42- concentration as the target variable. The feature set included PM_2.5, NO3-, SO₂, O₃, VOCs, alkene %, NO_x, NO₂ %, RH, wind speed (WS), and Fe. Training over this extended period ensures that the model captures the full range of variability in sulfate formation, including seasonal cycles, episodic pollution events, and varying meteorological regimes, thereby establishing a representative and well-generalized mapping between precursor conditions and SO42-. SHAP values were then extracted exclusively for the target episode (1 June to 15 July 2021) to attribute feature contributions during this specific period. As shown in Fig. 11a, the three highest-ranked features are NO3-, SO₂, and PM_2.5, all of which exhibit clear positive correlations with SO42-. The elevated NO3- co-occurs with SO42-, together with the concurrent increase in PM_2.5, consistent with the hallmark of secondary inorganic aerosol formation (Gao et al., 2021). The strong positive SHAP contribution of SO₂ directly corroborates its role as the primary precursor for SO42- production. Notably, WS also exerts a discernible positive contribution, suggesting a degree of regional transport influence during this episode, although its impact remains secondary to in situ chemical production. By contrast, RH shows no significant positive correlation with SO42- and ranks relatively low in feature importance. Fe, a key catalyst for aqueous-phase SO₂ oxidation via Fenton-type chemistry (Ye et al., 2023), shows no clear positive association with SO42-, with elevated ambient Fe concentrations not corresponding to enhanced sulfate formation. Taken together, these results indicate that aqueous-phase oxidation was not the dominant SO42- formation pathway during the target episode. Meanwhile, O₃, VOCs, and alkene %, which serve as key proxies of gas-phase oxidant pathways, exhibit positive correlations with SO42-, providing evidence that gas-phase oxidation constituted the primary sulfate formation pathway during this period. On this basis, ambient SO42- concentrations can be regarded as a reliable observational proxy for the variability in total gas-phase H₂SO₄ production during the target episode.

To further examine whether the sensitivity of SO42- to key precursors is consistent with the regime-dependent behavior of LSO2 identified in Sect. 3.2, the target episode was partitioned into high- and low-μsCIs subsets for daytime and nighttime periods separately, using the same classification thresholds applied in Sect. 3.2 (daytime: 1.1 %; nighttime: 8.0 %). SHAP values for O₃, VOCs, and alkene % were extracted for each subset and compared. During the daytime (Fig. 11b), the high-μsCIs subset exhibits systematically amplified SHAP responses relative to the low-μsCIs subset across all three features. O₃ shows the most pronounced regime contrast: in the high-μsCIs subset, high feature values (red) are associated with distinctly larger positive SHAP contributions and a considerably wider spread, whereas the corresponding responses in the low-μsCIs subset are substantially attenuated. VOCs and alkene % follow the same pattern, with high feature values driving larger positive SHAP contributions under high-μsCIs conditions. This daytime regime contrast is consistent with the finding in Sect. 3.2 that the sensitivity of SO₂ oxidation to O₃, VOCs, and alkene % is amplified under high-μsCIs conditions, providing observational corroboration of that mechanistic result. At night (Fig. 11c), VOCs and alkene % exhibit stronger positive SHAP contributions to SO42- in the high-μsCIs subset, consistent with their roles in promoting both sCIs and OH formation through nocturnal alkene ozonolysis. By contrast, O₃ exhibits negative SHAP contributions in both subsets, which can be attributed to the distinct behavior of O₃ at night: nocturnal O₃ is primarily of advective origin rather than in situ photochemical production, and elevated O₃ concentrations are often associated with suppressed local NO levels due to rapid O₃–NO titration. Taken together, the regime-dependent SO42- sensitivity patterns observed during the target episode (Fig. 11b, c) provide observational validation for the mechanistic findings derived from the AtChem-based surrogate model simulations in Sect. 3.2, confirming that these findings are manifested in ambient atmospheric measurements. This cross-validation between model-diagnosed sensitivity and observation-based attribution reinforces the conclusion that under high-μsCIs regimes, alkene-targeted emission control strategies can effectively reduce sCIs and suppress the total SO₂ oxidation rate, while rarely triggering a rebound in OH-driven oxidation pathways.