Modeling atmospheric sulfate oxidation chemistry via the oxygen isotope anomaly using the Community Multiscale Air Quality Model (CMAQ)

Atmospheric sulfate formation influences climate and air quality, yet its chemical pathways remain difficult to constrain. This study utilizes the oxygen isotope anomaly (Δ¹⁷O) of sulfate aerosol (ASO₄) as a tracer to distinguish formation processes. This work presents a simulation of Δ¹⁷O(ASO₄) within the contiguous United States, conducted over full annual cycles, which enables the quantification of seasonal and spatial patterns of sulfate oxidation pathways and their response to major emission reductions, for the first time at this scale and temporal coverage. In 2019, Δ¹⁷O(ASO₄) values were predicted to be below 1 ‰ in the Gulf Coast, indicating acidic, ASO₄-rich conditions dominated by S(IV) + H₂O₂ oxidation, while values above 2 ‰ in the West suggested less acidic conditions, leading to enhanced ASO₄ production via S(IV) + O₃ oxidation. Peak Δ¹⁷O(ASO₄) values of ∼4.5 ‰ in April across the Western US reflected O₃-driven ASO₄ formation during high ammonia (NH₃) emissions from fertilization. Between 2006 and 2019, mean Δ¹⁷O(ASO₄) was predicted to increase by up to 2 ‰, driven by declining sulfur dioxide (SO₂) emissions from regulatory measures. Model comparisons with historical measurements show reasonable agreement in the acidic southeastern US (RMSE = 0.20 ‰, Baton Rouge, LA). However, the model overpredicts Δ¹⁷O(ASO₄) in the Western US with RMSE values of 0.36 ‰ (La Jolla, CA) and 1.9 ‰ (White Mountain Research Center, CA). This overestimation suggests an excessive model response to aqueous S(IV) + O₃ reactions. These findings underscore the diagnostic potential of Δ¹⁷O(ASO₄) for assessing sulfate formation mechanisms and pinpointing shortcomings in chemical transport models. However, Δ¹⁷O(ASO₄) observations across the United States remain exceedingly limited, with most available data dating back to the late 1990s and early 2000s, highlighting the need for renewed measurement efforts.

1 Introduction

Atmospheric sulfate (SO${}_{\mathrm{4}}^{\mathrm{2}-}$) plays a critical role in climate and air quality. As a major component of aerosols, SO${}_{\mathrm{4}}^{\mathrm{2}-}$ influences aerosol pH, atmospheric chemistry, and precipitation acidity (Calvo et al., 2013; Weber et al., 2016). SO${}_{\mathrm{4}}^{\mathrm{2}-}$ aerosols (ASO₄) significantly contribute to radiative forcing by scattering sunlight and serving as cloud condensation nuclei, which impacts cloud properties and the Earth's radiation balance (Lohmann and Feichter, 1997; Jones et al., 1994; Kaufman and Tanré, 1994). The anthropogenic influence on the ASO₄ budget, primarily from fossil fuel combustion, has been widely documented, contributing to regional and global climate effects (Langner et al., 1992; Smith et al., 2011). The presence of ASO₄ alters cloud albedo and lifetime, affecting regional and global climate patterns through indirect radiative forcing (Jones et al., 1994; Haywood and Boucher, 2000). Additionally, the health impacts of ASO₄-containing particles underscore their importance in air quality management (Reiss et al., 2007). The formation of ASO₄ is influenced by complex interactions with secondary organic aerosols (SOA) and other atmospheric components. Emerging research highlights the significant role of highly oxygenated organic molecules (HOMs) in enhancing ASO₄ formation under humid conditions (Hallquist et al., 2009; Bianchi et al., 2019). These interactions highlight the complex connections between ASO₄, atmospheric chemistry, and climate dynamics. Despite a 70 % reduction in ASO₄ concentrations over the past 15 years, aerosol acidity has remained high, primarily due to the buffering effect of ammonia partitioning between the gas and particle phases (Weber et al., 2016). This persistent acidity impacts both air quality and health, as it enhances the solubility of harmful metals and promotes acid-catalyzed chemical reactions in the atmosphere.

Despite their significance, atmospheric chemistry models often face significant challenges in accurately reproducing ASO₄ concentrations, potentially due to uncertainties surrounding ASO₄ formation mechanisms (Harris et al., 2013; Li et al., 2020; Vannucci et al., 2024). ASO₄ can originate from both primary emissions and secondary formation. Primary sources include natural emissions, such as sea salt, volcanic eruptions, and soil dust (Alexander et al., 2005; Arimoto et al., 2001; Savarino et al., 2003), as well as anthropogenic emissions from fossil fuel combustion (Langner et al., 1992; Smith et al., 2011; Sofen et al., 2011). Secondary ASO₄ formation involves complex oxidation processes that occur in both the gas phase and the aqueous phase. In the gas phase, sulfur dioxide (SO₂) is oxidized by hydroxyl radicals (•OH), producing sulfuric acid (H₂SO₄). This sulfuric acid can either condense to form new particles or add mass to existing aerosols. The rate of this process is highly dependent on environmental conditions such as temperature and pH, which introduces significant uncertainties in predicting ASO₄ concentrations (Seigneur and Saxena, 1988). For instance, Vannucci et al. (2024) demonstrated that temperature plays a crucial role in modulating ASO₄ aerosol concentrations, particularly during summertime pollution episodes, where aerosol composition and temperature sensitivity can significantly impact model accuracy. Aqueous-phase ASO₄ formation occurs when dissolved sulfur species (S(IV) = SO₂⋅ H₂O + HSO${}_{\mathrm{3}}^{-}+$ SO${}_{\mathrm{3}}^{\mathrm{2}-}$) are oxidized by molecules including ozone (O₃), hydrogen peroxide (H₂O₂), and oxygen, catalyzed by transition metal ions (TMI) (e.g., Fe³⁺ and Mn²⁺). The role of other oxidants, such as hypohalous acids (HOX, X= Br and Cl), is increasingly recognized, particularly in marine boundary layers (Chen et al., 2016; Ishino et al., 2017). Chen et al. (2016) highlighted the significant contribution of HOX in ASO₄ formation in the remote marine boundary layer, estimating that 33 %–50 % of ASO₄ is produced via this pathway. This suggests that HOX may play a larger role in ASO₄ formation than previously recognized. Additionally, aqueous oxidation of S(IV) induced by nitrogen dioxide (NO₂) has also been proposed as a potential pathway, particularly under polluted and low-oxidant wintertime conditions (Sarwar et al., 2013). Although generally less important than H₂O₂ and O₃ oxidation, this pathway may contribute to ASO₄ formation in specific environments and conditions.

Sensitivity analyses have shown that the rate of aqueous-phase ASO₄ formation is particularly influenced by pH, oxidant availability, and environmental conditions, further complicating ASO₄ modeling (Pandis and Seinfeld, 1989). Harris et al. (2013) showed that TMI-catalyzed oxidation can dominate under specific conditions, particularly in the presence of coarse dust particles, significantly altering ASO₄ formation rates in cloud droplets. Similarly, Li et al. (2020) highlighted the critical role of TMI-driven SO₂ oxidation during haze episodes, where such pathways can account for up to 50 % of ASO₄ production under polluted conditions. Heterogeneous reactions on aerosol surfaces may also play a critical role in ASO₄ formation (Harris et al., 2013). These surface reactions involve the interaction of gaseous sulfur species with aerosols, significantly influencing ASO₄ formation and elevating the complexity of predicting ASO₄ concentrations. Meidan et al. (2019) emphasized the importance of Criegee intermediates (CIs) in ASO₄ formation, particularly in nocturnal power plant plumes, where SO₂ is oxidized under conditions with minimal photochemical activity. This study revealed that CIs could account for a significant portion of ASO₄ production in the absence of sunlight. Additionally, Liu et al. (2019) examined the role of stabilized Criegee intermediates (sCIs) in ASO₄ formation in the Beijing-Tianjin-Hebei region, showing that under certain atmospheric conditions, sCI-driven SO₂ oxidation can contribute substantially to secondary ASO₄ production, adding another layer of complexity to ASO₄ formation models. These interactions highlight the challenges in modeling ASO₄ concentrations, as heterogeneous reactions, TMIs, and Criegee intermediates all contribute to the uncertainty in atmospheric ASO₄ predictions.

The use of oxygen isotope mass-independent fractionation (${\mathrm{\Delta }}^{\mathrm{17}}\mathrm{O}={\mathit{\delta }}^{\mathrm{17}}\mathrm{O}-\mathrm{0.52}\times {\mathit{\delta }}^{\mathrm{18}}\mathrm{O}$) has emerged as a promising tool to explore atmospheric ASO₄ formation pathways (Alexander et al., 2004; Barkan and Luz, 2003; Kaiser et al., 2004; Michalski et al., 2003; Morin et al., 2007; Savarino et al., 2007; Walters et al., 2019; Weston, 2006). This isotopic indicator is crucial for tracking ASO₄ formation, providing a refined tool for model evaluation and prediction. This is because Δ¹⁷O has distinct values associated with different oxidation processes, making it a powerful tool in understanding ASO₄ production mechanisms. The dominant source of Δ¹⁷O in the lower atmosphere derives from O₃ formation. The average Δ¹⁷O(O₃) near the surface is approximately 26 ‰ (Vicars and Savarino, 2014). This contrasts with other tropospheric oxidants, which have Δ¹⁷O values near 0 ‰. Hydrogen peroxide (H₂O₂) has a Δ¹⁷O value of about 1.6 ‰ due to the influence of O₃ involved in H₂O₂ formation (Savarino and Thiemens, 1999). Laboratory studies have shown that oxidants will proportionally transfer their Δ¹⁷O values into the ASO₄ product. Table 1 summarizes the Δ¹⁷O ranges associated with major tropospheric ASO₄ production pathways based on oxygen isotopic mass balance (Alexander et al., 2005, 2009; Ishino et al., 2017; Savarino et al., 2000; Walters et al., 2019). The gas-phase oxidation of SO₂ by OH and metal-catalyzed O₂ oxidation yields Δ¹⁷O(ASO₄) values near 0 ‰, indicating a negligible transfer of the Δ¹⁷O signature. Similarly, aqueous-phase oxidation of SO₂ by hypohalous acids (HOX) results in Δ¹⁷O(ASO₄) values around 0 ‰. In contrast, aqueous-phase oxidation involving H₂O₂ and O₃ exhibits significantly higher Δ¹⁷O values. H₂O₂ oxidation produces Δ¹⁷O(ASO₄) values around 0.8 ‰, while O₃ oxidation results in Δ¹⁷O(ASO₄) values of about 6.5 ‰. These distinctions enable the ability to track ASO₄ formation.

Previous studies have utilized Δ¹⁷O(ASO₄) observations to evaluate the impact of anthropogenic emissions on ASO₄ production routes. In polluted regions, anthropogenic emissions of metals such as Fe³⁺ and Mn²⁺ enhance O₂-catalyzed ASO₄ formation, particularly in the Northern Hemisphere during winter. This metal-catalyzed ASO₄ formation can suppress ASO₄ production via O₃ and H₂O₂ pathways, impacting Δ¹⁷O(ASO₄) values and complicating model predictions (Savarino et al., 2000). Furthermore, ship emissions, which have been underrepresented in atmospheric models, significantly contribute to ASO₄ source in marine environments. Triple-oxygen isotope measurements suggest these emissions play a larger role in ASO₄ production than previously recognized, with implications for air quality and climate modeling (Dominguez et al., 2008). To fully utilize the diagnostic potential of Δ¹⁷O(ASO₄), a comprehensive model framework is essential for interpreting ASO₄ formation. Previous models, such as GEOS-Chem, have incorporated Δ¹⁷O tracking to investigate ASO₄ formation pathways, highlighting the growing importance of metal-catalyzed O₂ oxidation in polluted regions, which surpasses the traditional O₃ and H₂O₂ pathways (Sofen et al., 2011). Despite rising tropospheric O₃ levels since preindustrial times, Δ¹⁷O(ASO₄) values in the Arctic have declined due to enhanced metal-catalyzed ASO₄ formation. Recent studies have applied Δ¹⁷O of ASO₄ in chemical transport models to explore long-term changes and regional processes, including GEOS-Chem simulations coupled with ice core observations (Hattori et al., 2021; Peng et al., 2023) and CMAQ applications in East Asia (Itahashi et al., 2022; Lin et al., 2025). These works highlight the diagnostic potential of Δ¹⁷O across diverse regions and timescales. Building upon these advances, our study presents the first CMAQ simulations of Δ¹⁷O(ASO₄) within the contiguous United States over full annual cycles for 2006 and 2019, allowing for the assessment of seasonal and spatial patterns of ASO₄ oxidation pathways in response to emission reductions.

2 Methods

2.1 Model Description and EQUATES 2019 Dataset

This study utilizes the CMAQ (Community Multiscale Air Quality) version 5.4 model to simulate ASO₄ formation and its Δ¹⁷O values across the contiguous United States (CONUS). The CMAQ model is configured with the cb6r5_ae7_aq chemical mechanism, which stands for Carbon Bond 6 revision 5, with aerosol 7 for standard cloud chemistry (Yarwood et al., 2010). This mechanism encompasses both gas-phase and aqueous-phase oxidation processes of SO₂, which are essential for accurately modeling ASO₄ formation. Specifically, it involves the oxidation of SO₂ by •OH in the gas phase and by H₂O₂ and O₃ in cloud droplets and aqueous environments. Cloud water pH in CMAQ is calculated dynamically within the default cloud chemistry module, which is based on the work of Walcek and Taylor (1986) and assumes instantaneous equilibrium among gas, aqueous, and ionic species. The pH is determined by the charge balance between dissolved acidic and basic ions. As S(IV) is oxidized to S(VI) and additional species are scavenged from interstitial aerosols, the pH evolves dynamically throughout cloud processing. The resulting pH fields respond to emissions and meteorological variability, directly governing the relative importance of the H₂O₂ and O₃ oxidation pathways for aqueous S(IV) oxidation. Previous evaluations have demonstrated that CMAQ accurately reproduces observed cloud droplet acidity, with differences generally within 0.5 pH units across multiple sites in the United States (Pye et al., 2020). The model's ability to capture these complex interactions facilitates a detailed assessment of ASO₄ dynamics under various atmospheric conditions (Appel et al., 2021).

The CMAQ simulations are based on the EQUATES (EPA's Air Quality Time Series Project) dataset, which provides a comprehensive and high-resolution emissions inventory derived from the 2017 National Emissions Inventory (NEI) (Benish et al., 2022; Foley et al., 2023). This dataset spans over two decades and provides detailed information on both natural and anthropogenic emissions, including those from industrial sources, vehicular traffic, power plants, and wildfires. It also accounts for seasonal and regional variations in emissions, enhancing the model's accuracy. The EQUATES 2019 dataset supplies critical inputs for CMAQ simulations, including emissions data, meteorological variables, as well as boundary and initial conditions, capturing pollutant variability across different seasons and regions.

Meteorological inputs for the CMAQ simulations were integrated from the Weather Research and Forecasting (WRF) model version 4.1.1. This integration provides detailed representations of temperature, wind speed, relative humidity, cloud cover, and precipitation rates. These meteorological factors influence cloud formation, pollutant dispersion, and oxidation processes. Boundary and initial conditions for the CMAQ model were sourced from EQUATES to ensure accurate representation of pollutant inflows and outflows at the edges of the modeling domain. The initial conditions were established through a spin-up period starting on 15 December 2018, providing accurate starting concentrations for the 2019 simulation period. The CMAQ simulations were conducted at a resolution of 12×12 km over the CONUS domain using the Hyperion high-performance computing cluster at the University of South Carolina. This advanced computing infrastructure enabled the processing of large datasets and the execution of complex simulations necessary for this study.

2.2 Implementation of the Sulfur Tracking Mechanism (STM)

The Sulfur Tracking Mechanism (STM), utilized in the CMAQ model, provides a detailed analysis of ASO₄ formation pathways in the atmosphere (Appel et al., 2021). It distinguishes between various aqueous-phase and gas-phase formation processes and assesses contributions from emissions, initial conditions, and boundary conditions, offering valuable insights into the roles of these factors in overall ASO₄ production (Table 2). The sulfur budget comprises 14 ASO₄ species (AE) and 1 nonreactive ASO₄ species (NR), as documented in the CMAQ repository (https://github.com/USEPA/CMAQ/blob/main/CCTM/src/MECHS/README.md, last access: 1 March 2025). The STM output includes hourly simulations of the 15 tagged ASO₄ species across the model domain, which were then aggregated into monthly averages to analyze spatial and temporal variations in ASO₄ production. STM allows for an efficient way for the model to distinguish the contributions of different chemical pathways and emission contributions to ASO₄. This approach also enables a seamless calculation of Δ¹⁷O of ASO₄.

A known bookkeeping bug in the STM implementation in CMAQ v5.4 resulted in the systematic underestimation of ASO₄ formed via the gas-phase SO₂ + OH pathway, despite the pathway being chemically active in the model. This issue has been documented by the CMAQ development team (https://github.com/USEPA/CMAQ/wiki/CMAQ-Release-Notes:-Process-Analysis-&-Sulfur-Tracking-Model-(STM), last access: 3 October 2025; U.S. Environmental Protection Agency, 2025) and has since been corrected in version 5.5. In our study, we fixed the issue by adjusting the call order of STM update routines in the sciproc.F module (matching the v5.5 fix) and ran the simulations using the corrected code. The updated STM diagnostic module used in this work is publicly available for reproducibility at: https://doi.org/10.5281/zenodo.14954960 (Fang, 2025).

Table 1 Major ASO₄ formation pathways and their associated Δ¹⁷O signatures. The pathways that are included in the CMAQ model using the cb6r5-ae7-aq mechanism are indicated.

Table 2 Overview of the ASO₄ species in the Sulfur Tracking Mechanism (STM) incorporated into CMAQ.

N/A: Not applicable

2.3 Calculation and Analysis of Δ¹⁷O(ASO₄)

The fractional contributions of each pathway, obtained from the STM, are used to calculate Δ¹⁷O(ASO₄) across different grid cells.

$$\begin{array}{}\text{(1)}& f_i\left(\text{lat},\text{lon},\text{height},\text{time}\right)={\displaystyle \frac{X_i}{\sum _{i=\mathrm{1}}^n{X}_i}}\end{array}$$

where f_i represents the fractional contribution of pathway i; X_i is the amount of ASO₄ produced by pathway i; and $\sum _{i=\mathrm{1}}^n{X}_i$ is the total Aitken mode and accumulation mode ASO₄ produced by all pathways except initial conditions and boundary conditions in each grid cell.

The gas-phase oxidation of SO₂ by •OH radical results in ASO₄ with no significant Δ¹⁷O enrichment (∼ 0 ‰). ASO₄ formed via aqueous-phase oxidation by O₃ has a Δ¹⁷O value of ∼ 6.5 ‰, indicating significant cloud chemistry processes. ASO₄ formed via aqueous-phase oxidation by H₂O₂ has a Δ¹⁷O value of ∼ 0.8 ‰. Metal-catalyzed oxidation of SO₂ by O₂ in metal-rich environments results in a Δ17O value of ∼ 0 ‰ and does not exhibit a transfer of mass-independent fractionation signature. Although previous studies reported slightly negative Δ¹⁷O values (−0.1 ‰; Hattori et al., 2021; Itahashi et al., 2022), this pathway contributes less than 10 % to total ASO₄ formation in our simulations, leading to a negligible (<0.01 ‰) effect on the modeled Δ¹⁷O(ASO₄). Therefore, it is approximated as 0 ‰ in this study. Heterogeneous reactions, such as those involving organic peroxides on aerosol surfaces, contribute to ASO₄ formation and are expected to have a Δ¹⁷O ∼ 0 ‰. Although the fractional contributions (f_i) include all ASO₄ formation pathways diagnosed by the Sulfur Tracking Mechanism (STM), only H₂O₂ and O₃ carry non-zero Δ¹⁷O signatures, all other pathways are assigned Δ¹⁷O ≈ 0 ‰. Therefore, the Δ¹⁷O(ASO₄) is calculated using the following equation:

$$\begin{array}{}\text{(2)}& \begin{array}{rl}{\mathrm{\Delta }}^{\mathrm{17}}\mathrm{O}\left({\mathrm{ASO}}_{\mathrm{4}}\right)& =f_{\mathrm{ASO}\mathrm{4}\mathrm{AQH}\mathrm{2}\mathrm{O}\mathrm{2}\mathrm{J}}\times \mathrm{0.8}\mathrm{‰}\\ & +f_{\mathrm{ASO}\mathrm{4}\mathrm{AQO}\mathrm{3}\mathrm{J}}\times \mathrm{6.5}\mathrm{‰}\end{array}\end{array}$$

where ASO4AQH2O2J represents ASO₄ formed through the oxidation of SO₂ by H₂O₂; ASO4AQO3J represents ASO₄ formed through oxidation by O₃; the constants 0.8 ‰ and 6.5 ‰ correspond to the characteristic Δ¹⁷O values for each pathway.

3 Results and Discussion

3.1 Predicted Fractional ASO₄ Formation and Δ¹⁷O(ASO₄) in the Contiguous US in 2019

ASO₄ production in the contiguous United States arises from a combination of primary emissions and secondary formation pathways, the latter being dominated by H₂O₂- and O₃-driven aqueous S(IV) oxidation and gas-phase oxidation of SO₂ via •OH (Fig. 1). These secondary reactions occur within cloud water, where SO₂ is oxidized by H₂O₂, O₃, and by O₂ (catalyzed by TMI). Compared to these dominant pathways, the TMI-catalyzed oxidation and reactions involving organic peroxides, such as methyl hydrogen peroxide (MHP) and peroxyacetic acid (PAA), have a minimal impact on ASO₄ production. While primary emissions contribute little overall, they exhibit localized hotspots in certain regions.

The fractional contributions of ASO₄ formation pathways demonstrate distinct spatial patterns that align with the predicted Δ¹⁷O(ASO₄) variability. The H₂O₂ pathway ($f_{\mathrm{S}\left(\mathrm{IV}\right)+{\mathrm{H}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{2}}}$) is the most dominant, accounting for 35.4±14.0 % of the ASO₄ formation across the domain (Fig. 1). This pathway is particularly influential in the Gulf Coast States, where abundant cloud cover and water vapor, acidic conditions (cloud pH <6), and high concentrations of H₂O₂ (Figs. S1, S2 in the Supplement) support the oxidation of S(IV) in cloud droplets. The highest $f_{\mathrm{S}\left(\mathrm{IV}\right)+{\mathrm{H}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{2}}}$ in these regions contribute to the low Δ¹⁷O(ASO₄) values below 1 ‰, due to the relatively lighter Δ¹⁷O(ASO₄) resulted from the H₂O₂ pathway (0.8 ‰). Gas-phase oxidation of SO₂ by •OH ($f_{{\mathrm{SO}}_{\mathrm{2}}+\mathrm{OH}}$) contributes to 34.4±9.5 of the ASO₄ production across the domain (Fig. 1), exhibiting clear seasonal variability under photochemically active conditions, with the highest contributions occurring in summer (up to ∼75 %) and lowest in winter (<25 %) (Fig. 5). The O₃ pathway ($f_{\mathrm{S}\left(\mathrm{IV}\right)+{\mathrm{O}}_{\mathrm{3}}}$) is the third most significant, contributing approximately 18.7±5.2 % to the ASO₄ formation across the domain (Fig. 1). The highest $f_{\mathrm{S}\left(\mathrm{IV}\right)+{\mathrm{O}}_{\mathrm{3}}}$ occurs in the Western States, due to the high O₃ concentration and high cloud pH (Fig. S1), which facilitates the aqueous oxidation of S(IV) by O₃. With a higher Δ¹⁷O(ASO₄) value resulting from the S(IV) + O₃ pathway of 6.5 ‰, the higher $f_{\mathrm{S}\left(\mathrm{IV}\right)+{\mathrm{O}}_{\mathrm{3}}}$ in these regions results in elevated Δ¹⁷O(ASO₄) values, typically above 2 ‰. Minor pathways, such as those involving TMI, MHP, and PAA, contribute 2.3±1.8 %, 0.25±0.25 %, and 0.17±0.12 %, respectively (Fig. 1), to ASO₄ formation across the US continuous domain. Primary ASO₄ emissions account for 8.7±6.4 % of total ASO₄ (Fig. 1), with substantial contributions originating from urban and industrial regions. High SO₂ emissions from anthropogenic activities in these areas elevate the role of primary ASO₄, and their impact on Δ¹⁷O(ASO₄) is correspondingly notable but limited to these localized hotspots.

Cloud pH is a critical determinant of ASO₄ formation pathways and Δ¹⁷O(ASO₄) values, with lower cloud pH favoring the H₂O₂ pathway and higher cloud pH supporting the O₃ pathway (Seigneur and Saxena, 1988; Fahey and Pandis, 2001). The concentration of ASO₄ plays a dominant role in lowering cloud pH, primarily due to its origin from sulfuric acid (H₂SO₄). As a strong acid, H₂SO₄ dissociates completely, releasing significant amounts of hydrogen ions (H⁺) and causing substantial acidification of cloud water. In regions such as the Northeast, Southeast, and Midwest, relatively high SO₂ emissions result in elevated ASO₄ concentrations, which further favor the dominance of the H₂O₂ oxidation pathway over O₃, thereby sustaining low Δ¹⁷O(ASO₄) values in the Northeast and Southeast (Fig. S1). This is due to the efficient conversion of dissolved S(IV) species to ASO₄, primarily through the aqueous S(IV) + H₂O₂ pathway under acidic cloud water. Frequent cloud occurrence and abundant oxidant availability accelerate SO₂ to ASO₄ production. These high ASO₄ levels contribute significantly to lowering cloud pH in these areas, creating an acidic environment (Fig. S1). In contrast, in the Western States, SO₂ emissions and ASO₄ concentrations are comparatively lower (Fig. S1). This results in reduced acidification and a higher cloud pH, as the influence of ASO₄ on the acidity of cloud water is diminished. Ammonium in cloud water (ANH₄), on the other hand, primarily acts as a buffering agent, mitigating the acidity caused by ASO₄ (Fig. S1). NH₃ reacts with H₂SO₄ to form (NH₄)₂SO₄ (ammonium sulfate), which reduces the availability of free H⁺ and partially neutralizes the acidification caused by ASO₄. However, the neutralizing capacity of ANH₄ is limited. In regions with high ASO₄ concentrations, such as the Northeast and Southeast, the buffering effect of ANH₄ is insufficient to fully counteract the strong acidity introduced by ASO₄. In the Midwest, where NH₃ emissions from agricultural activities, particularly fertilization, are significant, the resulting high concentrations of ANH₄ partially neutralize the acidity from ASO₄ (Fig. S1). This interaction raises cloud pH slightly, preventing extreme acidification (Fig. S1). Nevertheless, even in regions with abundant NH₃ emissions, cloud water pH typically remains acidic because of the dominant influence of ASO₄ and other atmospheric acids.

Figure 1 The annual fractional contribution from each ASO₄ formation pathway, along with Δ¹⁷O(ASO₄) across the contiguous US in the year 2019, based on CMAQ simulation.

Figure 2 The simulated Δ¹⁷O(ASO₄) values across the contiguous US for the year 2019 in each season (winter: January, spring: April, summer: July, fall: October), based on CMAQ simulation.

Figure 3 The fraction of ASO₄ formation from S(IV) + O₃ pathway across the contiguous US for the year 2019 in each season (winter: January, spring: April, summer: July, fall: October), based on CMAQ simulation.

Figure 4 The fraction of ASO₄ formation from S(IV) + H₂O₂ pathway across the contiguous US for the year 2019 in each season (winter: January, spring: April, summer: July, fall: October), based on CMAQ simulation.

Figure 5 The fraction of ASO₄ formation from SO₂ + OH pathway across the contiguous US for the year 2019 in each season (winter: January, spring: April, summer: July, fall: October), based on CMAQ simulation.

Figure 6 The fraction of ASO₄ from primary emission across the contiguous US for the year 2019 in each season (winter: January, spring: April, summer: July, fall: October), based on CMAQ simulation.

3.2 Seasonal Variation in Fractional ASO₄ Formation and Δ¹⁷O(ASO₄) in the Contiguous US in 2019

ASO₄ formation across the contiguous United States exhibits distinct seasonal patterns, shaped by varying contributions from the H₂O₂ and O₃ pathways, as well as shifts in cloud pH and precursor concentrations (Fig. S1). The isotopic composition of ASO₄, represented by Δ¹⁷O(ASO₄), reflects the dominance of specific pathways under different meteorological and chemical conditions. In regions with low cloud pH, the H₂O₂ pathway dominates, resulting in low Δ¹⁷O values (Figs. S1, 2). Conversely, areas with high cloud pH favor the O₃ pathway, resulting in high Δ¹⁷O values (Figs. S1, 2). Meanwhile, gas-phase SO₂+•OH oxidation (Fig. 5) acts as a consistent background process throughout the year. Its near-zero Δ¹⁷O signature moderates the contrast between H₂O₂- and O₃-dominated regimes, with a stronger influence during summer when photochemical activity peaks. Together with seasonal variations in cloud pH, ASO₄, and ANH₄ (Figs. S3, S4, S6), this process shapes the overall spatiotemporal pattern of Δ¹⁷O(ASO₄), reflecting the coupled effects of emissions, atmospheric chemistry, and meteorology.

In January, the Western States exhibit the highest Δ¹⁷O(ASO₄) values, exceeding 2 ‰ (Fig. 2). This is driven by the increased importance of the S(IV) + O₃ oxidation pathway (Fig. 3), supported by elevated cloud pH levels resulting from low ASO₄ concentrations (Figs. S3, S4). Conversely, the Gulf Coast States show the lowest Δ¹⁷O(ASO₄) values, typically below 1 ‰ (Fig. S1), primarily due to the prevalence of the H₂O₂ pathway (Fig. 4). This pathway dominates under low cloud pH conditions caused by high ASO₄ concentrations and limited ANH₄ levels (Figs. S3, S4, S6). In the Midwest, moderate Δ¹⁷O(ASO₄) values are shown, reflecting a balance between pathways. Elevated ANH₄ levels partially neutralize the acidity from high ASO₄ concentrations (Figs. S4, S6). This neutralization raises cloud pH (Fig. S3), slightly lowering the fractional contribution of the S(IV) + H₂O₂ pathway (Fig. 4) and contributing to the intermediate Δ¹⁷O(ASO₄) values. During this period, the SO₂+•OH pathway remains weak due to limited photochemical activity but provides a modest background effect that slightly reduces the isotopic contrast between H₂O₂- and O₃-dominated regimes.

In April, Δ¹⁷O values increase significantly, particularly in the Western States, rising above 3 ‰ (Fig. 2). This trend indicates an enhanced influence of the O₃ pathway, supported by elevated cloud pH and increased O₃ levels (Figs. 3, S3, S8). In contrast, the Gulf Coast States continue to exhibit low Δ¹⁷O values (<1.5 ‰) (Fig. 2), as the H₂O₂ pathway remains dominant due to persistently low cloud pH (Figs. 4, S3). This acidity is driven by high ASO₄ concentrations and low ANH₄ concentrations (Figs. S4, S6). Meanwhile, in the Midwest, cloud pH begins to rise as increased NH₃ levels, partially neutralizing the acidity from ASO₄ and shifting the balance of ASO₄ formation pathways (Figs. S3, S4, S7). The influence of the SO₂ + •OH pathway decreases relative to January (Fig. 5), as O₃ oxidation becomes more dominant, thereby exerting a weaker moderating effect on the isotopic contrast across regions.

In July, Δ¹⁷O values decrease in the Western States as the $f_{\mathrm{S}\left(\mathrm{IV}\right)+{\mathrm{H}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{2}}}$ increases compared to April (Fig. 2). This shift is driven by higher water vapor levels and increased cloud cover (Fig. S10), despite the regional consistently high cloud pH (Fig. S3). In the Gulf Coast States, Δ¹⁷O values remain low, below 1.5 ‰ (Fig. S1), highlighting the continued dominance of the H₂O₂ pathway (Fig. 4) under conditions of abundant water vapor (Fig. S10), frequent cloud cover (Fig. S11), and persistently low cloud pH (Fig. S3). In the Midwest, cloud pH continues to rise from April (Fig. S3), driven by increasing NH₃ concentrations (Fig. S7), which partially neutralize the acidity caused by ASO₄ (Fig. S4). This elevation in cloud pH enhances the activity of the O₃ pathway (Fig. S2), leading to an increase in Δ¹⁷O values compared to April. At the same time, the SO₂+•OH pathway reaches its maximum importance (Fig. 5) under strong photochemical conditions, offsetting the isotopic enrichment from O₃ oxidation and contributing to the relative decrease in Δ¹⁷O(ASO₄) compared to April.

In October, Δ¹⁷O values in the Western States increase compared to July but remain slightly lower than in April (Fig. 2). This change is attributed to the enhanced $f_{\mathrm{S}\left(\mathrm{IV}\right)+{\mathrm{O}}_{\mathrm{3}}}$ (Fig. S2), supported by high cloud pH and low ASO₄ concentrations (Figs. S3, S4). In the Gulf Coast States, Δ¹⁷O values remain low (Fig. 2), reflecting the continued dominance of the H₂O₂ pathway under acidic conditions sustained by high ASO₄ levels and low ANH₄ concentrations (Figs. S3, S4, S6). In the Midwest, decreasing NH₃ levels from July reduce the neutralization of acidity (Figs. S3, S7), making conditions less favorable for O₃-driven ASO₄ formation (Fig. 3). This results in lower cloud pH (Fig. S3) and diminished Δ¹⁷O values compared to earlier months. As photochemical activity weakens, the relative contribution of the SO₂ + •OH pathway declines (Fig. 5), reducing its moderating effect and allowing O3-driven isotopic enrichment to strengthen in high-pH regions.

Seasonal variations in ASO₄ formation and Δ¹⁷O(ASO₄) highlight the interplay of chemical drivers and meteorological conditions. The dominance of the H₂O₂ pathway in acidic, ASO₄-rich regions, such as the Gulf Coast States, leads to low Δ¹⁷O values year-round. In contrast, the O₃ pathway prevails in higher pH regions such as the Western States, driving elevated Δ¹⁷O values, particularly in April. The Midwest experiences transitional conditions, where cloud pH and NH₃ concentrations modulate the relative contributions of ASO₄ formation pathways. Alongside these seasonal and spatial contrasts, the gas-phase SO₂+•OH pathway acts as a persistent, near-zero-Δ¹⁷O background that offsets isotopic enrichment from O₃ oxidation, particularly during summer when photochemical activity peaks. These findings underscore the dynamic nature of ASO₄ chemistry across seasons, emphasizing the importance of emissions, atmospheric composition, and cloud chemistry in shaping regional and seasonal patterns of ASO₄ formation.

3.3 Change in Fractional Annual ASO₄ Formation and Δ¹⁷O(ASO₄) from 2006 to 2019

From 2006 to 2019, the annual Δ¹⁷O(ASO₄) values across the contiguous US showed a consistent increase, highlighting the growing importance of the O₃ pathway in ASO₄ formation (Fig. 7). In the central and eastern US, Δ¹⁷O(ASO₄) values increased by up to 2 ‰ (Fig. 7), primarily driven by significant reductions in SO₂ emissions, largely attributable to regulatory measures such as the Clean Air Act. These reductions led to lower ASO₄ concentrations, which elevated cloud pH and shifted the ASO₄ formation process toward the O₃ pathway (Fig. S12), resulting in ASO₄ with higher Δ¹⁷O values. Conversely, the western US exhibited only modest increases in Δ¹⁷O(ASO₄), typically less than 1 ‰ (Fig. 7). This is because the region historically favored O₃-dominated ASO₄ formation due to consistently high O₃ and cloud pH levels (Fig. S13), making the impacts of rising cloud pH and reduced SO₂ emissions less obvious. Changes in H₂O₂ concentrations played a significant role in shaping these trends. In the central and eastern US, slight increases in H₂O₂ concentrations continued to support the H₂O₂ pathway, to a limited extent, even as the O₃ pathway became more dominant (Figs. 7, S12). In contrast, in the western US, H₂O₂ concentrations decreased slightly, resulting in a slight reduction in $f_{\mathrm{S}\left(\mathrm{IV}\right)+{\mathrm{H}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{2}}}$ (Fig. 7). A decrease in $f_{{\mathrm{SO}}_{\mathrm{2}}+\mathrm{OH}}$ across the domain along with the negligible contributions from other pathways caused a relative increase in f_EMIS in these regions (Fig. 7). Between 2006 and 2019, the domain-averaged $f_{{\mathrm{SO}}_{\mathrm{2}}+\mathrm{OH}}$ decreased by 12.5 %, primarily due to the enhanced contribution of the O₃ oxidation pathway ($f_{\mathrm{S}\left(\mathrm{IV}\right)+{\mathrm{O}}_{\mathrm{3}}}$) and lower SO₂ concentrations under reduced precursor emissions, which together shifted the overall oxidation balance toward aqueous-phase processes. Consistent with these trends, spatial patterns of concentration changes (Fig. S12) show substantial decreases in SO₂ and ASO₄, particularly in the eastern US, while NH₃ and ANH₄ increased, leading to higher cloud pH and favoring O₃ oxidation. Meanwhile, primary ASO₄ emissions, which do not carry a mass-independent signature and exhibit Δ¹⁷O values close to 0 ‰, directly added to ASO₄ levels and tempered changes in Δ¹⁷O(ASO₄) values (Fig. 7). This dynamic explains why the increases in Δ¹⁷O(ASO₄) values from 2006 to 2019 were smaller in the western US compared to the central and eastern regions.

Figure 7 The change in the fraction from each ASO₄ formation pathway and Δ¹⁷O values across the contiguous US, from 2006 to 2019, based on CMAQ simulation.

3.4 Comparison of Model Δ¹⁷O(ASO₄) with Observations

The CMAQ simulations of Δ¹⁷O(ASO₄) across the contiguous United States reveal significant insights into atmospheric ASO₄ formation over recent decades. However, observations of Δ¹⁷O(ASO₄) in the contiguous US are very limited, with data primarily collected in the late 1990s at La Jolla, CA, and White Mountain Research Station, CA (Lee and Thiemens, 2001), and in the early 2000s at Baton Rouge, LA (Jenkins and Bao, 2006). These historical Δ¹⁷O(ASO₄) data exhibit a range from 0.2 ‰ to 1.6 ‰ (Table S1). Due to the predicted change in ASO₄ chemistry from 2006 to 2019, the 2006 model simulation was chosen for evaluation against these observations (Figs. 8, 9). The comparison with historical Δ¹⁷O(ASO₄) data is intended as a preliminary evaluation rather than a strict validation, given the temporal mismatch between the available observations (1990s–early 2000s) and the simulation years (2006, 2019). The observed range of 0.2 ‰ to 1.6 ‰ provides a useful benchmark for assessing whether the model produces realistic isotopic signatures. However, the limited number and dated nature of these measurements preclude a comprehensive validation of ASO₄ chemistry. This further emphasizes the critical need for new Δ¹⁷O(ASO₄) observations within the contiguous United States to enable robust model-observation comparisons.

Generally, the CMAQ model reasonably reproduced Δ¹⁷O(ASO₄) at the Baton Rouge, LA site, with a Root Mean Square Error (RMSE) of 0.20 ‰ (n=17). This region is characterized by relatively low predicted Δ¹⁷O(ASO₄) values, consistent with high regional SO₂ emissions and low cloud water pH that favor ASO₄ formation through aqueous S(IV) + H₂O₂ reactions. In contrast, the CMAQ-simulated Δ¹⁷O(ASO₄) values tended to be overestimated at the California sites, suggesting possible inaccuracies in representing additional ASO₄ production pathways in this region. The La Jolla, CA site had an RMSE of 0.36 ‰ (n=31), while the White Mountain, CA site had a notably higher RMSE of 1.9 ‰ (n=6). Despite the limited number of Δ¹⁷O(ASO₄) observations, a temporal analysis of model simulations versus observations indicates a consistent overprediction during the spring (Fig. 9). The Δ¹⁷O(ASO₄) overestimation in spring could be associated with higher predicted cloud pH during this season, which promotes the S(IV) + O₃ oxidation pathway in the model (Fig. S26). The elevated cloud pH may result from increased NH₃ emissions, likely related to fertilizer use in surrounding agricultural areas or to underrepresentation of marine boundary layer processes that could influence ASO₄ production (Guo et al., 2017; Lim et al., 2022; Zheng et al., 2024; Wang et al., 2025). Given the strong nonlinear pH dependence of ASO₄ formation, even moderate NH₃ emission biases can produce significant changes in isotopic composition. Future work should include explicit sensitivity simulations to better quantify the coupled effects of NH₃, cloud pH, and oxidant chemistry on modeled Δ¹⁷O(ASO₄). While organic acids (e.g., formic, acetic) can locally influence cloud water acidity, their contribution to bulk pH is generally minor relative to the dominant SO₂-H₂SO₄-NH₃ system (Herrmann et al., 2015; Shah et al., 2020; Tsui et al., 2019). Still, future model developments should evaluate their role in regional cloud pH and isotopic composition. Additionally, certain ASO₄ formation pathways, such as marine boundary layer chemistry involving S(IV) oxidation by HOX, may not be fully captured, particularly at coastal sites like La Jolla, CA. These reactions can efficiently oxidize S(IV) even under moderately acidic conditions and produce ASO₄ with relatively low Δ¹⁷O signatures (Chen et al., 2016; Ishino et al., 2017), which may partly explain the model overestimation at this site. Another possible factor is the omission of S(IV) oxidation induced by NO₂, an emerging multiphase pathway in polluted environments. Such reactions can proceed alongside metal-catalyzed and other aqueous pathways and are anticipated to result in low or near-zero Δ¹⁷O. Sensitivity simulations suggest that this mechanism can enhance ASO₄ concentrations by ∼ 0.4 %–1.2 % with a low rate constant and up to 4 %–20 % with a higher rate constant, particularly under polluted, low-oxidant wintertime conditions, when the aqueous S(IV) oxidation by H₂O₂ and O₃ becomes less efficient (Sarwar et al., 2013), while its overall impact on Δ¹⁷O(ASO₄) is expected to be minor.

Overall, the model-observation comparison of Δ¹⁷O(ASO₄) suggests that CMAQ performs well in more acidic environments but struggles to simulate ASO₄ formation under less acidic conditions accurately. However, the limited availability of Δ¹⁷O(ASO₄) observations constrains a more comprehensive evaluation of regional and temporal ASO₄ chemistry variations. This highlights the critical need for expanded observational datasets and model refinements to better represent the complex atmospheric ASO₄ dynamics. While this study highlights consistent patterns in ASO₄ oxidation pathways across the contiguous US, the evaluation of Δ¹⁷O(ASO₄) remains constrained by the limited and dated nature of available measurements. Expanded and more recent datasets will be essential to validate and extend the findings presented here, particularly to quantify seasonal and regional variability in ASO₄ formation.

Figure 8 Temporal variations in Δ¹⁷O(ASO₄) measurements and model simulations at (a) Baton Rouge, LA (top); (b) La Jolla, CA (middle); and (c) White Mountain Research Station, CA (bottom). The x axis error bars correspond to collection times.

Figure 9 Comparison of Δ¹⁷O(ASO₄) measurements and model simulations at La Jolla, CA, White Mountain Research Station, CA, and Baton Rouge, LA from 1996 to 2005.

4 Conclusions

This study modeled ASO₄ formation pathways and the Δ¹⁷O(ASO₄) for the contiguous United States using the CMAQ model for 2006 and 2019. The results reveal distinct seasonal and regional patterns in ASO₄ chemistry, strongly influenced by photochemical conditions, emissions of SO₂ and NH₃, and variations in cloud pH. From 2006 to 2019, significant changes in ASO₄ formation dynamics were observed, driven primarily by regulatory-driven reductions in SO₂ emissions. These shifts highlight the evolving balance between aqueous-phase oxidation pathways, particularly those driven by H₂O₂ and O₃.

The reductions in SO₂ emissions due to the Clean Air Act resulted in lower cloud water ASO₄, which subsequently increased cloud pH. This change shifted ASO₄ production toward the O₃ pathway, particularly in the eastern US, where the O₃ pathway was once limited by lower pH levels in 2006. By 2019, ASO₄ formation via O₃ oxidation had increased significantly, indicating a more efficient production mechanism under elevated pH conditions. The sub-linear response of ASO₄ concentrations to SO₂ emission reductions highlights the complexity of ASO₄ formation chemistry and the role of co-emitted species, such as NH₃, in modifying pH levels and influencing pathway dominance.

The isotopic signature Δ¹⁷O(ASO₄) serves as a powerful tracer for tracking shifts in ASO₄ formation pathways. In regions with limited photochemical activity, such as during winter or in areas with high primary ASO₄ emissions, lower Δ¹⁷O(ASO₄) values were associated with greater contributions from primary ASO₄ emissions. Conversely, higher Δ¹⁷O(ASO₄) values reflected an increased role of the O₃ pathway, particularly in regions with elevated cloud pH, reduced SO₂ emissions, and higher ozone concentrations.

This work demonstrates a significant and predictable shift in ASO₄ chemistry over the study period. The introduction of Δ¹⁷O(ASO₄) as a diagnostic tool for probing ASO₄ formation mechanisms provides a novel approach for investigating these changes. Expanding the measurement of Δ¹⁷O(ASO₄) across diverse regions and time periods will be critical for validating and extending these findings. Future studies should prioritize exploring how changes in atmospheric composition and regulatory measures continue to influence ASO₄ chemistry, with a particular focus on understanding the increasing prominence of O₃-driven chemistry. This effort will be crucial for enhancing atmospheric models and understanding the implications of ASO₄ chemistry on air quality, human health, and climate.