We used the 3D chemical transport model GEOS-Chem to examine the sensitivity of PN formation to NO_x, NH₃, and VOCs. The simulation parameters are summarized in Table 1. In this study, we used GEOS-Chem version 14.4.2, and all the simulations were performed at the nested 0.5° × 0.625° horizontal resolution with boundary conditions from a global 4° × 5° resolution simulation (10.5281/zenodo.12807579, Yantosca et al., 2024; Wang et al., 2004). Next, we assumed that January could represent the entire winter season to reduce computational burden (Dang et al., 2023b). Although GEOS-Chem underestimates observed PN mass concentrations, trends in wintertime PN simulated by GEOS-Chem and observations from the IMPROVE and CSN networks agree well (R2 > 0.6 between GEOS-Chem and ground monitoring networks) (Fig. S3). We will evaluate the performance of GEOS-Chem further in Sect. 2.5.

All sensitivity simulations were conducted using 72 vertical pressure levels from 2007 to 2022. GEOS-Chem includes detailed HO_x-NO_x-VOC-O3-BrO_x-aerosol tropospheric chemistry with over 200 species. We used the reanalysis product Modern-Era Retrospective analysis for Research and Applications, Version 2 (MERRA-2), developed by the NASA Global Modeling and Assimilation Office (GMAO), for meteorological inputs (Gelaro et al., 2017). Emissions were computed by the Harvard-NASA Emissions Component (HEMCO) (Keller et al., 2014). All global anthropogenic emissions were provided by the Community Emissions Data System inventory (Hoesly et al., 2018). Until winter 2018, these emissions were overwritten over the CONUS by the National Emissions Inventory 2016 (NEI 2016) at 0.1° × 0.1° resolution, which was created by NEI Collaborative for air quality modeling over the United States (National Emissions Inventory Collaborative, 2019). Since NEI emissions in the model were only available through January 2019, we used the CEDS inventory at the 0.5° × 0.5° resolution after to simulate anthropogenic emissions over the CONUS (Hoesly et al., 2018). Despite some differences in estimates of emissions magnitudes, which mainly arise from differences in horizontal resolution and the methods used in estimating agricultural emissions, the CEDS and NEI2016 inventories show similar trends (Fig. S4), and both predict the same wintertime PN sensitivity at various time slices and locations from 2007 to 2019 (see Sect. 3.1 and Fig. S5), suggesting the sensitivity findings are continuous regardless of inventory (Hoesly et al., 2018; Inventory Collaborative 2016v1 Emissions Modelling Platform, 2020).

Aircraft emissions were taken from the Aviation Emissions Inventory Code 2019 (AEIC 2019), which covered up to 2019 (Simone et al., 2013). Emissions after 2019 were kept constant at 2019 values. Offline soil NO_x emissions were used, which were provided by Hudman et al. (2012), and offline biogenic VOC emissions were provided by the Model of Emissions of Gases and Aerosols from Nature version 2.1 (MEGAN) as implemented by Hu et al. (2015) from 2007 to 2020 (Guenther et al., 2012; Hu et al., 2015; Hudman et al., 2012). Similar to aircraft emissions, emissions after 2020 for soil NO_x and biogenic VOC emissions were kept constant at 2020 values. Biomass burning emissions were provided by the Quick Fire Emissions Dataset, version 2 (QFED2) (Darmenov and da Silva, 2015). Thermodynamic PN formation was calculated with ISORROPIA-II (Fountoukis and Nenes, 2007). We used the Luo et al. (2020) wet deposition scheme to improve the accuracy of modelled PN (Luo et al., 2020). The PN photolysis scheme is described by Shah et al. (2023).

Sensitivity simulations used to quantify formation regime cutoffs are summarized in Table 2. The standard simulation (“Base”) was conducted from 2007 to 2022, where no modifications were applied to any emissions. The sensitivity of PN formation to the precursor gases NO_x, NH₃, and VOCs was evaluated with 3 simulations: (1) “Reduced-NO_x”, where NO_x emissions were decreased by 20 %; (2) “Reduced-NH₃”, where NH₃ emissions were decreased by 20 %; and (3) “Reduced-VOC”, where VOC emissions were decreased by 20 % (Dang et al., 2023b; 2024). The total quantities (in Tg) for NO_x, NH₃, and VOC emissions for each sensitivity simulation from 2007 to 2022 are shown in Fig. S6. In each sensitivity simulation, the decrease of the precursor gas applied to all emissions sources (natural and anthropogenic). We chose a perturbation of 20 % because it is in line with the model's ability to capture changes in PN. Throughout the timeframe, GEOS-Chem captures wintertime PN trends well (see Sect. 2.5) through changes in NO_x and NH₃ emissions that span 20 %–50 % (Fig. S4), suggesting the model will be able to accurately capture the impacts of a 20 % perturbation in emissions. Other analyses using this method similarly use 20 % (Dang et al., 2023b, 2024). Each sensitivity simulation was run with a full-year spin up for boundary conditions (4° × 5°) followed by 1-week spin up for nested simulations (0.5° × 0.625°). Production runs were performed for January of each year. These sensitivity simulations allowed us to examine the influence of each precursor gas on wintertime PN formation, how that sensitivity changed over time, and quantify cutoffs for PN formation regime determination.

The descriptions of all ground monitoring observations and the locations of each site are summarized in Fig. 1 and Table 3. We define winter in this analysis to be November, December, January, and February to match satellite retrievals. In addition, we analyze trends in gas concentrations, wet deposition, and particle speciation and compare them to satellite NO₂ column densities, NH₃ column densities, and model simulations to place results into context. We assume NWD and surface NH₃ concentrations trends are representative of the entire MWUS. While this introduces uncertainty, the agreement of trends between satellite and ground observations is excellent. This will be further discussed in Sect. 3.

We calculated the local PN sensitivity to each precursor gas, S_i, for individual 0.5° × 0.625° grid cells from GEOS-Chem using Eq. (3). Here, we calculated the ratio of the changes in monthly PN concentrations to changes in emissions of species i, Ei between the sensitivity and Base simulations. In Eq. (3), i is NO_x, NH₃, or VOCs (Dang et al., 2023b). 3Si=Δlog⁡(PN)Δlog⁡Ei We then chose all the pixels with sensitivity ratios of 0.95 ≤ S_i / S_j ≤ 1.05 from 2007 to 2023 (i.e., sites without a distinct dominant regime for PN sensitivity), where S_i is the dominant sensitivity, and S_j is the one of the other two sensitivities different from S_i (e.g., if S_i is S_NOx, then S_j is S_NO3 or S_VOC), to perform reduced-major-axis linear regression and deduce the wintertime PN sensitivity regime cutoff (Fig. S7) (Dang et al., 2023b). In this work, we chose to derive the regime cutoffs for the whole timeframe instead of deriving for individual years because there was not enough data without a dominant regime in some years to perform the regression. However, it is important to note that long-term trends in the formation sensitivity are the same whether using individual year or multi-year regressions (Fig. S8). We focused on the NO_x-sensitive and NH₃-sensitive regime because MWUS PN had limited sensitivity to VOC emissions during wintertime (Sect. 3.1). After diagnosing the PN sensitivity for each pixel for each winter season, we analyzed the changes in PN sensitivity from 2007 to 2023.

We perform a series of simulations in GEOS-Chem to assess the sensitivity of PN to changes in precursor gas emissions from 2007 to 2022. First, we establish the reliability of GEOS-Chem for this analysis by evaluating the ability of the GEOS-Chem Base simulations to reproduce ground monitoring observations and trends. We compare PN magnitudes and trends during January and sample GEOS-Chem at the IMPROVE and CSN monitoring locations (Fig. S3). On average, GEOS-Chem underestimates wintertime PN mass concentrations by -33.6 % compared to ground observations (GEOS-Chem: 1.3 µgm-3, IMPROVE: 1.6 µgm-3, CSN: 2.3 µgm-3). The biases in modelled PN may be due to uncertainties in nighttime chemistry, especially N₂O₅ uptake and the extent to which residual upper-planetary boundary layer PN sinks to the ground, emissions inventories, aerosol liquid water, and wet deposition of HNO₃ (Norman et al., 2025; Travis et al., 2022; Heald et al., 2012; Curci et al., 2015; Tang et al., 2021). Despite underestimation, GEOS-Chem shows good agreement with ground monitor trends, indicating that the sensitivity of PN to changes in emissions is captured. PN mass concentrations from GEOS-Chem show a decreasing trend from 2007 to 2013 (-10.3 ± 2.3 % yr⁻¹), which then flattens from 2014 to 2022 (-0.14 ± 1.16 % yr⁻¹). This is consistent with the trends from CSN and IMPROVE on average: PN decreases by -11.0 ± 4.5 % yr⁻¹ from 2007 to 2013, and it flattens afterward to 1.1 ± 1.9 % yr⁻¹. Thus, GEOS-Chem successfully captures the decrease and subsequent flattening trends of wintertime PN over both rural (IMPROVE) and urban (CSN) areas from 2007 to 2022. Modeled nitrate wet deposition is overestimated by 139 %, but nitrate wet deposition trends are also captured well by GEOS-Chem (Fig. S9) (Luo et al., 2020; Christiansen et al., 2024; Silvern et al., 2019).

The local model sensitivity of PN, S_i, is calculated by Eq. (3) for each model grid cell to derive the regime cutoffs using reduced-major-axis linear regression. PN is not sensitive to changes in VOC emissions (Reduced-VOC) at any point during the timeframe. In the Reduced-VOC simulation, changes in PN as a result of a 20 % decrease in VOC emissions range from 0.84 % to 4.0 %, which is substantially lower than changes seen in the Reduced-NO_x and Reduced-NH₃ simulations (range of 6.0 % to 21.6 %) (Fig. 2). Hence, S_VOC is excluded from the regression, although it is shown in Fig. 3a for illustration.

In Fig. 3, each point represents a GEOS-Chem grid cell with a dominant wintertime PN sensitivity regime (i.e., S_i / S_j > 1.1) plotted at its corresponding independent satellite NO₂ column densities and satellite tropospheric NH₃ / NO₂ ratios. Some overlap of data points in Fig. 3a is expected for two reasons: (1) this figure combines all dominant sites from 2007 to 2022, and (2) wintertime NO_x and NH₃ concentrations shift drastically across the timeframe. As noted previously, the trend in the shift of PN formation regimes is the same regardless of whether we determine formation regimes with individual-year or combined-year data (Fig. S8). After performing reduced-major-axis linear regression, the diagnostic cutoffs for NO_x and NH₃-senstive regimes are expressed by Inequalities (4) and (5). 4NH3-sensitive:log⁡NH3NO2<0.72-0.92×log⁡NO25NOx-sensitive:log⁡NH3NO2>0.72-0.92×log⁡(NO2)

The percent differences in PN mass concentrations between the Base and Reduced-NO_x simulations increase from 14.6 % in 2007 to 21.6 % in 2022. By contrast, the percent differences between the Base and Reduced-NH₃ simulations decrease from 12.3 % in 2007 to 6.0 % in 2022 (Fig. 2). Together, these results suggest that PN is becoming increasingly sensitive to NO_xemissions and less sensitive to NH₃ emissions. Our satellite-based results are consistent with an independent analysis of chemical mechanics (Sect. S1 in the Supplement) and PN thermodynamic sensitivity (Sect. S2). This is covered in more detail in the Supplement, but briefly, we use the thermodynamic equilibrium model ISORROPIA-II to investigate the thermodynamic sensitivity of PN and the roles of other potential drivers of trends (Fountoukis and Nenes, 2007). Our results suggest that the thermodynamics of wintertime PN formation over the MWUS is shifting away from NH₃-sensitivity (Fig. S10 and Sect. S2), consistent with our satellite-based diagnostic, and that PN trends cannot be explained by changes in aerosol liquid water, meteorological variability, or N₂O₅ uptake (Sect. S1).

Quantitatively, the NO_x-sensitive regime is the dominant regime in the MWUS, as the distribution of NO_x-sensitive grid cells is always > 50 % (Fig. 4), and this is especially prevalent over the Central MWUS (Movie S1 in the Video supplement). In 2007, 60.4 % of the diagnosed pixels are NO_x-sensitive, but this increases to 89.0 % in 2023 (Figs. 3 and 4). The largest shift in PN sensitivity over the MWUS occurs after 2013, where 76.9 % of the total diagnosed pixels are classified as NO_x-sensitive on average from 2014 to 2023, compared to 66.0 % on average from 2007 to 2013 (Fig. 4). Satellite NO₂ and NH₃ column uncertainties may propagate to errors in classification. We find that accounting for the extreme ends of the uncertainty may cause a change in diagnosed sensitivity regime in ∼ 30 % of the classified grid cells, but wintertime PN formation shows a consistent shift toward a predominant NO_x-sensitive regime after 2013 in all cases (Fig. S11). PN sensitivity over urban areas also follows the shifts in regime found for the rural MWUS (Fig. 4). Our findings are consistent with previous studies which diagnosed PN sensitivity over agricultural areas. Holt et al. (2015) found that the wintertime sensitivity of inorganic PM_2.5 over Northern Midwest has become more sensitive to NO_x emissions in 2012 compared to 2005 (Holt et al., 2015). Wintertime PN formation is also NO_x-sensitive over South Korea, where 76 % of anthropogenic NH₃ emissions originate from livestock (Oak et al., 2025). In addition, Guo et al. (2018) found that PN formation is more sensitive to NO_x than NH₃ during wintertime over an agricultural area in the Netherlands (Guo et al., 2018). Overall, our findings suggest that MWUS PN formation was sensitive to both changes in NO_x and NH₃ emissions from 2007 to 2013, but this has shifted to a predominantly NO_x-sensitive regime afterward.

The distribution of PN sensitivity regimes from 2007 to 2023 over the MWUS is shown in Movie S1. Spatially, much of the shift in PN formation sensitivity is driven by changes in emissions over the eastern portion of the MWUS, which is more densely populated. In 2007, MWUS PN formation was highly sensitive to NH₃ emissions over the eastern part of MWUS (Fig. 3b, c), which shifted strongly toward NO_x sensitivity by 2023. The shift in formation regime is consistent with the spatial trends of NO₂ and NH₃ column densities (Movies S2–S4, Fig. S12).

The shift in PN sensitivity regime over the MWUS is consistent with the trends in wintertime NO₂ and NH₃ satellite column densities and ground observations. We find that these trends cannot be explained by meteorological variability, and instead rely on aerosol chemistry and thermodynamic processes (Fig. S13 and Sect. S2). The trends of satellite NO₂ and NH₃ column densities from 2007 to 2023 with uncertainties are shown in Fig. S14. Trends in NO₂ column densities stayed relatively flat from 2007 to 2023 (0.48 ± 0.60 % yr⁻¹) (Fig. 5a). The relatively flat trends in satellite NO₂ are consistent with prior analyses of satellite trends over rural areas and nitrate wet deposition (NWD), a good proxy for regional NO₂. Prior decreases in rural NO₂ have flattened out over time due to the increasing relative importance of static background NO₂ sources, such as soils, lightning, and biomass burning, as anthropogenic NO_x emissions decrease (Fig. S4) (Christiansen et al., 2024; Jiang et al., 2018; Silvern et al., 2019). This is consistent with the flattening trends in NWD, a proxy for regional NO_x trends (Fig. S15). When we compare satellite NO₂ to EPA monitors over urban areas, which are dominated by anthropogenic NO_x emissions, by matching grid cells exactly, we find that NO₂ concentrations and NO₂ column density exhibit decreasing trends, which are -2.5 ± 0.5 % yr⁻¹ and -1.2 ± 0.8 % yr⁻¹, respectively. In contrast, wintertime NH₃ column densities have increased from 2007 to 2023 by 1.3 ± 0.3 % yr⁻¹ (Fig. 5b). The increase in NH₃ columns agree with increases in surface NH₃ concentrations reported by AMoN (8.2 ± 1.0 % yr⁻¹) (Fig. 5b) and prior studies (Wang et al., 2023b). Interestingly, NH₃ column densities significantly increase by 2.2 ± 0.5 % yr⁻¹ from 2014 to 2023, a stronger rate compared to the relatively flat trends from 2007 to 2013 (-0.1 ± 1.2 % yr⁻¹). This acceleration in NH₃ column density over the MWUS may be attributed to wintertime agricultural emissions (Vo and Christiansen, 2024; Wang et al., 2023b; Yu et al., 2018). Over the MWUS, fertilizer application contributes ∼ 62 % of total agricultural NH₃ emissions, and livestock waste contributes ∼ 38 % in 2020 (US EPA, 2020). The observed trends from both satellites and at the surface are consistent with PN sensitivity shifts toward the NO_x-sensitive regime. This suggests that controlling wintertime NO_x emissions over the MWUS is a critical mitigation strategy for reducing wintertime PN and PM_2.5 burden.

Throughout the region, PN is the dominant wintertime component of the particle matrix. The average contributions of particle chemical components are 25.7 % for PN, 10.3 % for SO42-, and 19.5 % for OC over urban areas. The contribution of PN, SO42- and OC to total PM_2.5 mass concentrations over rural areas are 32.3 %, 18.7 %, and 25.3 %, respectively (Fig. S16). Trends in observed PM_2.5 and PN also align with our findings regarding formation sensitivity. Observations from the IMPROVE network and CSN show decreases in wintertime PM_2.5 mass concentrations of -3.3 ± 0.6 % yr⁻¹ from 2007 to 2023 over the MWUS (Fig. 6a). Prior to 2013, the decrease in PM_2.5 was stronger compared to the trends after 2013, during which time the trends in PM_2.5 started to level off (-7.1 ± 1.9 % yr⁻¹ from 2007 to 2013, -1.0 ± 1.0 % yr⁻¹ from 2014 to 2023). This similarity persists in PN mass concentrations. Overall, PN shows a decreasing trend of -3.4 ± 0.9 % yr⁻¹. Prior to 2013, PN decreases by -6.3 ± 2.9 % yr⁻¹, while the decreases after 2013 slow to -1.0 ± 2.3 % yr⁻¹. These results suggest that PN and PM_2.5 trends are mostly driven by changes in NO₂, especially after 2013, when NH₃ concentrations increase strongly and NO₂ remains relatively constant (Fig. 6b). These trends are consistent across urban and rural sites (Fig. S13). Our model simulations also suggest that overall PM_2.5 formation sensitivity is becoming more sensitive to NO_x emissions (Fig. 7), similar to our findings for PN (Fig. 2).

The prominence of PN in the particle matrix, the similarity of PN and PM_2.5 trends, and the increasing sensitivity of both PN and PM_2.5 to NO_x emissions all suggest that PN may be critical for determining wintertime PM_2.5 burden and trends over the MWUS (Fig. S17). Hence, reducing PN would be most effective for reducing PM_2.5 burden over the MWUS during winter. The most impactful timeframe for controlling wintertime PM_2.5 via NH₃ reduction in the MWUS may have already passed. Prior to the mid-2010s, regulating NH₃ emissions during wintertime would have decreased PM_2.5 mass concentrations more effectively over the MWUS compared to reducing NO_x emissions, as reported in many studies starting in the mid-2000s (Gu et al., 2021; Makar et al., 2009; Pinder et al., 2007; Yang et al., 2022). This is consistent with our findings prior to 2010, in which the changes in PM_2.5 burden are more sensitive to changes in NH₃ emissions in almost half the region. However, during this time period, regulations focused on NO_x and SO₂ emissions, increasing formation sensitivity to NO_x as emissions continued to decrease. After the late 2000s, reducing NH₃ emissions has become increasingly less effective in controlling wintertime PN and thus PM_2.5 burden. The percentage difference in wintertime PM_2.5 mass concentrations between the Base and Reduced-NO_x simulations gradually increases by 0.31 % yr⁻¹ from 2007 to 2022 (2.2 % in 2007, 6.6 % in 2022), while it decreases by -0.33 % yr⁻¹ in the Reduced-NH₃ simulation (7.5 % in 2007, 2.7 % in 2022). This is consistent with the shifts in wintertime PN sensitivity. These trends are captured using both NEI2016 and CEDS emissions inventories (Fig. 7). Our findings are also consistent with more recent studies. In 2015, it was estimated that effective mitigation of PM_2.5 in the MWUS may require anthropogenic NH₃ emissions cuts of 60 %–90 % (Guo et al., 2024). This requirement will have only become harder to achieve since then. Similarly, Pan et al. (2024) suggested that regulating NH₃ is becoming less effective as secondary inorganic aerosols have become less sensitive to NH4+, and reductions in NH4+ concentrations of 40 %–70 % would be needed to reduce annual secondary inorganic aerosols over the rural United States (Pan et al., 2024). Holt et al. (2015) found that the sensitivity of wintertime inorganic PM_2.5 shifted toward NO_x emissions from 2005 to 2012, especially over the northern Midwest (Holt et al., 2015). Currently and in the future, NO_x emissions reductions are likely the most effective way to control wintertime PN formation and PM_2.5 burden in the MWUS.

It should be noted that, while PN is most sensitive to NO_x in the winter, reducing NH₃ emissions can still decrease PM_2.5 burden with significant benefits within this season. Over the MWUS, despite having the lowest agricultural NH₃ emissions compared to other seasons, a reduction of 0.01 Tg NH₃ could decrease PM_2.5 burden up to 3.7 % during wintertime, suggesting that reducing agricultural NH₃ emissions may still have significant impacts over agricultural regions (Vo and Christiansen, 2024). Controlling NO_x emissions will become increasingly costly, but agricultural NH₃ emissions may be able to be targeted at a lower cost (Gu et al., 2021; Makar et al., 2009; Muller and Mendelsohn, 2007; Pinder et al., 2007). In addition, controlling local NO_x production may become less effective for mitigating air quality concerns as regional sources (e.g., lightning, soils) become dominant contributors to NO_x emissions and trends. Careful consideration of technological advancements and economic concerns will be needed for new regulations aimed at reducing PM_2.5 burden over agricultural regions. This study was only focused on wintertime PN and PM_2.5 burden, and sensitivity conditions in other seasons may differ, as both NO_x and NH₃ emissions show distinct seasonal patterns. This is an area for future investigation.