A widely adopted method to simulate NO3- and SO42- formation on coarse particles involves incorporating irreversible heterogeneous reactions of gas species on dust and SS through a first-order uptake parameterization. Specifically, the uptake of HNO3(g) on coarse particles is commonly assumed to drive coarse NO3- formation , while the uptake of SO2(g) is known to lead to the formation of coarse SO42- . Most models assume constant uptake coefficients (γ) for these reactions, for example γ=0.1 for HNO3(g) uptake on dust . However, recent studies have shown that using this value tends to overestimate NO3- formation . This suggests that the uptake coefficient for HNO3(g) should be lower and that it is highly influenced by RH and dust alkalinity . Recent studies increasingly implement γ as a function of RH and employ different parameterizations of this function to account for dust alkalinity.

For our study, we extended the chemical mechanism of MONARCH to incorporate pathways for the formation of coarse NO3- and sulfate aerosols (Fig. ). This extension involved refining irreversible heterogeneous parameterizations within the model, specifically the uptake of HNO3(g) on dust and SS particles (Reactions R4–R5 in Table ), as well as the uptake of SO2(g) on dust particles (Reaction R3 in Table ). No additional heterogeneous chemistry, such as the transformation of NO2(g) to HNO3(g) on the surface of dust particles, was considered due to its relatively low significance .

Our implementation incorporates dependencies of γ on RH and on the alkalinity of dust . The γ dependency on RH is modeled akin to a Brunauer–Emmett–Teller (BET) isotherm, which characterizes water adsorption on dust particles . We employed a modified BET function to formulate γ, extending it to account for dust alkalinity. This formulation is represented by the following equation: 2γ=Sc⋅|c1⋅RH|(1-RH)|1+c2⋅RH|, where RH is the relative humidity (ranging from 0 to 1), c1 and c2 denote the water adsorption scaling factors , and Sc is a factor dependent on dust alkalinity. For the uptake of HNO3(g) on dust (Reaction R4 in Table ), typical values assumed for c1 and c2 are 8.0 and 7.0, respectively . For Sc, however, the literature reports varying values based on dust alkalinity assumptions, ranging from Sc=130 for the industrially standardized Arizona test dust (Möhler et al., 2006; Herich et al., 2009; Suman et al., 2024) to Sc = 0.018 for samples from the China loess with 39 % CaCO3 content .

We adopt the uptake RH functions for both HNO3(g) and SO2(g) on dust from . To fit experimental data from and the RH function reported by , for γ(HNO3) (Reaction R4 in Table ) we determine c1=3.84×10-4 and c2=0.56. Additionally, assumed an NVC content of 3.0 % Ca and 0.6 % Mg, which differ from the NVC values used in the present study. Therefore, we use the alkalinity scaling factor Sc to normalize the function accordingly. Specifically, values for Sc are defined as the ratio of Ca and Mg percentages used in our study relative to those assumed by , resulting in Sc=1.80 and Sc=1.52 for the two average alkalinity values derived from and , respectively, that are used in our experiments (see Sect.  below). Note that Sc is zero if no alkalinity is considered and that a constant value of γ(HNO3)=Sc⋅1.05×10-3 is used for RH higher than 80 %.

Similarly, we determined the γ(SO2) on dust (Reaction R3 in Table ), fitting Eq. () to experimental data from and the RH function from , yielding values of c1=2.7×10-6 and c2=-1.06. The same Sc values used for γ(HNO3) are applied for γ(SO2): Sc=1.80 and Sc=1.52.

However, if alkalinity is not considered, Sc is set to 1.0 (and not zero, as is the case for γ(HNO3)) to account for the oxidation of SO2(g) by deliquesced O3 and NO2 . For RH above 90 %, γ(SO2) remains constant at γ(SO2)=Sc⋅5.0×10-4.

For the HNO3(g) uptake on SS (Reaction R5 in Table ), we adopted the γ(HNO3) values of , which provide experimental estimates of this factor for different particle sizes and RH. However, a clear uptake function on these parameters has not been found in the literature. Therefore, for the sake of simplicity, we defer an implementation of an uptake coefficient dependent on these metrics to future research. In this study, we did not account for the RH dependency of γ(HNO3), and instead we used average values at 80 % RH, resulting in γ(HNO3)=0.15 for SS particles in the range of 0.1 to 2.5 µm and γ(HNO3)=0.05 for particles larger than 2.5 µm.

While larger values have been reported by , we opted for these values as they align with more widely accepted ranges found in the literature . Using higher values could potentially overestimate the uptake on SS particles.

The condensation of H2SO4(g) (Reactions R1–R2 in Table ) on dust and SS is another relevant source of SO42- introduced in our model. Due to the extremely low volatility of H2SO4(g) at atmospheric temperatures, its condensation onto existing particles is assumed to be irreversible and complete. This process signifies a direct mass transfer from the gas to the aerosol phase . The amount of H2SO4(g) that condenses in the fine and coarse modes is determined using the kinetic diffusive coefficients calculated as described in Sect. .

The gas–aerosol partitioning of semivolatile inorganic aerosols in previous studies with MONARCH was based on the EQSAM v03b TEQ model. EQSAM provides a computationally efficient approach that bypasses the expensive iterative activity coefficient calculation employed in other thermodynamic models. EQSAM was originally designed to handle the partitioning of the ammonium–sulfate–nitrate–water system, excluding solid components, and was extended to include solids, HCl, and Cl-/Na+ in version v03b, the one used in MONARCH. One of the limitations of this version is the lack of information on NVCs and/or mineral species in traced species.

For this study, we implemented the ISORROPIA-II v1 TEQ model as an additional option in MONARCH to investigate the sensitivity of the partitioning of semivolatile inorganic compounds to NVCs. While a more recent version of ISORROPIA-II (v2.3) exists, which improves aerosol pH estimations at near-pH-neutral conditions , global-scale simulations have shown only minor differences when compared to ISORROPIA-II v1 .

ISORROPIA-II v1 determines TEQ concentrations of gas, liquid, and solid phases. It can assume either stable conditions, where compounds precipitate into solids, or metastable conditions, where compounds remain as supersaturated liquid solutions. To enhance computational efficiency, ISORROPIA-II employs a segmented approach to calculate TEQ concentrations. This approach defines five different regimes based on the ratios of precursor species (i.e., sulfate, sodium, and crustal species), RH, and temperature. Each regime addresses a specific subset of relevant species and equilibrium equations. Efficiency is further improved by retrieving species' activity coefficients from lookup tables . The medium's acidity is determined by the concentrations of acidic and basic gaseous species (HNO3(g), NH3(g), H2SO4(g)), particles (NH4+, SO42-, NO3-), and crustal ions (K+, Ca2+, Mg2+, Na2+, Cl-), which are inputs to ISORROPIA-II. After TEQ is calculated with these species, the resulting pH is provided by the thermodynamic model.

In this work, we use the metastable solution of ISORROPIA-II, assuming that all the resulting particulate compounds from the TEQ computation remain in the liquid phase. Previous studies comparing stable and metastable methodologies with ISORROPIA-II have reported only marginal differences in global nitrate budgets between both modes. At global scales, these differences showed slightly higher pH values (0.5) and nitrate formation (2 %) when using the metastable assumption , although these differences are reported to be more important (<2 pH units and < 60 % nitrate concentrations) close to regions with low RH and a high concentration of crustal species or in their downwind areas. However, given the global-scale scope of the present study, we used the metastable assumption since it allows for full traceability of total aerosol nitrate, ammonium, and sulfate formation (Reactions R6–R12 in Table ).

We also adopt the temperature and pressure applicability range for ISORROPIA-II proposed by , which highlights potential instabilities in reactions occurring below 250 °K and 200 hPa. Consequently, ISORROPIA-II computations are limited to cells with temperature and pressure values above these thresholds.

Alkalinity refers to the ability of a substance to neutralize acids and maintain a stable pH level. Both dust and SS particles contain NVCs that contribute to the overall alkalinity of the aerosol, thereby neutralizing gas acidic species such as HNO3(g) and sulfates.

To investigate the importance of representing dust alkalinity, we derive a global average size-dependent NVC content from 5-year-long MONARCH simulations that explicitly track dust mineral species . To assess the uncertainty arising from our limited knowledge of the soil mineralogy of dust sources, we relied on two different MONARCH experiments detailed in , which utilized the and soil mineralogical datasets. The simulation based on accounts for 8 distinct minerals, whereas the simulations based on for 12 minerals (Table S3). The dataset includes quartz, feldspar, illite, smectite, kaolinite, calcite, gypsum, and hematite. The dataset includes those minerals as well as chlorite, vermiculite, mica, and goethite (Table S5). In this study, we adopt an upper bound for the mineral solubility and reactivity with gas species based on . Moreover, we assume size-dependent but globally homogeneous values for dust mineralogy, and consequently dust alkalinity and NVC, to focus on understanding heterogeneous reaction parameterizations. We defer the analysis of the potential importance of geographical dust mineralogical variations on dust heterogeneous chemistry to a forthcoming study.

Based on the global average mineral mass fraction for each dust size bin derived from the mineralogy simulations and the elemental composition associated with each mineral (see the Supplement Tables S4 and S6), we estimate the average NVC content per dust size bin at each time step following Eq. (): 3NVCi,j=∑kfNVCk,j⋅Mi,k⋅DUi, where the NVC concentration for each element j (i.e., Ca, Mg, K, Na) and size bin i (NVC_i,j) at a given location is derived by considering the molar fraction of each element in each mineral k (fNVCk,j), the global average mass fraction of each mineral and size bin (Mi,k), and the bin's dust concentration at the specified location (DU_i). NVC_i,j serves as input to the TEQ calculation. We consider only minerals soluble in water or acids that may at least partly dissolve in the liquid coating of the particles , and only NVCs reacting with the gas species in ISORROPIA-II are used (calcite, magnesium, potassium, sulfate, chlorite, or sodium) for the calculation.

The dust NVC global average content results in 5.17 % Ca2+, 0.79 % Na+, 2.37 % K+, and 1.32 % Mg2+ for the dataset and 3.68 % Ca2+, 0.87 % Na+, 3.15 % K+, and 1.75 % Mg2+ for .

The size-resolved NVC percentages for each dust bin are reported in the Supplement Tables S3, S4, S5, and S6.

In most of the sensitivity runs, the global average is employed if not stated otherwise (see Table 3). Values for are used solely in one sensitivity test, as explained in Sect. . These values are within the range reported by (5.36 ± 3.69 % Ca2+, 2.46 ± 1.90 % Na+, 2.08 ± 1.34 % K+, and 1.96 ± 2.20 % Mg2+). The dataset results in a higher proportion of Ca2+ compared with the one, while similar fractions for Na+ and K+ are reported.

Additionally, as discussed in Sect. , the dust NVCs derived imply the application of the scaling factors Sc=1.80 and Sc=1.52 in Eq. () for the irreversible uptake experiments, assuming the average alkalinity derived from the and simulations, respectively.

Regarding SS, we use a global average composition from , with 55 % Cl−, 30.6 % Na+, 7.7 % SO42-, 3.7 % Mg2+, 1.2 % Ca2+, and 1.1 % K+.

In the fTEQ_noAlk sensitivity run, fine particulate NO3- primarily forms in regions with significant anthropogenic pollution – areas where emissions of NOx(g), NH3(g), and SO2(g) are dominant – such as northern China and India, Europe, and eastern North America. In these regions, NO3- reaches average concentrations of 2 to 10 µg m⁻³ (Fig. e). At the surface, NH4+ is mostly associated with fine NO3-, presenting concentrations between 1 and 3 µg m⁻³ (Figs. e and S4e in the Supplement). At higher altitudes, fine NH4+ also forms in the presence of dust and SS, resulting in column burdens ranging from 1 to 3 mg m⁻² (Figs. S5 and S8 in the Supplement). This occurs because NH4+ neutralizes particulate SO42-, which forms when H2SO4(g) and SO2(g) condense on fine dust and SS particles.

The omission of dust and SS alkalinity leads to globally low pH values. Over oceanic and dusty regions, aerosol pH typically ranges from 1 to 2, while in industrialized regions, such as Europe and Asia, pH values can reach up to 5 (Fig. a).

Aerosol pH increases significantly when dust and SS NVC are included in the fTEQ_du-ssAlk run (Fig. b). This effect is especially pronounced over the open ocean, where pH increases from 1 to 5, and over dust source regions such as the Sahara Desert, where pH increases from 1 to 9.

Column burdens of HNO3(g) are notably affected by the elevated pH, decreasing by approximately 5 mg m⁻² across the Northern Hemisphere compared to the fTEQ_noAlk scenario (Fig. S1d, g in the Supplement). This decline predominantly happens in the upper troposphere (above 500 hPa, Fig. S2d, g), where concentrations decrease by about 0.5 µg m⁻³ (Fig. S2 in the Supplement). Conversely, column burdens of fine NO3- increase substantially, by more than 5 mg m⁻² over dusty regions such as the Saharan Desert and Middle East (Fig. S1e, h). In remote oceanic regions, fine NO3- column burdens increase by approximately 1 mg m⁻², with transoceanic transport at low latitudes showing column loads ranging from 4 to 7 mg m⁻² (Fig. S1h in the Supplement).

At the surface, the inclusion of dust and SS alkalinity has a minimal impact on continental HNO3(g) concentrations (Fig. d, g). Surface fine NO3- concentrations of about 0.5 µg m⁻³ are present across the equatorial belt, with higher values, up to 2 µg m⁻³, over remote dusty regions. However, no significant increase in fine NO3- concentrations is simulated in polluted areas such as Europe and Asia (Fig. e, h and Fig. S2e, h).

These results suggest that the condensation of HNO3(g) on dust and SS happens mostly during long-range transport, representing a key driver of nitrate formation in this scenario. They also indicate that incorporating Reactions (R8)–(R12) increases fine NO3- concentrations, with the majority forming on dust rather than on SS. This is attributed to the relatively higher alkalinity of dust compared to SS, as derived from the dataset (see Sect. ).

The HYB methods exclude the possibility of coarse NO3- evaporating back to the gas phase, which may lead to positive biases in global NO3- burdens.

In the HYB_duUPTK sensitivity run, coarse NO3- forms exclusively on dust, redistributing the available HNO3(g) towards coarse NO3- production in regions affected by dust, such as the Middle East and East Asia. Coarse NO3- column loads average between 0.5 and 4.0 mg m⁻² across the Northern Hemisphere, with peaks reaching 10–20 mg m⁻² (Fig. S1l in the Supplement). Notably, this impact is less pronounced in the Saharan dust belt, where limited HNO3(g) availability constrains coarse NO3- formation. The production of coarse NO3- is accompanied by a modest reduction in fine NO3- column loads over dusty regions (around 1 mg m⁻²) compared to that in the fTEQ_du-ssAlk simulation, driven by the availability of HNO3(g) for fine NO3- formation.

The uptake of HNO3(g) significantly influences the long-range transport of NO3-, showcasing notable transatlantic and transpacific transport (Fig. S1 in the Supplement). This transport predominantly occurs below 800hPa, with concentrations around 1 µg m⁻³, although lower concentrations of coarse NO3- are also discernible at altitudes up to 400 hPa (Fig. S2 in the Supplement). At the surface, coarse NO3- concentrations also increase, ranging from 2 to 10 µg m⁻³ over regions such as China, India, and the Middle East (Fig.  l).

The HYB_du-ssUPTK run investigates the role of SS by enabling both Reaction (R4) and Reaction (R5) (Table ).

The uptake of HNO3(g) on SS enhances the formation of coarse NO3- over the open ocean and those coastal areas affected by SS outbreaks (Fig. S11 in the Supplement). Surface concentrations in Europe and North America reach 1–2 µg m⁻³, with regions exceeding 5 µg m⁻³ significantly expanding (Fig. o). Coarse NO3- also becomes notable over western Siberia, eastern South America, and southern Africa (0.5–1 µg m⁻³) and over remote oceanic regions (0.2 µg m⁻³). Its presence extends to high altitudes in the Southern Hemisphere (Fig. S2o in the Supplement). Long-range transport of coarse NO3- is enhanced over oceans, with column burdens increasing by approximately 3.5 mg m⁻² (Fig. S1o in the Supplement) compared to those in the HYB_duUPTK case. This increase is attributed to greater depletion of HNO3(g) through irreversible uptake over dust and SS (Fig. S1m in the Supplement), resulting in lower HNO3(g) concentrations in the atmosphere compared to the other simulations.

Results obtained by increasing the value of γ(HNO3) in the HYB_g0p1 scenario (Supplement Sect. S5 and Fig. S3) provide insights into the nature of the coarse NO3- transoceanic transport. While the inclusion of UPTK on SS enhances long-range transport, the HYB_g0p1 run shows a slight increase in coarse NO3- compared to HYB_du-ssUPTK, particularly over the Sahara and across the Atlantic and Pacific oceans. Although these differences are not major, they suggest that the availability of HNO3(g) may act as a limiting factor for coarse NO3- formation.

To further explore this phenomenon, we used the HYB_DL run, which is equivalent to the HYB_du-ssUPTK run but constrains the available gas using the DIFFLIM calculation (see Methods section). This approach results in coarse NO3- column burdens just below those obtained in HYB_g0p1. The similarity between HYB_DL and HYB_du-ssUPTK can be attributed to two possible factors: (1) HYB_DL conserves more HNO3(g) for reactions on coarse dust during long-range transport via Reactions (R4) and (R5) (Table ) or (2) there is an intrinsic overestimation of the uptake coefficients, leading to similar coarse NO3- formation rates regardless of the HNO3(g) available. This is further discussed in Sect. .

Overall, results show that the HYB mechanisms preferentially condense HNO3(g) via TEQ in the fine mode and over SS through R5 in the coarse mode rather than over coarse dust through R4, as noted here and also assessed in subsequent sections.

A comparison of the spatial distributions obtained by the EMEP, INCA, and GMI models in , which employ HYB approaches similar to our HYB_du-ssUPTK run, reveals comparable trends. All models show significant formation of total NO3- (fine and coarse) over polluted regions, although our results, ranging from 10 to 25 mg m⁻², generally exceed the column loads reported by AeroCom models, which range from 7 to 16 mg m⁻² (Fig. S1n, o in the Supplement). AeroCom models do not show such the pronounced transport of coarse NO3- across the North Atlantic, as was observed in our study, with column burdens of 0.2–0.5 mg m⁻² compared to 4 mg m⁻² in our results. Section  further investigates the excessive formation of particulate NO3- in the HYB mechanism in terms of the total nitrogen budget.

A closer comparison with , using the LMDz-INCA model with UPTK reactions on dust and SS, shows strong agreement with our HYB_duUPTK run but not with HYB_du-ssUPTK. For instance, concentrations of total NO3- over polluted areas in align with HYB_duUPTK in both geographical distribution and magnitude (14–20 mg m⁻² in HYB_duUPTK vs. 10–20 mg m⁻² in , Fig. S1l). Similarly, simulate fine NO3- transport downwind of the Sahara and coarse NO3- across the North Atlantic, with column burdens around 1–2 mg m⁻², slightly below our HYB_duUPTK results of 1–5 mg m⁻². This preferential similarity of to HYB_duUPTK rather than HYB_du-ssUPTK, may be attributed to the HNO3(g) UPTK coefficient for SS employed in . For this reaction, instead of a constant value as used in HYB_du-ssUPTK, use a function of RH ranging from 1×10-3 to 0.1, leading to lower NO3- formation over SS in their model. This comparison suggests a potential overestimation of the UPTK coefficient for HNO3(g) on SS in the HYB_du-ssUPTK simulation. This conclusion is further discussed in the observational evaluation (Sect. ) and the budget analysis (Sect. ).

As a final remark, it is important to note that, similar to the findings of , the HYB_duUPTK simulations overestimate particulate NO3- concentrations compared to observational data, as discussed in Sect. .

To further investigate the source of the coarse NO3- overestimation in the HYB_du-ssUPTK simulation, we compare our spatial distributions with those from , which employ a similar HYB mechanism using the Met Office Unified Model (UM). In , fine NO3- formation is computed using adaptations from , specifically by testing different accommodation coefficients for HNO3(g) onto preexisting ammonium nitrate aerosols – although this adjustment has minimal impact on coarse NO3- concentrations. Coarse NO3- is formed through the uptake of HNO3(g), with coefficients sourced from for dust and for SS. Despite using different uptake coefficients for HNO3(g) on SS, the resulting coarse NO3- distribution is broadly comparable to that of the HYB_du-ssUPTK simulation. However, key differences emerge between the two models. Compared to the model, HYB_du-ssUPTK exhibits a stronger tendency for coarse NO3- formation over polluted areas such as Europe, eastern North America, and Asia (8–20 mg m⁻² in HYB_du-ssUPTK vs. 4 mg m⁻² in ), as well as over oceanic regions (1.5–3.0 vs. 0.4–2.0 mg m⁻²) rather than over sub-Saharan areas. Remarkably, significant North Atlantic transport of coarse NO3- (2.0–4.0 mg m⁻²) is only present in our simulation and is absent in . The global budget comparison in Sect.  and Table  further highlights the fact that report significantly lower global NO3- burdens compared to our HYB runs, including HYB_duUPTK. This suggests that the HYB mechanisms in our simulations may produce coarse NO3- excessively, as both the burdens and distributions of coarse NO3- in are consistently lower, despite also accounting for SS in nitrate formation.

Nevertheless, several alternative explanations could account for the differences between the models. These include differences in the fine NO3- formation mechanism, variations in the study period (2018 in our study vs. a 20-year average in ), and differing parameterizations of HNO3(g) uptake on SS.

Overall, the comparison of spatial distributions between our HYB mechanisms and those reported in the literature supports the initial hypothesis that the assumption of irreversible HNO3(g) uptake, and potentially the uptake coefficients used, may contribute to the overestimation of NO3- formation. This issue is examined in greater detail in Sects.  and .

The DBCLL simulations (described in Sect.  and Tables  and 3) assess the impact of reversible chemistry and the roles of dust and SS NVC in nitrate partitioning.

The DBCLL_noAlk run produces spatial distributions of HNO3(g) and fine NO3- similar to those in the fTEQ_noAlk run. HNO3(g) remains predominantly in the gas phase across the Northern Hemisphere (Fig. S1p in the Supplement), while fine NO3- primarily associates with fine NH4+ over regions lacking dust or SS influence, such as parts of China, India, Europe, and eastern North America (Fig. q). Minimal concentrations of fine NO3- are simulated at higher altitudes (Fig. S2q in the Supplement), although fine NH4+ coexists with sulfate particles at elevated levels, as observed in the fTEQ_du-ssAlk case. In contrast, coarse NO3- is nearly absent in DBCLL_noAlk, with only minimal surface concentrations over northern China (0.4 µg m⁻³) and no clear correlation with dust and SS presence (Fig. r). Coarse NH4+ formation is similarly limited, with a slight presence over the Persian Gulf and the Sahara (0.02–0.1 mg m⁻²), primarily in anthropologically polluted regions where it forms alongside coarse SO42- (0.2 mg m⁻²) (Figs. S5r and S8r). The simultaneous formation of coarse NH4+ and SO42- particles is attributed to diffusion limitation, where NH3(g) preferentially neutralizes coarse sulfate particles.

The differences between fTEQ_noAlk and DBCLL_noAlk illustrate the impact of diffusion limitation before the partitioning of semivolatile species. While fine NO3- formation remains consistent between both runs, the assumption of allowing all acid species to partition into the fine mode in fTEQ_noAlk leads to enhanced fine particle production and long-range transport – an effect not observed in DBCLL_noAlk. Consistently, the pH in the fine mode closely mirrors that in fTEQ_noAlk, while the pH of particles in the coarse mode indicates even greater acidity (Fig. f1, f2).

Including dust and SS alkalinity in DBCLL_du-ssAlk produces an important increase in the pH over arid regions and oceanic regions – from 1 to 5–6 in the fine mode and above 7 in the coarse mode – compared to DBCLL_noAlk (Fig. h1, h2). Relative to DBCLL_du-Alk (dust alkalinity only; see Supplement Sect. S5), DBCLL_du-ssAlk redistributes the NO3- partitioning toward the coarse mode: fine NO3- concentrations approximately halve across regions, while coarse NO3- surface concentrations and column loads roughly double over dusty regions but not over the ocean (Fig. w, x and S1w, x). This shift leads to enhanced transatlantic and transpacific transport, with column loads of 2–4 mg m⁻², surface concentrations of 0.4 µg m⁻³, and zonal averages of 0.5–1.0 µg m⁻³. Over continental regions with dust concentrations, coarse NO3- reaches column loads of 4–5 mg m⁻² and surface concentrations of 0.5–1.0 µg m⁻³. Additionally, HNO3(g) surface concentrations increase from 0.1 to 1.0 µg m⁻³ in the heavily polluted areas (Fig. s, v). The enhancement of coarse NO3- formation is attributed to SS NVCs (see Sect. ), with Cl- suppressing fine NO3- formation and leaving more HNO3(g) available for transport and subsequent coarse NO3- formation over dusty regions.

Including SS alkalinity reduces fine NH4+ loads over Europe and eastern North America from 3 to 1 mg m⁻² and slightly lowers values over Asia (2–3 mg m⁻²). Conversely, coarse NH4+ increases over Europe and eastern North America (0.1–0.2 mg m⁻²), Asia (up to 1.0 mg m⁻²), and transoceanic regions (0.1 mg m⁻²) (Fig. S5x in the Supplement). This redistribution mirrors the particulate NO3- patterns, highlighting the strong coupling between these species when TEQ is applied to both fine and coarse partitioning. These results emphasize the sensitivity of nitrate formation to SS alkalinity, particularly due to basic NVCs like Na+.

Compared to the HYB_du-ssUPTK run, DBCLL_du-ssAlk shows lower coarse NO3- concentrations and shifts coarse NO3- formation toward dusty rather than anthropologically polluted areas. For example, over Europe, surface concentrations in DBCLL_du-ssAlk do not exceed 0.5 µg m⁻³, while HYB_du-ssUPTK reports 1–2 µg m⁻³ (Fig. x).

Overall, regardless of the mechanism used, the results demonstrate the high sensitivity of NO3- formation to dust and SS alkalinity, significantly altering its spatial distribution (Reactions R8 to R12, Table ). However, implementing the DIFFLIM calculation in the DBCLL mechanism has a limited impact, as shown by the comparison between fTEQ_noAlk and DBCLL_noAlk.

We compare DBCLL_du-ssAlk and the results from the EMAC model , which similarly employs TEQ for the bulk gas and aerosol mass, followed by DIFFLIM. Additionally, EMAC makes use of globally heterogeneous dust alkalinity based on 12 mineralogy source data points. Results from the EMAC model are reported in and (Table  and Supplement Sect. S4). Surface distributions of aerosol NO3- are closely aligned in both models over Europe and North America, with surface concentrations ranging from 1 to 3 µg m⁻³. However, DBCLL_du-ssAlk shows higher concentrations over Asia, India, and the Middle East compared to EMAC (5–10 µg m⁻³ vs. 6–15 µg m⁻³, respectively). Additionally, our results show some variations over secondary areas compared to those of . EMAC reports biases, such as underestimating coarse NO3- over southern Europe and central-eastern Asia, attributed to excessive sulfate condensation on dust – a limitation mitigated in our study due to lower sulfate levels (Fig. S7 in the Supplement). Additionally, while EMAC overestimates fine NO3- over the Arctic, this is not observed in our results due to the RH and temperature restrictions applied in ISORROPIA-II (see Sect. ). Over central Africa, EMAC overpredicts coarse NO3- due to excessive HNO3(g) from biomass burning coupled with low H2SO4(g) concentrations from where suggested that an HYB approach could reduce the bias. Our DBCLL_du-ssAlk and HYB runs report lower concentrations, although still potentially overestimated due to too-low HNO3(g) levels. Total particulate SO42- and NH4+ are in close agreement in both EMAC and the DBCLL_du-ssAlk run (Fig. S4w, x and S7w, x in the Supplement), with only slightly higher formation of coarse NH4+ over the Indian subcontinent in MONARCH compared to EMAC.

Fine particulate nitrate (PM2.5NO3) is consistently formed by all mechanisms (through TEQ), with the exception of the DBCLL scheme, which incorporates a DIFFLIM coefficient to limit its formation. Consequently, the fTEQ and HYB mechanisms produce higher PM2.5NO3 from October to April (0.5–1.0 µg m⁻³) than DBCLL does, which reports approximately half of these values. This discrepancy is more pronounced over North and Central America than in Europe, although both regions exhibit similar seasonal patterns. From April to October, differences among mechanisms diminish, except in the HYB_du-ssUPTK, which significantly overestimates PM2.5NO3 during these months.

Notably, the runs considering the effects of dust and SS alkalinity in the partitioning process reduce the negative bias in PM2.5NO3 significantly, especially during February.

Greater variability among experiments emerges when evaluating HNO3(g) and Total NO3-, with more observational data available over North and Central America than over Europe or Asia. This variability is highly influenced by how each mechanism models coarse NO3- formation, especially over Asia (Fig. S12 in the Supplement). For example, the HYB runs, which rely on irreversible uptake reactions, consistently overestimate total NO3- across all regions. In contrast, the DBCLL runs, which assume reversible partitioning, align better with observations.

From the HYB simulations, the HYB_duUPTK run demonstrates strong correlation coefficients for both fine and total NO3- concentrations (0.8 and 0.9, respectively). The seasonal variability in this run closely resembles that of the fTEQ_noAlk and fTEQ_du-ssAlk experiments, which fully neglect coarse NO3- formation. This similarity suggests a limited number of sites affected significantly by coarse NO3- formation, while highlighting the relevant role of the TEQ calculation in the fine mode. Despite showing a systematic positive bias (0.03, 0.04, and 0.29 µg m⁻³ for HNO3(g), fine NO3-, and total NO3-, respectively), HYB_duUPTK maintains consistency across continents. However, it notably overestimates total NO3- over Asia in November and over Europe from May to September, likely due to dust events affecting the monitoring sites.

Including the UPTK reactions on SS in the HYB_du-ssUPTK run exacerbates this overestimation due to excessive HNO3(g) condensation into coarse NO3-. Specifically, the correlation for total NO3- drops from 0.9 to 0.66, HNO3(g) concentrations are underestimated (bias of -0.10 µg m⁻³), and total NO3- surface concentrations are overestimated by 1.50 µg m⁻³ – the highest bias among all sensitivity runs (Table ). This overestimation is most pronounced over Asia (3–5 µg m⁻³ vs. 1 µg m⁻³) and North and Central America (1.5–2.5 µg m⁻³ vs. 1.0 µg m⁻³). Discrepancies in European sites are more pronounced during summer and fall (Fig. S12 in the Supplement).

To evaluate whether this overestimation results from unlimited HNO3(g), we examined the HYB_g0p1 and HYB_DL configurations (Supplement Sect. S5). Increasing the uptake coefficient γ(HNO3) in HYB_g0p1 further enhances the overestimation of total NO3- by an additional 30 %, suggesting that HNO3(g) availability is not the limiting factor. Similarly, HYB_DL shows only a marginal reduction in total NO3- bias (from 1.5 to 1.3 µg m⁻³), reinforcing the idea that the overestimation stems from the overly high γ(HNO3) values for SS particles, as previously discussed in Sect. . This highlights the need to refine HYB schemes.

Conversely, DBCLL mechanisms markedly reduce surface concentration biases. Without alkalinity, the total NO3- bias shifts from 0.29 to -0.43 µg m⁻³ between the HYB and DBCLL runs. Incorporating dust and SS NVCs further improves the bias, reducing it from 1.5 to -0.1 µg m⁻³ between the HYB_du-ssUPTK and DBCLL_du-ssAlk runs (Table ). All consistently achieve high correlation coefficients (approximately 0.8).

However, the DBCLL_noAlk run tends to underestimate total NO3-(bias of -0.43 µg m⁻³) and overestimates HNO3(g) (bias of +0.13 µg m⁻³), failing to capture its seasonal cycle (correlations of 0.06). Surprisingly, the fTEQ runs outperform DBCLL_noAlk despite neglecting coarse NO3- formation.

Including dust and SS alkalinity in DBCLL_du-ssAlk substantially improves these biases. Enhanced condensation of HNO3(g) into both fine and coarse NO3- (Fig. ) yields a reduced bias in total NO3- (-0.10 µg m⁻³) and a strong seasonal agreement, with correlation coefficients of 0.82 and 0.78 for fine and total NO3-, respectively. These results also outperform the DBCLL_duAlk run, which excludes SS alkalinity (Supplement Sect. S5 and Table S7).

The evaluation of the DBCLL experiments highlights the paramount importance of accounting for NO3- formation on both dust and SS to accurately represent HNO3(g) and particulate NO3- concentrations.

The sensitivity of model performance to the dust NVC representation is further assessed using the DBCLL_Claq run, which applies an average dust alkalinity based on instead of on (see Sect. ). Results show limited differences compared to DBCLL_du-ssAlk, with the correlation and bias for total NO3- just slightly improved in DBCLL_Claq, at 0.81 and -0.09 µg m⁻³, respectively (Supplement Sect. S5 and Table S7). The time series from Fig. S14 compared to Fig.  also shows comparably similar results when using DBCLL with the or mineral datasets. Overall, based on the limited number of observation sites used in our evaluation, the impact of dust NVC representation on surface NO3- concentrations does not appear to be significant at the observational points.

Results for NH3(g) and particulate NH4+ are generally more consistent across all mechanisms compared to NO3- outcomes. This consistency is expected, as all sensitivity runs use the same condensation pathway for the conversion of NH3(g) to fine NH4+ through Reactions (R6) and (R7) (Table ).

All mechanisms effectively capture the seasonal cycle of both NH3(g) and fine NH4+. Correlation coefficients for NH3(g) range from 0.85 to 0.88, while those for fine NH4+ range from 0.59 to 0.77. However, model performance is slightly weaker for total NH4+, with correlations between 0.41 and 0.54.

The DBCLL_du-ssAlk and DBCLL_Claq runs yield the lowest errors for NH4+. RMSEs are 0.17 µg m⁻³ for fine and 0.12 µg m⁻³ for total concentrations, with corresponding biases of -0.02 and 0.08 µg m⁻³ (Tables  and S7). These results highlight the significant sensitivity of NH4+ predictions to the treatment of dust and SS NVCs. Including or omitting NVC representation notably affects the biases across different schemes. Unlike NO3-, increased particle alkalinity reduces the condensation of NH3(g), thereby limiting NH4+ formation. This effect helps mitigate biases when compared to observational data.

Overall, biases for both fine and total NH4+ remain relatively low in most experiments, ranging from -0.02 to 0.29 µg m⁻³.

Results for SO2(g) and particulate SO42- are consistent across all sensitivity simulations. This consistency is expected since sulfate formation is independent of the pathways used for coarse NO3- formation. In all cases, particulate SO42- is produced from SO2(g) and H2SO4(g) in a similar manner (see Sect. ). Differences arise solely from variations in the treatment of the γ(SO2) coefficient when accounting for dust alkalinity, which introduces slight differences in SO42- formation. Overall, the model slightly underestimates both SO2(g) and total SO42-, particularly at European monitoring sites. In contrasts, fine SO42- is marginally overestimated, mainly driven by observations from Central and North American sites. Temporal correlation coefficients average around 0.6, with slightly lower values for total SO42-.

For SO2(g), the slight mismatch with observational data primarily stems from the European evaluation, which presents a consistent negative bias of -0.5 µg m⁻³ throughout the period studied (Fig. S12 in the Supplement). Fine and total SO42- concentrations also show generally good agreement with observations. However, there is a modest overestimation of fine SO42- concentrations, with an average bias of 0.30 µg m⁻³, particularly over Central and North America. Conversely, total particulate SO42- surface concentrations are underestimated over Europe, with an average bias of -0.43 (Table  and Fig. S12 in the Supplement).

The negative bias in SO42- concentrations may be attributed to the sulfate formation scheme and sulfur emission inventories employed in our runs. Reevaluating the SO2(g) uptake coefficient could provide valuable insights. The current implementation uses the uptake coefficient function from . Alternative formulations have been suggested in the literature, such as the uptake coefficient values proposed by for SO2(g) uptake on dust and those by for uptake on SS, as reported in . Exploring these alternatives may help improve the model's representation of sulfur species.

Results for PM2.5 and PM10 are consistent across the different sensitivity runs (Fig. ), indicating that the total mass is more influenced by components other than secondary inorganic species.

Globally, the seasonal cycles of PM2.5 are reproduced well across all sensitivity runs, with correlation coefficients consistently around 0.75. However, annual PM2.5 concentrations are overestimated by an average of 20 µg m⁻³ (Table ). In contrast, PM10 concentrations over Asia show good agreement with observations, indicating that the model underestimates coarse particulate matter (PM), especially at monitoring sites in mainland China (Supplement Figs. S12 and S13). It is important to note that regions with significant PM2.5 overestimation do not overlap with the limited sites where chemical composition measurements are available – locations where the model accurately represents total particulate NO3- and NH4+ (Supplement Fig. S12). Our results suggest that the absence of anthropogenic coarse dust emissions in the CAMS emission inventory may hinder the formation of coarse inorganic species, including NO3-. The formation of coarse NO3- is critical for scavenging HNO3(g) and suppressing the formation of fine particulate NO3- by providing surfaces for heterogeneous reactions. The significant influence of typically neglected anthropogenic coarse PM emissions on nitrate formation has been emphasized in previous studies (e.g., ), highlighting the need for improved emission inventories to better capture the interactions between coarse particles and nitrogen species.

In contrast, PM2.5 model results over Europe and North and Central America are well aligned with observations (Fig. S12). The evaluation of PM10 shows just slightly worsened RMSEs (ranging from 22.49 to 30.42 µg m⁻³) and correlation coefficients (from 0.36 to 0.46) compared to PM2.5 (RMSEs from 24.74 to 26.16 µg m⁻³ and correlations from 0.74 to 0.76, Table ). This is attributed to the PM10 surface concentration underestimations over North and Central America, especially from April to September, which do not seem to be caused by the underestimation of any secondary inorganic aerosol species studied in this work. Over Europe, our results are in agreement with those reported by .

The partitioning of atmospheric nitrogen species into the gas and aerosol phases varies according to the underlying chemical assumptions. We analyze the average atmospheric burden and deposition of nitrogen species in the MONARCH model across sensitivity runs (Fig.  and Table S13 in the Supplement).

The simulation labeled noHC, excluding heterogeneous chemistry involving nitrate, serves as the baseline for understanding the distribution of nitrogen species in the gas phase. Under this configuration, the dominant nitrogen species are HNO3(g), peroxyacetyl nitrate (PAN), NH3(g), and NOx, with burdens of 1.06, 0.8, 0.71, and 0.38 TgN, respectively. The longer atmospheric lifetimes of HNO3(g) and PAN result from their chemical stability compared to more reactive NOx species. Notably, N2O5(g) plays a key role in nighttime HNO3(g) production via heterogeneous hydrolysis .

The total nitrogen burden is highly sensitive to the nitrate formation mechanism. Schemes promoting efficient coarse mode NO3- formation significantly reduce nitrogen burdens.

For example, assuming irreversible condensation of HNO3(g) onto coarse particles reduces nitrogen load by 32 % and 40 % when considering dust only (HYB_duUPTK) and both dust and SS (HYB_du-ssUPTK), respectively. In HYB_duUPTK, 0.13 TgN partitions into fine and coarse NO3- on dust. Including SS (HYB_du-ssUPTK) further increases consumption of HNO3(g) and coarse NO3- formation, leading to a total NO3- burden of 0.27 TgN, while the fine NO3- burden remains unchanged at 0.12 TgN (Supplement Table S13).

Comparing HYB runs to fTEQ_du-ssAlk reveals that dust and SS uptake reduces HNO3(g) burdens by 0.21 TgN (dust) and 0.50 TgN (dust and SS) relative to TEQ-only partitioning. This is driven by irreversible uptake in the coarse mode. Consequently, the deposition rate of NO3- increases from 80 to 140 Tg yr⁻¹, and its atmospheric lifetime decreases from 2.6 to 2.3 d (Table ). The combined UPTK on dust and SS nearly depletes HNO3(g), leaving only 0.15 TgN, which contributes to the overestimation of surface NO3- (Sects.  and ).

Irreversible condensation also reduces the NO(g), NO2(g), and N2O5(g) burdens to 0.11, 0.17, and 0.01 TgN, respectively, due to enhanced N2O5(g) hydrolysis on increased particle surfaces. This reduction can be attributed to increased NO3- particle formation and, consequently, the available surface where hydrolysis of N2O5(g) can take place. Ultimately, this produces more HNO3(g) available for partitioning into the particle phase.

Conversely, nitrogen loads increase when reversible condensation of HNO3(g) and NH3(g) is considered in the fTEQ and DBCLL sensitivity simulations. A larger proportion of nitrogen remains in the gas phase compared to in the HYB schemes. Notably, neglecting dust and SS alkalinity (fTEQ_noAlk, DBCLL_noAlk) slightly increases HNO3(g) burdens (from 1.11 to 1.14 TgN) and elevates NO(g) and NO2(g) by 0.29 % and 0.12 %, respectively. When dust and SS alkalinity are considered (fTEQ_du-ssAlk, DBCLL_duAlk, DBCLL_du-ssAlk), HNO3(g) burdens decrease by 40 %–50 %, enhancing particulate NO3- formation. This shift towards the aerosol phase results from the neutralization of NVC from dust and SS by HNO3(g). In these cases, the NO(g), NO2(g), and N2O5(g) budgets decrease by approximately 20 % compared to analogous mechanisms without alkalinity, driven by the more efficient N2O5(g) aqueous dissociation due to the increased particle presence. SS alkalinity alters the partitioning of aerosol NO3- from fine (-72 %) towards coarse mode (+63 %) when comparing DBCLL_duAlk and DBCLL_du-ssAlk, resulting in burdens of 0.06 (fine) and 0.18 TgN (coarse) (Fig. ). This surge in coarse NO3- formation with dust and SS alkalinity causes a 26 % decrease in the total NO3- burden and a 14 % increase in deposition rates compared to the DBCLL_duAlk case, mainly driven by the enhanced wet deposition of coarse NO3-, from 11.0 to 27.5 Tg yr⁻¹ (Table ). This can be attributed to the higher deposition efficiency of SS particles due to their larger size ranges and abundances near the surface. Consequently, the presence of SS decreases the atmospheric lifetime of particulate NO3- from 4.9 to 3.1 d, contrasting with scenarios that consider only dust alkalinity.

Additionally, SS NVCs (e.g., Na+) inhibit NH3(g) condensation into NH4+, reducing NH4+ burdens from 0.31 to 0.22 Tg (Table S11).

Figure  presents the annual averaged burdens and depositions of oxidized (HNO3(g) and NO3-) and reduced (NH3(g) and NH4+) nitrogen for each sensitivity run. These results are compared with global estimates from the AeroCom phase III nitrate experiment , which offers a comprehensive range of budgets derived from different global aerosol models employing mechanisms similar to those analyzed in our study. As additional references, the results from the EMAC model and the LMDz-INCA model are shown separately from the average of AeroCom in Fig.  due to their similarities to the DBCLL and HYB mechanisms, respectively.

The HYB mechanisms yield an annual average burden of oxidized nitrogen of 0.55 TgN, slightly below the AeroCom multimodel mean but in close agreement with that of .

Compared to the fTEQ and DBCLL mechanisms that account for dust and sea salt (SS) alkalinity, which show higher oxidized nitrogen burdens (0.6–0.8 TgN), the HYB mechanisms fall on the lower end of the distribution. This reduction is primarily due to the efficient deposition of particulate NO3- and the limited atmospheric presence of HNO3(g) under the assumption of irreversible uptake, as discussed in Sect.  and .

For reduced nitrogen species, the HYB mechanisms produce an average burden of approximately 0.3 TgN, aligning well with the AeroCom mean. However, HYB configurations yield lower particulate NH4+ burdens (0.15 TgN, Table S11 in the Supplement) and higher NH3(g) levels in the gas phase compared to the mechanism and others. Among HYB cases, NH3(g) budgets show an inverse relationship with HNO3(g), indicating that HNO3(g) acts as a limiting factor for the NH3(g) neutralization in the fine mode. Given that most HNO3(g) is consumed by the UPTK reactions in the HYB mechanism, these results suggest that the NH4+ mass formed with this configuration is mainly a product of NH3(g) neutralization with sulfate through the fTEQ calculation.

The fTEQ and DBCLL mechanisms exhibit a high sensitivity in the partitioning of oxidized and reduced nitrogen to alkalinity, regardless of whether coarse NO3- formation is considered. When dust and SS alkalinity are neglected (fTEQ_noAlk and DBCLL_noAlk), oxidized nitrogen burdens rise significantly, to 1.1 TgN, primarily due to the accumulation of unreacted HNO3(g), which slightly exceeds the burden in the noHC run (1.05 TgN). This is attributed to the sensitivity of N2O5(g) hydrolysis to aerosol loading. Conversely, reduced nitrogen burdens in these schemes remain relatively low compared to other mechanisms due to the high consumption of NH3(g) by the neutralization of HNO3(g), which acts as an important sink of reduced nitrogen as particulate NH4+. The introduction of dust and SS NVCs into the reactions decreases oxidized nitrogen by an enhanced consumption of HNO3(g) to form NO3-. Furthermore, reduced nitrogen concentrations increase as a consequence of the lower availability of HNO3(g) to neutralize NH3(g). This phenomenon is similarly observed in simulations, including TEQ calculations over fine (fTEQ_du-ssAlk) and over both fine and coarse modes (DBCLL_duAlk and DBCLL_du-ssAlk). Comparatively, the presence of dust and SS alkalinity decreases the oxidized nitrogen burdens by approximately 27 % compared to analogous simulations neglecting NVCs. However, contrasting the results between DBCLL_duAlk and DBCLL_du-ssAlk shows that while the presence of SS NVCs further enhances the consumption of HNO3(g) by 20 %, it concurrently reduces NO3- burdens by 5 %. This is likely due to SS contributing acidic anions such as Cl- and SO42- (see Sect. ), which hinders the formation of particulate NO3- in the fine mode and leaves more HNO3(g) available to form coarse NO3- over dust. This is consistent with the spatial distributions discussed in Sect.  and the nitrogen budgets presented in Sect.  and Fig. .

Alkalinity leads to higher reduced nitrogen budgets due to enhanced basic conditions (high pH, as shown in Fig. ) facilitated by dust and SS NVCs. This environment inhibits NH3(g) condensation over dust and SS particles, thereby increasing the NH3(g) atmospheric lifetime (Table S10) and allowing it to mix with sulfate from polluted areas, as can be seen in the spatial correlation between particulate SO42- and NH4+ (see discussion in Sect.  and Figs. S4 and S7). Consequently, alkalinity facilitates the formation of NH4+ through the neutralization of NH3(g) by sulfate, contrasting with the neutralization process involving HNO3(g) observed in the DBCLL_noAlk simulation.

Overall, the DBCLL_du-ssAlk run aligns with the average of AeroCom in both oxidized and reduced partitions, although its reduced phase falls below EMAC levels. This discrepancy can be attributed to EMAC showing very low deposition rates of NH3(g) (see Table S10), which enhances its atmospheric burden.

The observational evaluation of both reduced and oxidized species, along with the monitoring stations used, can be found in the Supplement Sect. S6. Overall, general good agreement with observations is obtained. Oxidized nitrogen species exhibit low biases in all mechanisms except HYB_du-ssUPTK, which overestimates observations throughout the period studied, supporting the conclusion that the UPTK coefficients used are excessively efficient. Reduced nitrogen species, while slightly underestimated, remain well within the observational variability range.