Recent intercomparisons between regional air-quality model predictions and observations in both North America and Europe under the AQMEII4 initiative (Makar et al., 2025) have shown that these regional models have a tendency towards positive biases in the concentrations of sulphur dioxide (SO₂) and particulate sulphate. One possible cause of these positive biases are underestimates in the deposition velocity of SO₂, which if corrected would result in lower SO₂ concentrations and hence reduced production of particulate sulphate via SO₂ oxidation. Enhanced deposition of SO₂ through its co-deposition with ammonia (NH₃) has been reported in the past (cf. Fowler et al., 2001; Flechard et al., 1999; Nemitz et al., 2001). However, in addition to ammonia, substantial deposition fluxes of other reactive base cations in the form of depositing dust have been recorded (Scheuvens et al., 2013; Wang et al., 2005; Avila et al., 1998; Rosas et al., 2025). These deposition fluxes may also influence the rate of SO₂ deposition. However, a detailed process description of this influence has been heretofore unavailable. We examine here the potential for simultaneous co-deposition of multiple base cations and acidic gases including SO₂, making use of a case study domain in the Athabasca Oil Sands Region, reporting the results as part of the AQMEII4 special issue on deposition.

The Athabasca Oil Sands Region (AOSR) in northeastern Alberta, Canada contains one of the world's largest bitumen reserves, spanning approximately 142 000 km² (Government of Alberta, 2025). It is well established that this region is a significant source of various gaseous and particulate emissions (You et al., 2024; Zhang et al., 2018a; Li et al., 2017). Among these, sulphur dioxide (SO₂) has drawn particular attention due to its known potential to adversely impact ecosystem health. SO₂ plays a central role in the development of acid rain (Irwin and Williams, 1988; Clarke and Radojevic, 1987) and acid fog (Pandis and Seinfeld, 1989; Munger et al., 1983), both of which have been implicated in widespread ecosystem degradation throughout the world (Hames et al., 2002; Cape, 1993; Cox et al., 1989; Schindler et al., 1989; Gilbert, 1986; Hutchinson and Whitby, 1977). An input of excess SO₂ and particle sulphate (SO42-) onto plant foliage can disrupt metabolic function (Rennenberg, 1984; Knabe, 1976), cause irreversible damage to guard cells that regulate stomatal activity (Knabe, 1976), and may lead to leaf necrosis or plant mortality in sensitive species (Hutchinson and Whitby, 1977; Gordon and Gorham, 1963).

Two recent measurement campaigns in the AOSR investigated dry deposition of oxidized sulphur. The first was an aircraft-based study (13 August to 7 September 2013; Hayden et al., 2021), which showed that dry deposition fluxes of total oxidized sulphur (SO₂ + particulate SO₄) decrease exponentially with increasing distance downwind from major AOSR sources. Their inferred deposition fluxes were 2 to 14 times higher than predicted by the GEM-MACH model (Makar et al., 2018), with inferred SO₂ deposition velocities (VaSO2) of 1.2 to 3.4 cm s⁻¹, compared to modelled values of 0.58 to 0.72 cm s⁻¹. Additional ground-based measurements at Fort McKay (6 to 8 June 2018) yielded even higher median VdSO2 values (median: 4.1 cm s⁻¹; range: 2.9 to 5.3 cm s⁻¹). Both the aircraft and Fort McKay tower data reflect daytime conditions. The second study (Gordon et al., 2023) involved continuous tower based SO₂ measurements from July to October 2021 at a forest site approximately 40 km north of Fort McMurray (located within the AOSR). Using the flux-gradient method, they reported inferred VdSO2 values of 2.1 to 5.9 cm s⁻¹ (mean: 4.6 cm s⁻¹), in agreement with the range reported by Hayden et al. (2021). These data may include both daytime and nighttime periods, although Gordon et al. (2023) acknowledge greater uncertainty during stable nighttime atmospheric conditions. Given the typically lower VdSO2 at night due to an increased aerodynamic resistance (Wu et al., 2018; Finkelstein et al., 2000), the reported range likely remains dominated by higher daytime deposition events.

To investigate the discrepancy in VdSO2 found between their observations and the model predictions from GEM-MACH, Hayden et al. (2021) performed a Monte Carlo simulation using five common inferential dry deposition algorithms (Wu et al., 2018; Makar et al., 2018). They employed this approach to study the importance of various parameters, including foliage pH. The Monte Carlo simulation demonstrated that VdSO2 can be highly sensitive to the choice of foliage pH assumed in an algorithm developed by Wesely (1989) for cuticular resistance calculation, which is used in GEM-MACH. For example, as the foliage pH is increased from 6.68 to 8.0, the VdSO2 predicted by the GEM-MACH algorithm shifted from 0.6 to 1.4 cm s⁻¹. However, the foliage pH in such algorithms is usually assumed to represent neutral or near-neutral conditions; in GEM-MACH, the foliage pH is assumed to be constant at 6.68 (Makar et al., 2018). Hayden et al. (2021) hypothesized that the deposition of anthropogenic dust to forests downwind of the AOSR might cause the pH of foliage water layers to become alkaline (higher pH levels), in turn leading to an increase in VdSO2 (see Sect. 3). To support this hypothesis, the remainder of this Introduction summarizes key processes influencing foliage surface pH, including canopy particle deposition, leaf water dynamics, and dust-gas interactions, which form the foundation for our modelling approach.

The importance of leaf surface water pH on determining VdSO2 over wet foliage surfaces is cited in the development papers of some inferential dry deposition algorithms (Wesely, 1989; Erisman, 1994). Moreover, the effect of pH on VdSO2 has been demonstrated explicitly by wind tunnel measurements investigating the co-deposition of SO₂ and NH₃ into thin water layers (Adema and Heeres, 1995), by field observations of foliage water pH made after precipitation (Wu et al., 2016; Neirynck et al., 2011), and by a leaf-scale model that predicts the pH of foliage water layers to better simulate the dry deposition of NH₃ (Flechard et al., 1999). To the authors' knowledge, the impact of base cation co-deposition with SO₂ has remained unstudied in the literature.

The assumption of alkaline material on foliage surfaces in the forests downwind of the AOSR is supported by in-situ measurements of particulate matter (PM) obtained from the processing facilities. The AOSR emits substantial primary and secondary PM from multiple sources, including surface mining and quarrying, bitumen extraction and processing, vehicle-induced dust on haul roads, natural gas power generation and natural sources such as soil erosion and forest fires (Zhang et al., 2018a). Oil Sands processing is the dominant PM source (43 %– 60 %), with surface mining and haul-road dust contributing 22 % to 46 % (Wang et al., 2015; Mamun et al., 2021; Landis et al., 2019). Wang et al. (2015) analysed 27 dust samples from the AOSR and found (i) a significant amount of water-soluble Na⁺ originates from sodium hydroxide (NaOH) used during bitumen extraction (Tamiz Bakhtiari et al., 2015) and road salt, (ii) Ca mostly in ionic form, with an abundance of calcite (CaCO₃) and some dolomite (CaMg(CO₃)₂), and (iii) consistently basic dust, with ratios of measured of cations / anions > 1.0. Similarly, Watson et al. (2014) found that without accounting for the carbonate ion (CO32-) in the charge balance equation, cations in AOSR dust were 11 to 12 times more abundant than anions on average. With CO32- included, anions were about 55 % greater than cations on average. These studies confirm that AOSR dust is rich in base cations such as Ca²⁺, Mg²⁺, K⁺ and Na⁺.

The significance of alkaline dust towards deposition fluxes in the AOSR has also been demonstrated in throughfall measurements made in the boreal forest adjacent to the processing facilities. Watmough et al. (2019) found that within 3 km of open pit mines, deposition of Ca²⁺, Mg²⁺ and Na⁺ exceeded that of sulphur and nitrogen combined, with Ca²⁺ dominating base cation inputs. Similarly, Proemse et al. (2016) reported elevated calcium levels in ground Jack Pine needles collected at various distances downwind of Oil Sands facilities. Previous GEM-MACH modelling by Makar et al. (2018) indicated that base cations likely remain in excess up to 140 km downwind, suggesting that alkaline soil and foliage conditions may persist over this regional scale.

Outside of the AOSR, the impact of alkaline dust deposition on vegetation and soil health has been documented downwind of cement plants and limestone quarries. When moisture is present, dissolved cement-kiln dust can reach pH values of 10 to 13 due to high hydroxyl ion concentrations (Darley, 1966; Mandre and Tuulmets, 1997; Siqueira-Silva et al., 2016). Similarly, hydrated dust collected from foliage near a limestone quarry had pH values between 9 and 11 (Manning, 1971). Cement-kiln dust may contain up to 36 % acid-extractable base cations (Ca²⁺, K⁺, Na⁺) by mass (Darley, 1966), whereas AOSR-derived dust contains about 5 %–6 % ionic base cations, primarily as Ca²⁺, Mg²⁺, K⁺, and Na⁺ (Wang et al., 2015). Despite this lower concentration, the base cation content in AOSR dust is sufficient to neutralize the observed ∼ 2 % SO42+ content (Wang et al., 2015), suggesting a likely excess of alkaline species such as CaCO₃. Under moist conditions, this chemical composition can raise surface pH on foliage, paralleling effects observed near cement plants and limestone quarries. Supporting evidence comes from dew studies using inert surfaces (i.e., Teflon), which show that dew pH can exceed 8, and sometimes 10, in regions with significant alkaline dust deposition (Odeh et al., 2017; Beysens et al., 2017; Lekouch et al., 2010). In contrast, dew in regions without significant alkaline dust deposition has a pH typically ranging from 3 and 7 (Wisniewski, 1982; Pierson et al., 1986; Foster et al., 1990; Hughes and Brimblecombe, 1994; Beysens et al., 2006; Wentworth et al., 2016), with the most acidic values (i.e., pH < 4) reported downwind of major roadways due to acid deposition (Flückiger et al., 1978). We note here that the AOSR has sources of both anions and cations – the former from emissions of SO₂ and NO_x from large stacks and off-road vehicle fleets, and the latter from fugitive dust (Zhang et al., 2018a). Both acidifying and neutralizing deposition in the AOSR would thus be expected (Makar et al., 2018).

Particulate matter, such as dust, is deposited onto foliage through “dry” physical processes, including gravitational sedimentation, Brownian diffusion, turbulent impaction and interception, but also through “wet” processes such as precipitation and fog (occult deposition). Dry deposition dominates PM accumulation on foliage outside of persistently wet regions, and to a first order approximation, wet deposition can be neglected in a simplified process model representation (Freer-Smith et al., 2005). In general, the dry deposition characteristic of a particle is strongly affected by its diameter (Dp) and velocity, and so these factors strongly impact the canopy collection efficiency of PM (Emerson et al., 2020). The canopy collection efficiency of particles is defined here as the fraction of particle dry deposition that is to the forest canopy as opposed to the ground surface under the canopy. For foliar deposition of ultrafine particles (Dp≤0.1 µm), Brownian diffusion is the most efficient dry deposition mechanism, while for particles in the PM₁₀ range (0.1<Dp≤10 µm) interception and impaction dominate (Tiwary et al., 2006; Beckett et al., 2000). The sedimentation process becomes significant only for coarse particles (Dp>8 µm) (Beckett et al., 1998, 2000). Wind speed also enhances the rate of particle dry deposition by increasing particle velocity (Beckett et al., 2000; Hwang et al., 2011). More recent work by Emerson et al. (2020) compared observed deposition velocities as a function of size and vegetation classes, with a shift of the minimum deposition velocity to smaller sizes, and higher deposition velocities for the coarse mode. Once deposited, some PM may eventually become encapsulated into the leaf wax, especially when deposited onto newly expanding foliage, where it typically remains until leaf senescence (Przybysz et al., 2014).

Beyond particle specific properties, vegetation type plays a key role in determining the canopy PM collection efficiency. Coniferous species generally capture more PM than broadleaf species, particularly in the PM_2.5 size range (0.1<Dp≤2.5 µm) due to their narrow needle-like foliage and associated aerodynamic properties (Emerson et al., 2020; Chen et al., 2017; Przybysz et al., 2014; Hwang et al., 2011; Freer-Smith et al., 2005). This difference is reflected in the Stokes number, which is higher for conifers (∼ 0.05) than for broadleaf species (∼ 1.2×10-5), and in the thickness of the leaf-boundary layer, which is thinner in conifers, enhancing the deposition efficiency (Beckett et al., 2000; Chen et al., 2017). The leaf-boundary layer is defined as the region of the atmosphere near the leaf surface where a reduction of the ambient wind speed occurs due to surface friction, impacting mass exchange (Schuepp, 1993; Grace and Wilson, 1976). At the leaf level, traits such as high surface roughness (i.e., wrinkles, ridges, furrows and folds), abundant leaf hairs and glandular secretions have all been correlated to an increased PM capture efficiency (Corada et al., 2021; Chen et al., 2017). While PM can deposit to both sides of leaf surfaces, it typically accumulates more on the upper side (Ottelé et al., 2010). However, when leaf hairs are present only on the underside, that surface can become the dominant location of PM deposition (Hwang et al., 2011). Canopy collection efficiencies of PM vary between 0.40 to 0.95, with higher values observed for coarse PM and dense forests (Emerson et al., 2020; Pryor et al., 2013; Grönholm et al., 2009; Donat and Ruck, 1999). Spatial variability within forests also matters: deposition is typically greater near forest edges than within the forest interior (Raynor et al., 1974; Draaijers et al., 1994; Ould-Dada et al., 2002; Wuyts et al., 2008).

In addition to PM, gaseous species are also deposited to foliage, but through a broader range of pathways. While PM typically deposits only to the external leaf surface (except perhaps ultrafine particles), gases and their chemical transformation products can also be accommodated onto the external surface (i.e., dry cuticles, drops and thin layers of dew water) or be assimilated by the leaf through the stomata. For example, over 80 % of HNO₃ is deposited to the external leaf surface and can be directly recovered via leaf washing (Cadle et al., 1991; Dasch, 1989). In contrast, SO₂ shows more variable behaviour; the percentage deposited to the external leaf surface can range from near 0 to greater than 40 %, with the remainder assimilated into the leaf interior via the stomata (Dasch, 1989; Taylor et al., 1983; Fowler and Unsworth, 1979).

Estimating leaf surface pH in the presence of exogenous substances requires accounting for the removal fluxes of deposited ions and gases from the foliage surfaces. Once deposited, any mass (i.e., particle or gas) not immobilized by leaf waxes can be removed from the foliage and transferred to the ground or lower canopy layers. Under dry conditions, strong winds can remove PM either by directly dislodging particles from the leaf surface or through branch movement (Zheng and Li, 2019; Ould-Dada and Baghini, 2001). However, outside of extremely arid regions, precipitation is the dominant removal process (Popek et al., 2019). During rainfall, soluble PM can dissolve in surface water and is typically washed off almost completely given sufficient runoff (Pullman, 2009; Chiwa et al., 2003; Hansen et al., 1994; Potter and Ragsdale, 1991; Fortmann and Johnson, 1984; Carlson et al., 1976). In contrast, insoluble PM may remain adhered to the leaf surface regardless of precipitation intensity, duration or amount (Xu et al., 2024; Zhang et al., 2018b; Xu et al., 2019; Cai et al., 2019; Weerakkody et al., 2018; Xu et al., 2017; Fortmann and Johnson, 1984). Fine and ultrafine insoluble particles, which often become embedded in leaf microstructures, are most likely to be retained despite precipitation (Xu et al., 2024; Weerakkody et al., 2018; Przybysz et al., 2014). Observations suggest precipitation washoff is governed more by the cumulative precipitation amount rather than precipitation intensity or precipitation pH (Xu et al., 2017; Fortmann and Johnson, 1984), although extremely intense rainfall can still mechanically dislodge PM (Zhang et al., 2019). On the scale of an individual tree, removal efficiency tends to be lowest near the inner crown, where less rainfall reaches the foliage (Kwak et al., 2023).

As noted earlier, the deposition of PM (i.e., alkaline dusts) and gases may influence the dry deposition characteristics of the forest through a pH feedback effect. However, pH is only defined in aqueous solutions (Pye et al., 2020), requiring the presence of water on leaf surfaces to estimate surface pH. This water may exist as small droplets or thin water layers, forming aqueous reservoirs for gas dissolution. The likelihood of water condensation and hence the formation of foliage water droplets or layers is increased in the presence of leaf hairs (Konrad et al., 2014). Meteorological conditions can directly encourage the development of water droplets or thin water layers on foliage, either through precipitation or the development of dew, fog, or guttation. Guttation is the process where water droplets form and appear at the edges or tips of healthy leaves, occurring mainly because of pressure generated in the roots. The roots absorb water from the soil due to differences in ion concentrations (osmosis) between soil water and the root cells. Living cells in the roots actively help push this water (along with dissolved minerals) up through special tubes called xylem; this pressure builds up forcing the water out through small pores at the leaf edges (Singh, 2016).

In addition to direct sources of water, hygroscopic particulate matter can deliquesce as it interacts with a combination of atmospheric water vapor and transpired water from the leaf stomata (Tredenick et al., 2022; Coopman et al., 2021; Katata and Held, 2021; Burkhardt et al., 2001, 1999; Eiden et al., 1994), as might be expected from the related chemical thermodynamics of salts found in PM (Miller et al., 2024). The presence of hygroscopic material can reduce the surface tension of the resulting droplet (El Haber et al., 2024; Dutcher et al., 2010), promoting a likelihood of initially isolated droplets spreading into a thin water layer. Further spreading (even over a hydrophobic surface) can be achieved if the deliquesced PM is able to act as a surfactant (e.g. Rafaï et al., 2002). Thus, the general result of hygroscopic aerosol deposition on plant foliage is the potential development of a thin (microscopic) water layer that can become quite concentrated (i.e., high ionic strength), as implied in studies from the observations of changes in electrical conductance in relation to relative humidity and the spreading behaviour of artificial salt deposits on leaf surfaces (Burkhardt and Eiden, 1990; Burkhardt et al., 2012). These water layers may make a connection with the substomatal cavity of the leaf, forming a “wick” that maintains the water layer even in hot and sunny meteorological conditions (Burkhardt, 2010; Burkhardt et al., 2009; Burkhardt, 1995). Furthermore, if the canopy is thick and the wind is weak, a substantial mass transfer barrier due to the leaf boundary layer may be present. This leaf boundary layer acts to limit moisture exchange near the leaf surface with the ambient atmosphere, keeping the relative humidity higher, and increasing the likely presence of thin water layers on the foliage (Burkhardt et al., 2001; Boulard et al., 2002). It is worth noting, however, whether this aqueous solution takes the form of droplets or a thin layer is not necessarily essential for determining the gas uptake rates. In a study of modelling dew chemistry for reactive uptake of gases (including SO₂) from ambient air, Chameides (1987) noted that only minor quantitative differences were obtained in the simulated results regardless of whether the same volume of dew water was assumed to exist as droplets or a thin layer covering the leaf surface.

The work described herein investigates how the emission of large quantities of base cations from atmospheric dust impacts the pH of foliage water layers in the forests downwind of the source, and how this, in turn, modulates VdSO2. While our air-quality model domain is focused on dust emissions from a major anthropogenic source in the AOSR, the co-deposition effects explored here are also applicable to other sources of particulate base cations, both anthropogenic (i.e., cement production) and natural (i.e., wind-blown topsoil and desert dust). Long-range transported dust, such as Saharan and Asian dust, often contains large fractions of CaCO₃ (>25 %) and CaSO₄ (Scheuvens et al., 2013; Wang et al., 2005), and has been shown to influence forest biogeochemistry through base cation deposition (Avila et al., 1998; Rosas et al., 2025). These examples illustrate that the pH-mediated modulation of SO₂ deposition via co-deposited alkaline particles may have a broader global relevance, beyond the AOSR.

The pH-modulation of VdSO2 results from a pH-driven term in the leaf cuticle resistance formula of the dry deposition algorithm (see Sect. 3), which is parameterized based on the effective Henry's law constant for SO₂ (HSO2∗). Hayden et al. (2021), using box modelling and a Monte-Carlo approach, hypothesized that alkaline foliage conditions in the AOSR could substantially increase VdSO2 by reducing the leaf cuticle resistance via this HSO2∗ dependence. We test this hypothesis through the development of a mechanistic foliage pH model that includes a thin water layer representation, embedded within the GEM-MACH regional chemical transport model. We find that the pH effect is sufficiently strong to account for the large observed SO₂ deposition velocities in this region, that including the co-deposition effect significantly improves model performance, supporting the hypothesis of Hayden et al. (2021), and that local changes in SO₂ concentrations due to this effect can be on the order of a factor of two.

The following methodology sections begins by describing the original deposition flux components used in GEM-MACH, starting with gaseous dry deposition, including how it may be influenced by the leaf surface pH, followed by particle dry deposition. We explain how the net deposition flux to leaf surfaces is calculated, and how this information is used to estimate the leaf surface pH, thereby introducing a feedback mechanism that modulates gas-phase deposition velocities and fluxes of soluble species. We then present results showing the predicted foliage pH and how the pH-dependent leaf cuticle resistance parametrization impacts VdSO2 and the SO₂ dry deposition flux. These results are evaluated against both surface monitoring and aircraft observations in the AOSR to assess model performance improvements. Finally, we discuss potential uncertainties and confounding factors, including precipitation-driven removal of deposited mass. The impact of the pH-modulation mechanism is demonstrated through a comparison with a Base Case assuming a fixed, near-neutral foliage pH of 6.68 (Makar et al., 2018).

The simulations reported herein were generated using a research version of the 3D deterministic Global Environmental Multiscale – Modelling Air-quality and CHemistry (GEM-MACH) numerical air-quality model (Makar et al., 2018; Moran et al., 2010, 2018). The underlying meteorological model is version 5.1.2 of the Global Environmental Multiscale (GEM) weather forecast model (Côté et al., 1998a, b; Caron et al., 2015; Milbrandt and Morrison, 2016; Morrison and Milbrandt, 2015). Updates to the chemistry module (MACH) since Makar et al. (2018) include new or updated processes representations for aerosol speciation, biogenic violatile organic compounds and nitrogen oxide emissions, cloud processing of gases and aerosols, gas-phase chemistry, forest fire smoke emissions, inorganic heterogeneous chemistry, major point source plume rise, NO₂ reactions on particle surfaces, particle and gas dry deposition, secondary organic aerosol formation and vehicle-induced turbulence (Makar et al., 2025 and references therein). In this study, we used GEM-MACH in a nested configuration, with an outer domain covering North America at a resolution of 0.09° (i.e., ∼ 10 km grid cell size). The rotated inner domain has a resolution of 0.0225° (i.e., ∼ 2.5 km grid cell size) and covers the entire Canadian provinces of Alberta and Saskatchewan as well as sections of British Columba, Manitoba, Northwest Territories, and the northwestern contiguous United States. The chemistry module is “fully coupled” to the meteorological model – this means that atmospheric aerosols can modulate the predicted meteorology through radiative transfer and cloud microphysics effects (Makar et al., 2015a, b; Gong et al., 2015; Makar et al., 2021). Simulations were carried out for May through August 2018, with a two-week spin-up period in April. The deposition algorithms are described in detail in Sect. 3 and the Supplement.

To assess the performance of the pH-modulated dry deposition algorithm an evaluation is performed against two main sources of data: (1) the literature-reported values of VdSO2 from Hayden et al. (2021) and Gordon et al. (2023) made in the vicinity of the AOSR and (2) the Wood Buffalo environmental Association (WBEA) continuous monitoring station data that reported nearly continuous hourly observations of SO₂ during the period investigated in this work. The geographic locations of the 21 WBEA stations are shown in Fig. 1. SO₂ measurements made at a single point at a WBEA monitoring station may not necessarily be representative of the predicted grid cell mean because the GEM-MACH model predictions of SO₂ are representative of the 20 m level of an entire grid cell which has area of ∼ 6.25 km² (∼ 2.5 × 2.5 km grid cell size).

In the GEM-MACH model, the deposition of a gaseous species to foliage has two main pathways: (1) to the leaf surface (leaf cuticle) and (2) to the leaf interior (trans-cuticular and stomatal deposition). The relative importance of the different pathways may depend on both the vegetation type and the identity of the gas. In this investigation, the fraction of gaseous deposition that occurs to the leaf surface in a grid cell is estimated via effective conductances for each land-use type containing “natural vegetation”. While GEM-MACH has 15 unique land-use types for dry deposition modelling, only 4 of these are considered in our high resolution foliage pH co-deposition simulations, including: (1) evergreen needleleaf forests, (2) deciduous broadleaf forests, (3) mixed forests and (4) dwarf trees and shrubs (Fig. 3). Vegetation classes containing grassland or crops were not considered since these types of vegetation may have non-trivial anthropogenic interventions at the leaf foliage level (i.e., fertilizer application, harvesting, pruning), thus generating a large uncertainty in the deposition accumulators, and as a result, the predicted foliage pH. In all cases, deposition accumulation (and pH calculation) is only considered for forest canopies with canopy heights hc>1 m, but in almost all cases hc is well above this limiting value for the selected vegetation classes.

The cuticle resistance pathway is the only pathway present in the Wesely parameterization wherein an H∗ dependent term critically controls the entire pathway's contribution to the deposition flux. For example, the mesophyll pathway, which also includes an H∗ dependence, is already characterized by a very low resistance for the mesophyll portion, consistent with observations that show the stomatal resistance is the dominant barrier to SO₂ assimilation (Pfanz et al., 1987). The mesophyll resistance is added in series to the stomatal resistance, and the latter lacks an H∗ dependence. The net deposition flux via the overall stomatal pathway is determined largely by the stomatal resistance itself, and consequently the influence of H∗ on the combined pathway is likely to be small. Furthermore, the mesophyll pH, representative of the apoplastic fluid within the leaf, remains relatively constant at a neutral to slightly acidic pH, making the use of a constant H∗ in this term more appropriate (Yu et al., 2000; Savchenko et al., 2000). For the soil pathway, the rac term adds in series with the rg term, the former of which is not dependent on H∗ in the above formulation. Since typically rac≫rg for the forest categories of the land-use type, the H∗ term has a minor influence on the soil pathway. The lower canopy (rexp) term's H∗ dependence, coupled with the low value of rconv, implies it may be a candidate pathway for an H∗ dependence. However, the relatively high values of the rexp,SO2 and rexp,O3 coefficients ensure that this overall pathway has relatively little mass flux (and is often left out of deposition algorithms altogether). In contrast, the cuticle pathway's H∗ dependence is capable of controlling (and greatly reducing) the cuticle resistance without interferences from additional resistances acting directly within this pathway and hence may have a significant impact on the resulting deposition velocity. We therefore focus specifically on the pH influence on the cuticle pathway, in our work that follows.

From the above development, a requirement for calculating cuticle surface pH is the need to track and accumulate the past history of that portion of the deposition flux which ends up on the cuticles of natural vegetation foliage. This calculation is specific to the deposition algorithm employed: Eqs. (6), (7) and (8), below, and their theoretical development in the Supplement (Sects. S2.0 and S3.0), are specific to GEM-MACH's deposition algorithms, but the methodology employed is generalizable to any deposition algorithm.

Particles deposited onto the leaf surface can be removed from the foliage surface by precipitation, a process referred to as washoff. The precipitation may dissolve solid soluble particles forming an aqueous solution or physically dislodge insoluble particles captured in the grooves or by the hairs of the leaf (Sect. 1). The net result is a reduction in the particle mass on the leaf surface. Experimental investigations into washoff under controlled conditions have shown that the cumulative precipitation amount is the dominant factor determining how much mass is removed from the leaf (Fortmann and Johnson, 1984; Potter and Ragsdale, 1991; Pullman, 2009; Xu et al., 2019). Potter and Ragsdale (1991) investigated the removal of SO42- and K⁺ ions by precipitation from freshly collected broadleaf forest species in North Carolina (Acer rubrum L., Quercus prinus L., Cornus florida L., and Rhododendron maximum L.) using sequential simulated rainfall events. Their results showed that sulphate removal approached zero after 8 to 11 mm of precipitation, suggesting complete removal of soluble material is possible. Pullman (2009) similarly studied the washoff of applied KNO₃ particles from coniferous needles (Pinus strobus, Taxus cuspidate and Tsuga canadensis) and found that 70 % to 90 % of deposited mass was removed after 18.5 mm of simulated rainfall. To parameterize the washoff, Pullman (2009) suggested the function 9RP=y0+ae-bP, where R(P) is the remaining fraction of surface mass after cumulative precipitation P (in mm) and y0, a and b are observation-based fitted constants. In Pullman (2009), the fitted y0 value is nonzero, suggesting some residual mass is retained even after extensive precipitation – potentially due to insoluble material or mechanical retention within leaf structures. In this work, we adopt a simplified approach based on the sulphate data reported in Potter and Ragsdale (1991), where it is assumed that all particle species are fully soluble and subject to complete washoff with sufficient precipitation. Accordingly, we set y0=0, a=1 and determine B=0.189±0.032 via least-squares regression of the Potter and Ragsdale (1991) sulphate washoff measurements. The least squares regression is shown in Fig. 4 as a dashed line. This simplification assumes that all modelled particulate matter is readily water-soluble, representing a significant source of uncertainty and a likely oversimplification, especially for modelling the washoff of insoluble or the partially soluble part of material deposited on leaf surfaces (see Sects. 4.4 and 6.0). Nonetheless, we believe that it is not a major drawback for this study because our primary purpose is the simulation of pH in the hygroscopic material.

Since GEM-MACH is a timestep based model, it is necessary to determine the washoff that would occur over the timestep Δt. For each rainfall event, this requires tracking of (1) the concentration of each species (gas and particle) in the canopy volume at the commencement of the rainfall (Minit), and (2) the cumulative precipitation (P) at the current (i) and previous (i-1) timestep. Here the cumulative precipitation is tracked per timestep per rainfall event. Over timestep Δt where q mm of rainfall occurs (Pi=Pi-1+q), the mass of a deposited soluble species removed from the canopy volume after a timestep of precipitation (WOt) is modelled as 10WOt=WOt-1e-bPi-1-e-bPi. It should be noted that dry deposition is not accumulated on the leaf surface during precipitation events, and thus during precipitation events only removal is considered. Furthermore, a lower concentration limit of 1.0×10-20 mol m⁻³ is used in the case of complete removal, to avoid division by zero.

An important requirement in calculating cuticle surface pH is an accurate estimate of the amount of water residing on the leaf surface. The quantity of liquid water retained on the leaf, defined here in terms of the leaf water layer thickness, crucially affects the leaf water layer pH (Burkhardt and Eiden, 1990; Chameides, 1987; Klemm et al., 1987). Chemical thermodynamics solvers such as HETP (see Sect. 4.6.1) predict foliage water that would result from aerosol deliquescence, but additional water may be present on the foliage due to meteorological conditions such as rain, dew, fog and leaf guttation (the secretion of plant water from foliage). These additional water inputs were not considered in the original HETP calculations, and if present, neglecting these additional sources of water would result in a bulk leaf water solution that is too concentrated. However, the GEM weather forecast model (upon which the GEM-MACH air-quality model is based) simulates rainfall and dew water intercepted by the canopy in its physical parameterization based on the ISBA (Interactions between Soil, Biosphere and Atmosphere) land surface scheme, providing an estimate of the canopy water content wr (kg m⁻² ground area) (Bélair et al., 2003a, b), hereafter referred to as “meteorological water”. We convert this wr to a bulk canopy-level estimate (kg m⁻³ of canopy volume) by dividing by the canopy height as 11Wmet=wrhc. In this work, HETP has been modified to accept the meteorological water Wmet as an input at the start of the thermodynamic calculations used in cuticle surface pH estimation. Wmet remains constant during the iterative process within HETP to determine [H⁺] – hence this additional non-aerosol water is allowed to perturb the thermodynamic equilibrium. In addition to Wmet predicted by the GEM weather model, HETP may increase the total foliage water by an amount determined from aerosol deliquescence (Waero). Waero is not accounted for in Wmet, since the ISBA parameterization used in GEM does not consider aerosol deliquescence (Bélair et al., 2003a, b). Since it is often the case that Wmet≫Waero, Waero becomes important only during times when Wmet≈0. Upon the exit of its process calculations, HETP provides the total foliage water (Wtot) with units of kg m⁻³ of canopy volume, calculated as the sum of Wmet (unchanged) and Waero, that is, Wtot=Wmet+Waero. Wtot is then used in conjunction with Hair+ (with units of mol m⁻³) to estimate a bulk foliage pH as 12pHleaf=-log⁡10Hair+Wtot×1L1kg From Wtot, a leaf-level bulk estimate of the water layer thickness (in µm) is calculated

Note that the 2 in the denominator of Eq. (13) is required to produce an estimate of the water layer that would cover both sides of the entire leaf surface, as opposed to one side (i.e., LAI defines the single-sided leaf area per unit ground area).

Previous studies have estimated microscopic water layers on foliage surfaces to typically be in the range of 0.05 to 5 µm (Burkhardt and Hunsche, 2013; Van Hove et al., 1989; Sutton et al., 1998), while some studies have suggested the possibility of much thinner water layers, between 1 and 4 nm (Adema and Heeres, 1995; Burkhardt and Eiden, 1994; Burkhardt and Eiden, 1990). To investigate the impact of the choice of the LwThres on the resulting dry deposition velocities of SO₂, two thresholds were investigated: 5×10-4 and 0.1 µm. We investigated the impact of these alternative values of LwThres on resulting pH estimates in multi-month simulations on a North American domain (see Fig. S2 in the Supplement): the lower threshold resulted in unrealistically extreme pH values, either very acidic (pH < 2) or very basic (pH > 10). The higher threshold also resulted in better performance in comparison with surface SO₂ observations in the relatively dry month of May. In that month, foliage water layers are often sustained only by aerosol deliquescence (Waero), resulting in very high ionic strength. Under these conditions, simulations employing the higher water layer threshold and hence lower ionic strength) had better statistical agreement with observations than those with the lower threshold. Hence in the sections that follow, we employ LwThres=0.1 µm.

The effect of LwThres on the predicted SO₂ deposition velocity via foliage water pH is demonstrated in Fig. 5, which shows predicted VdSO2 for our final configuration, “CALCCO3_Lw_high”, from the 2.5 km resolution model for May 2018. We highlight this month since it featured many dry periods where Lw became very small and is largely dominated by aerosol water Waero – later months are wetter overall. To avoid skewing the data shown in Fig. 5, times when the pH = 6.68 are excluded: a pH = 6.68 is used as the “reset” pH applied during times of insufficient foliage water, or in regions where there is insufficient natural vegetation (i.e., crops). The panels of Fig. 5 thus show model results when the thin water layer threshold of 0.1 µm has been exceeded in each case.

Figure 5a clearly demonstrate the influence of foliage pH on VdSO2; when the pH is increased above 7.0 there is an almost monotonic increase in VdSO2(as shown by the increasing median and spread of the box plots). In contrast, in the base case (not shown) where a constant foliage pH of 6.68 is assumed, there are very few instances where VdSO2 exceeds 1 cm s⁻¹. Compared to the base case, a much larger incidence of VdSO2 exceeding 1 cm s⁻¹ are predicted in CALCCO3_Lw_high coinciding with times when the predicted foliage pH exceeds 6.68. Although the distribution of VdSO2 still peaks in the 0.3 to 1.0 cm s⁻¹ range, a significant percentage of values now fall above 1 cm s⁻¹ (top three bars of Fig. 5a), which is rarely seen in the Base Case where a constant pH of 6.68 was assumed.

Figure 5b show the foliage pH as a function of the calculated thickness of the foliage water layer Lw, where Lw has been separated into 8 discrete bins; the corresponding box plot gives the range of foliage pH in that bin. pH is the most acidic for thin water layers, and least acidic for thicker water layers. Water layer thickness under the relatively dry conditions of May peaks between 50 to 158 µm.

Combined, the two panels of Fig. 5 show that the highest foliage pH corresponds to the highest deposition velocities, and that the higher pH levels occur for thicker water layers.

The model's monthly average estimates of surface pH in the AOSR, and the corresponding (CALCCO3_Lw_high): (Base Case) ratios of monthly average SO₂ deposition velocities, surface concentrations and deposition fluxes over the entire model domain, are shown in Figs. 6, 7, and 8 for the months of May, June and July of 2018, respectively. Figures S3, S4 and S5 in the Supplement provide the corresponding Base Case and CALCCO3_Lw_high values of the latter three quantities in each month, and Fig. S6 shows the differences in monthly mean deposition velocity and surface concentrations of SO₂.

The AOSR appears as a distinct region of relatively alkaline foliage (7.5 ≤ pH ≤ 9.0), Figs. 6–8, panels (a). Downwind of the AOSR, the foliage pH decreases – first becoming neutral, then progressively more acidic (pH < 5.5) in May (Fig. 6a), with pH's of 6.5 to 7.5 downwind of the Oil Sands facilities in June (Fig. 7a) and July (Fig. 8a). The highest pH levels (>9, orange to yellow colours in panel (a) of Figs. 6–8) are located close to the open pit mine facilities for all three months – that is, close to the source of base-cations originating in fugitive dust. This spatial trend is consistent with the known behaviour of atmospheric PM in the region. The alkaline leaf surfaces in the AOSR are primarily due to coarse mode dust, which contains high levels of base cations and is deposited relatively close to emission sources (Zhang et al., 2018a). In contrast, particulate sulphate is predominately found in the fine mode and can be transported much further downwind, beyond the zone of significant alkaline dust deposition. As a result, acidic conditions dominate further from the source region, where the neutralizing influence of base cations diminishes. This pattern is also consistent with findings from Makar et al. (2018) who showed that at downwind distances less than 140 km from Oil Sands sources base cations are likely in excess relative to anions. Further insight is provided by examining the predicted composition of particulate matter deposited onto foliage in areas where high foliage pH values are predicted (e.g. central high pH region, Figs. 6–8, panels a). These regions receive a large fraction of deposited mass as particulate calcium, mainly in the form of calcium carbonate (CaCO₃) (Watson et al., 2014; Wang et al., 2015). Upon deposition and dissolution in the leaf water layer, CaCO₃ hydrolyses, raising the pH, consistent with the alkaline areas predicted in Figs. 6–8, panels (a). This results in substantial increases in the SO₂ deposition velocity (brown regions, Figs. 6–8, panels b), decreases in the SO₂ surface concentration (blue regions, Figs. 6–8, panels c), and increases in the SO₂ dry deposition flux (brown regions, Figs. 6–8, panels d).

Outside of the region influenced by Oil Sands facility fugitive dust, background pH levels increase from May and June (compare Fig. 6a with Figs. 7a, 8a) due to additional base cation deposition originating in forest fire particulate matter emissions, which increase towards the summer.

All three months show a substantial increase in VdSO2 relative to the base case (Figs. 6–9, panels b) with the use of the CALCCO3_Lw_high pH-dependent deposition algorithm in regions influenced by substantial base cation deposition. Base case deposition velocities over the domain range from 0.4 to 1.0 cm s⁻¹, while reaching 4.0 cm s⁻¹ for CALCCO3_Lw_high (see Figs. S3, S4, S5), with monthly average (CALCCO3_Lw_high) : (Base Case) ratios between 1.33 and 2.5 becoming common in the latter months in the boreal forest area. Ratios between 2.5 and 10 are present in the Oil Sands area in all three months due to the emissions of open pit mine fugitive dust from those facilities. Ratios of VdSO2 also reach values greater than 2.5 in areas of forest fire emissions in all three months (e.g. top left corner Fig. 8b). The ratios of VdSO2 in the AOSR are consistent with aircraft measurements from Hayden et al. (2021), who observed that measured (inferred) VdSO2 was 1.7 to 5.4 times larger than Base Case predictions from GEM-MACH simulations lacking the pH correction described here.

Investigation of wildfire ash chemical composition support the importance of forest fire emissions towards foliage pH, with studies showing that CaCO₃ is a major component; its dissolution in water often resulting in alkaline solutions with pH > 7.5, and sometimes as high as 11 (Sánchez-García et al., 2023; Pereira et al., 2013, 2012). Conversely, in the Foothills of Alberta where the foliage pH is often predicted to be acidic (blue regions Figs. 6–8, panels b), CALCCO3_Lw_high predicts a 20 % to 25 % reduction in VdSO2, highlighting that the pH-modulated VdSO2 can vary substantially across the domain, depending on the chemical composition of the mass deposited onto foliage.

As the pH increases above 9.0, both rcutzha(SO2) and the canopy resistance rc(SO2) approach zero (see Fig. 2). In this work, a minimum value of 10⁻² s m⁻¹ was imposed on rcut, which is much lower than the 20 s m⁻¹ limit suggested by Zhang et al. (2003) under wet conditions. Applying the 20 s m⁻¹ threshold would dampen the pH effects on VdSO2 beyond a pH of 8.0. However, the Zhang et al. (2003) threshold was not based on field measurements. While Sorteberg and Hov (1996) noted that no such measurements existed, more recent studies have reported rc(SO2)≈0, particularly in wet conditions (Neirynck et al., 2011; Feliciano et al., 2001). These findings suggest that rcutSO2≪20 s m⁻¹ is plausible. If very low rcutzha(SO2) lead to unrealistic Vd estimates, this may reflect issues with the parameterization of ra and rb, rather than with rcutzha itself.

Figures 6–8 (panels c) show the response of surface SO₂ concentrations towards these changes in VdSO2. The largest decreases occur in the AOSR (ratios between 0.40 and 0.75; reductions of 0.25 to 0.75 ppb, see also Figs. S3, S4, S5). Large ratio decreases in SO₂ of between 0.40 and 0.75 can also be seen throughout the northern part of the domain in June (Fig. 7c), a particularly active forest fire base cation emissions and deposition month in 2018. However, in these areas the absolute change is small (<0.1 ppb, see Fig. S4), limiting practical significance despite the large percentage difference. Localized SO₂ concentration increases of 10 % to 30 % are predicted in some regions, including the Foothills of Alberta and west of Cold Lake (orange colours, Figs. 6–8, panels c), where corresponding decreases in VdSO2 have been predicted (panels b). Although the absolute increases are typically <0.1 ppb (Figs. S3, S4, S5), there are localized areas exceeding 0.25 ppb. In absolute terms this decrease in the mean VdSO2 is much less than the increase seen in the AOSR, which often exceeds 1.0 cm s⁻¹. This result demonstrates that even a relatively small decrease in the mean VdSO2 (due to acidic foliage conditions) may cause a disproportionately large (localized) increase in the simulated mean surface SO₂ concentration. We note that the largest concentration decreases (blue colours, Figs. 6–8, panels c) correspond to areas and times where there is a high local deposition flux of base cations, from the Oil Sands facilities' fugitive dust emissions, or from forest fires.

The net impact of the changes on the SO₂ deposition flux (DSO2) is shown in Figs. 6–8 (panels d). As outlined in Sect. 4, DSO2 is the flux calculated on a time-step basis as the product of VdSO2 and the surface SO₂ concentration. Thus, increases in VdSO2 only translate to increased DSO2 where appreciable surface SO₂ concentrations are present. Where SO₂ is available, however, higher VdSO2 will proportionally increase DSO2, all else being equal. Accordingly, the largest absolute increases in DSO2 under CALCCO3_Lw_high occur in the AOSR, where elevated VdSO2 (2.5–10 cm s⁻¹) coincide with elevated surface SO₂ concentrations (>2 ppb). Since SO₂ emissions are identical in both Base Case and CALCCO3_Lw_high simulations, this increased flux is entirely attributable to changes in VdSO2 resulting from base cation-driven co-deposition. This enhancement is consistent with aircraft-based measurements reported by Hayden et al. (2021), who found that an earlier version of GEM-MACH, lacking the pH VdSO2 enhancement, underpredicted the dry deposition flux of total oxidized sulphur (TOS) by 2 to 14 times. While TOS measured in their study also included particulate sulphate, over 92 % of TOS their campaign was in the form of gaseous SO₂ making it reasonably representative of VdSO2.

Further downwind, particularly beyond 100 km from the AOSR, DSO2 is reduced relative to the Base Case by up to 40 %, especially in May (Fig. 6). Two factors contribute to this reduction – (1) depletion of SO₂ from upwind deposition and (2) local inhibition of deposition to acidic foliage conditions. The latter likely dominates, based on the spatial patterns: in regions where DSO2 is reduced under CALCCO3_Lw_high, surface SO₂ concentrations are increased relative to the Base Case, particularly in May (Fig. 6) – this occurs despite enhanced SO₂ removal to forests just upwind.

Three locations in the 2.5 km model domain; Oski-otin (near the village of Fort Mackay), the York Athabasca JackPine site (YAJP), and a downwind evergreen forest location near the Saskatchewan border (DWEF) are superimposed on the monthly average leaf pH field in Fig. 8a, and their corresponding diurnal cycles of VdSO2 for the months of May and June are shown in Fig. 9. The DWEF site was selected to represent a downwind location where anthropogenic dust deposition is minimal and foliage water layers are often acidic to near neutral. This contrasts with both YAJP and Oski-otin, where deposition of alkaline dust frequently raises the foliage pH above 7.5 (see Figs. 6–8, panels a). As expected from Figs. 6–8 (panels a), YAJP and Oski-otin show substantial increases in VdSO2 when CALCCO3_Lw_high is applied. At these sites, the mean VdSO2 exceeds 1.0 cm s⁻¹ at all hours of the day, except in May at Oski-otin. Although the average remains high, individual values of VdSO2 vary widely – from as low as 0.5 cm s⁻¹ to over 4.0 cm s⁻¹ – as reflected in the large interquartile range (IQR). In the afternoon, the IQR exceeds 2 cm s⁻¹ at YAJP and Oski-otin indicating strong temporal variability. In contrast, the Base Case rarely predicts a VdSO2 that exceeds 0.5 cm s⁻¹ at these locations, with a much narrower IQR around 0.2 cm s⁻¹. A notable exception occurs at Oski-otin in May between 12:00 to 00:00, where the median, 25th and 75th percentile for CALCCO3_Lw_high closely match those of the Base Case. This is due to insufficient predicted foliage water, leading to the pH being reset to 6.68 (the same constant value used in the Base Case). Nonetheless, the mean VdSO2 during this period is still much higher than median, implying that a small number of very high values significantly raises the mean.

The VdSO2 predicted by CALCCO3_Lw_high at Oski-Otin and YAJP are in the range of VdSO2 inferred from tower and aircraft measurements reported in Hayden et al. (2021) and Gordon et al. (2023). Specifically, Hayden et al. (2021) measured VdSO2 at a tower site in the AOSR over a three-day period (6 to 8 June 2018), finding a mean afternoon value (13:00 to 19:00 Mountain Daylight Time) of 4.1 cm s⁻¹, with minimal uptake of SO₂ during the night (VdSO2 < 0.5 cm s⁻¹). These values fall well within the diurnal ranges predicted by CALCCO3_Lw_high at Oski-otin (see Fig. 9). Aircraft-based estimates from Hayden et al. (2021) (conducted between 13 August and 7 September 2013) reported afternoon VdSO2 values ranging from 1.2 to 3.4 cm s⁻¹. Although these measurements were made in a different year and spanned various surface types (i.e., forests, lakes, wetlands and tailings ponds) they also align well with the CALCCO3_Lw_high predictions. At YAJP, Gordon et al. (2023) inferred VdSO2 between July and October 2021, reporting values between 2.1 and 5.9 cm s⁻¹. While the Gordon et al. (2023) measurement period does not overlap with the 2018 model simulations shown in Fig. 9, similar magnitudes of anthropogenic dust deposition in both years suggest comparable pH conditions, and consequently, similar SO₂ uptake rates. In summary, all three observational datasets report VdSO2 values within the range predicted by CALCCO3_Lw_high, reinforcing that the pH-dependent deposition algorithm offers a substantial improvement over the Base Case in replicating observed VdSO2 in the AOSR.

Time series of both observed and simulated mean diurnal cycles of the surface SO₂ concentration at 20 different WBEA continuous monitoring stations (Figs. 10, S7, S8, S9, and 11, S10) show that the pH-modulation effect has the most pronounced impact on the mean surface SO₂ concentrations (relative to the Base Case) at the stations BGFM, FMCS, HRZN, MUSK, FTHL and WAPI, though improvements in NMB can be seen in 13 and 15 out of 21 stations in June and August 2018 respectively (Fig. 11a, b). At the six stations with larger improvements, CALCCO3_Lw_high yields a substantial reduction in the normalized mean bias (NMB) relative to the Base Case (Table 1, see also Fig. 11a, b).

Notably, WAPI is the same tower site where Hayden et al. (2021) inferred VdSO2 during a 3 d period in June 2018. During May 2018, these same stations often show an improvement in the NMB during the afternoon when CALCCO3_Lw_high is applied. However, at night CALCCO3_Lw_high tends to underpredict surface SO₂ concentrations more severely than the Base Case. This systematic underprediction, also present to a lesser extent in the Base Case (typically by ∼ 0.5 ppb), suggests a broader issue likely related to the quasi-laminar sublayer resistance (rb). Specifically, it may indicate that the nocturnal atmospheric stability is not properly represented in the model; rb may not be sufficiently enhanced in response to suppressed turbulence, leading to an overestimation of SO₂ deposition. This may also suggest that the GEM model underrepresents nocturnal atmospheric stability, possibly due to excessive turbulent mixing or an inadequate parameterization of resistances in stable boundary layers. A similar nighttime underprediction pattern appears in July. In August, however, CALCCO3_Lw_high does a better job simulating the nighttime SO₂ surface concentrations than the Base Case. The Base Case often overpredicts the mean surface SO₂ concentration during the nighttime, while CALCCO3_Lw_high shows much better agreement overall, with a NMB at most stations that is closer to 0 % (i.e., Fig. 11a, b).

Figure 11 presents Taylor diagrams for (panel a) July and (panel b) August 2018 (see Fig. S10 for May and June); these summarize graphically how closely modelled surface SO₂ concentrations match observations (Taylor, 2001). The diagrams simultaneously depict three key statistics: the correlation coefficient, the centred root-mean square difference (CRMS), and the standard deviation (amplitude of variation). In this work, both model and observed values are normalized by the observed standard deviation, giving a normalized standard deviation. This implies that the observations always have a standard deviation of 1.0, marked as a black dashed line (semicircle) at a radius of 1.0 on each plot. Arrows that move closer to this dashed line indicate improved agreement in the amplitude of variation. The azimuthal angle represents the correlation, increasing clockwise from 0.0 to 1.0. To aid interpretation, the normalized mean bias (NMB) for each station is listed in the legend as (Base Case → CALCCO3). Red text and red arrows highlight stations where CALCCO3_Lw_high produces a better NMB than the Base Case. Black arrows indicate no improvement or a deterioration in the NMB. A general result of the comparison is that NMB values “shift towards negative numbers” – that is, all NMB values are decreasing. For stations where the base case NMB was positive this usually results in a smaller magnitude positive or negative NMB (red tabulated numbers), and for stations where the base case NMB was negative, the NMB becomes more negative (black tabulated numbers). Additional factors aside from the pH effect studied here are therefore likely to result in the remaining station-to-station variations in NMB. The results show that CALCCO3_Lw_high improves the standard deviation at several stations compared to the Base Case, especially in June (e.g., at BGFM, HRZN, FMCS, FTCH, FTHL, LOWC) and even more so in August, where all stations except BVPT, ANZC, MKRV and WAPS show improvement. In contrast, July exhibits mostly a deterioration in the standard deviation (see Fig. S10), with many arrows pointing away from the reference line at 1.0, indicating poorer agreement with observed variability.

Despite modest to large statistical improvements in NMB in May, June, July and August at some stations, substantial discrepancies remain between modelled and observed surface SO₂ concentrations, particularly in the form of low correlation coefficients (i.e., correlation ≪ 1.0). While dry deposition plays a key role in determining the surface SO₂ concentrations in GEM-MACH, other factors may also contribute significantly to correlation, including: i.

the accuracy of meteorological variables predicted by GEM (i.e., air temperature, wind speed and direction, boundary-layer stability, precipitation occurrence and timing),