Sulfate fragmentation data were obtained using an Aerodyne high-resolution time-of-flight aerosol mass spectrometer (AMS) (Aerodyne Research Inc., Billerica, MA, USA; DeCarlo et al., 2006). The ambient data used here are from aircraft observations from the following campaigns (Table 1): Deep Convective Clouds and Chemistry (DC3) (Barth et al., 2015); Studies of Emissions and Atmospheric Composition, Clouds and Climate Coupling by Regional Surveys (SEAC4RS) (Toon et al., 2016); Wintertime Investigation of Transport, Emissions, and Reactivity (WINTER) (Schroder et al., 2018); Korean–United States Air Quality (KORUS-AQ) (Nault et al., 2018); and Atmospheric Tomography Mission 1 and 2 (ATom-1 and ATom-2) (Guo et al., 2020; Hodzic et al., 2020). Flight paths for all six campaigns are shown in Fig. S1 in the Supplement. These campaigns span polluted urban, partially polluted biogenic, biomass burning smoke, rural, and remote regions of the atmosphere. DC3 sampled continental and rural conditions with diffuse pollution and some biomass burning events. WINTER and KORUS-AQ were airborne campaigns that focused on urbanized regions (although from different regions and times of year; Table 1); therefore, the campaigns had appreciable mass concentrations of ammonium nitrate due to anthropogenic emissions of NOx and the subsequent production of HNO3 that partitions into the aerosol with ammonia (Seinfeld and Pandis, 2006). SEAC4RS focused on regional background chemistry of the continental United States, which included impacts from biomass burning, biogenic, and pollution emissions and upper-tropospheric chemistry impacted by convection. Finally, ATom-1 and ATom-2 sampled the remote Pacific and Atlantic basins with continuous full vertical profiling in order to study the composition of the remote marine atmosphere, impacted by long-range-transported chemical species and marine emissions and far from anthropogenic sources. Not all campaigns are usable for all the analyses in this paper, depending on the quality and completeness of the data. Table 1 indicates which campaigns were usable for each analysis.

The highly customized University of Colorado-Boulder aircraft AMS was used in all campaigns and has been described elsewhere (DeCarlo et al., 2008; Dunlea et al., 2009; Nault et al., 2018; Schroder et al., 2018; Guo et al., 2020), so only details relevant to this study are summarized here. Ambient air is drawn through a National Center for Atmospheric Research (NCAR) high-performance instrumented airborne platform for environmental research modular inlet (HIMIL; Stith et al., 2009) with a constant standard flow rate of 9 L min-1, and all data are reported at a constant standard temperature (T = 273 K) and pressure (P = 1013 hPa). The sampled air enters a pressure-controlled inlet (Bahreini et al., 2008) and is then introduced into an aerodynamic focusing lens (Liu et al., 1995; X. Zhang et al., 2004). Particles then impact onto an inverted-cone porous-tungsten “standard” vaporizer (SV), operated at ∼ 600 ∘C under high vacuum. The standard vaporizer is used in this study. A “capture vaporizer” has been recently demonstrated; it leads to more thermal decomposition while still retaining similar (although noisier) fragment information (Hu et al., 2017a; Zheng et al., 2020), but it is not used here. Non-refractory species, those that evaporate in less than a few seconds (such as sulfate, nitrate, ammonium, and organic material), are subsequently ionized by 70 eV electrons. Some refractory and semi-refractory species such as sea salt, lead, and potassium can be detected by the AMS in some cases (Lee et al., 2010; Salcedo et al., 2010; Ovadnevaite et al., 2012; Hodzic et al., 2020). A cryopump reduces background in the ionizer by orders of magnitude during the flights, leading to low detection limits, in particular for NH4, which is critical for acidity quantification in the remote troposphere. Data were taken at 1 Hz but were processed at both 1 Hz and 1 min resolution, and the latter product is primarily used here due to higher signal-to-noise ratios. The 1 min datasets were further filtered by removing points where the sulfate signal was below 3 times its detection limit. Detection limits were estimated continuously via the methods of Drewnick et al. (2009) and confirmed with frequent in-flight filter blanks. For the laboratory studies, everything was kept the same as on the aircraft other than no use of the HIMIL aircraft inlet. Data were processed and analyzed with the standard Squirrel and PIKA ToF-AMS data analysis software packages within Igor Pro 7 (Wavemetrics) (DeCarlo et al., 2006; Sueper, 2018).

One important parameter for AMS quantification is collection efficiency (CE). CE is the probability that a particle entering the AMS is detected. It is affected by several particle properties (Huffman et al., 2005), the most important being particle bounce off the vaporizer without detection (Middlebrook et al., 2012). Bounce is controlled by particle phase (Quinn et al., 2006; Matthew et al., 2008) and is estimated for ambient particles based on their ammonium balance (acidity) and ammonium nitrate content (Middlebrook et al., 2012). This parameterization performs well for ambient particles (Middlebrook et al., 2012; Hu et al., 2017a, 2020; Guo et al., 2020). Still, potential variability in CE that is not perfectly captured by the parameterization contributes a major fraction of the AMS uncertainty for ambient-particle analysis (Bahreini et al., 2009). Alternative methods to estimate ambient CE for ambient particles are of interest; we explore a potential alternative method here.

Two methods have been proposed to quantify OS contribution to total sulfate using AMS sulfate ion fragment fractions. The first method uses different sulfate ions to attribute measured total sulfate to either OS, AS, or methanesulfonic acid (MSA). Due to the structure of OS, only non-hydrogenated sulfate ions, i.e., SO+, SO2+, and SO3+, are produced in the AMS for OS. AS does produce hydrogenated sulfate ions, i.e., H2SO4+ and HSO3+, as well as the same non-hydrogenated sulfate ions produced by OS. Chen et al. (2019) proposed a “triangle method” to estimate these two species and MSA, based on the observed fragments. Note that mineral sulfates such as sodium sulfate fragment similarly to OS, and thus these methods need to be interpreted differently in regions with significant submicron mineral sulfates. MSA calibrations show variability for the fragments (Chen et al., 2019) and were not performed for all the studies in this work. Since MSA can be quantified without using the sulfate fragments, here we apply this method to estimate the fractions of OS and AS by using a one-dimensional version of the triangle (i.e., just the hypotenuse connecting pure OS to pure AS). An alternative method is based on the same assumptions but uses different equations to quantify the relative concentration of OS (Song et al., 2019).

Both literature methods for deconvolving sulfate as OS and AS assume that the main factor impacting sulfate fragmentation in the AMS is sulfate structure (OS, AS, or MSA). Chen et al. (2019) briefly mention that acidity can impact sulfate fragmentation, but this effect has not been studied and quantified. In addition, Chen et al. (2019) used pure standards to quantify the AMS fragmentation of different species but did not explore potential matrix effects in AMS fragments, which could impact internally mixed ambient particles.

To compare our field data to those analyzed in Chen et al. (2019), we use the variables defined in that study, fH2SO4+ and fHSO3+, and define the normalized nfH2SO4+ and nfHSO3+ (normalized to the values of fH2SO4+ and fHSO3+ for pure AS): 1fH2SO4+=H2SO4+H2SO4++HSO3++SO3++SO2++SO+2nfH2SO4+=fH2SO4+fH2SO4+(pure AS)3fHSO3+=HSO3+H2SO4++HSO3++SO3++SO2++SO+4nfHSO3+=fHSO3+fHSO3+(pure AS). It should be noted that while that study includes methanesulfonic acid (MSA) data, the impact of MSA on fH2SO4+ and fHSO3+ is minimal for the ATom campaigns (see Fig. S2). Additionally, one study over the western United States (representing a rural, continental region) observed MSA concentrations of ∼ 50 ng m-3 (Sorooshian et al., 2015), which results in a very small deviation in the Chen triangle and can hence be neglected for the purposes of this work. All variables were normalized to the values of the same variables for pure-AS calibrations (conducted during each field experiment) in order to eliminate some of the spread in the sulfate ions that is likely due to instrument-to-instrument or instrument-in-time variability (Fry et al., 2013; Chen et al., 2019) (Fig. S3). We also define a new AMS sulfate ion ratio, HySOx+ / SOx+, and create the normalized nHySOx+ / SOx+ to reduce the influence of instrument-to-instrument or instrument-in-time variability: 5HySOx+/SOx+=HySOx+SOx+=H2SO4++HSO3+SO3++SO2++SO+6nHySOx+/SOx+=HySOx+/SOx+HySOx+/SOx+(pure AS). The submicron aerosol molar ammonium balance (NH4_bal) is calculated as 7NH4_bal=NH4/18(SO4/48)+(NO3/62)+(Chl/35). The concentration of non-refractory chloride is only included for non-remote campaigns (KORUS-AQ, WINTER, and SEAC4RS) since it was negligible for others and strongly impacted by sea salt in the marine boundary layer. The fraction of ammonium nitrate in the particle phase (ammonium nitrate mass fraction, ANf) (by mass) is 8ANf=(80÷62)×Inorganic NO3NO3+SO4+NH4+Chl+Org. The fraction of total AMS aerosol mass comprised of OA (OAf) is 9OAf=OrgNO3+SO4+NH4+Chl+Org. The sulfate equivalent concentration of OS in the Song et al. (2019) paper is calculated as 10COS=MSO42-SOobs+-Rcd,SO+/HySOx+,∗⋅HySOx,obs+,∗MSO++SO2,obs+-Rcd,SO2+/HySOx+,∗⋅HySOx,obs+,∗MSO2+, where “cd” stands for “clean and dry”. Clean and dry conditions are defined in Song et al. (2019) as ambient data points where PM1 = 10 µg m-3 and RH = 30 %. Clean and dry conditions are assumed to represent nearly pure AS. M is for the molar mass of the different sulfate ions, and “obs” represents the ambient data for specific sulfate fragments. HySOx+,∗ (which differs from the notation used in Song et al., 2019, but is necessary to differentiate HySOx+ between Chen et al., 2019, and Song et al., 2019) is defined in Song et al. (2019) as SO3++HSO3+ + H2SO4+. For the Chen method, the COS is defined based on the AS-normalized nfH2SO4+ values: 11COS=SO4-nfH2SO4+×SO4. OSf, the fraction of OS : total sulfate, is defined as 12OSf=COSSO4, where COS is calculated from Eq. (10) or (11).

As ambient aerosols contain mixtures of chemical species, we investigated if matrix effects may impact the fragmentation of sulfate species. Different solution mixtures, composed of various amounts of AS (certified American Chemical Society (ACS), 99.7 % purity) and ammonium nitrate (AN) (certified ACS, 99.9 % purity) in water (Milli-Q-grade, R > 19 MΩ), were atomized to generate particles and size-selected using a differential mobility analyzer (DMA) (TSI Model 3081), analyzed with a condensation particle counter (CPC) (Model 3775), and electrostatic classifier (Model 3080) for mobility diameters between 350–400 nm. We investigated AS–AN mixtures, ranging from ANf = 0 % to 95 %.

In order to assess effects on the sulfate fragmentation from mixing with OA, chamber experiments, where different types of secondary organic aerosol (SOA) were formed by gas-phase reactions and condensation onto AS seeds, were investigated. SOA was formed from alkanol and toluene photooxidation under high-NOx conditions (Liu et al., 2019) as well as Δ-3-carene and α-pinene reactions with nitrate radicals (Kang et al., 2016). Experiments were initiated with 100 % AS in a dry chamber (RH < 5 %, ∼ 298 K) followed by either rapid, gradual, or stepwise increases in SOA until a maximum OA / (OA + AS) ratio of ∼ 70 % was reached. Aerosol composition was monitored by the AMS, and size distributions were monitored with a scanning mobility particle sizer (SMPS; DMA was TSI Model 3081, electrostatic classifier was Model 3080, and the CPC was Model 3775). The relative ionization efficiency (RIE) of sulfate was directly calibrated with pure ammonium sulfate, while RIE * CE of the SOA produced was estimated by comparison to the SMPS-integrated volume, together with OA density estimated from the AMS-derived elemental ratios per Kuwata et al. (2012), in order to accurately quantify OA / (OA + AS). Humid experiments were not considered here due to the potential of forming organosulfates.

Aerosol pH was estimated using the Extended Aerosol Inorganic Model (E-AIM) IV (Clegg et al., 1998; Massucci et al., 1999; Wexler and Clegg, 2002). We input into the model (run in “forward mode”) the total nitrate (gas-phase HNO3 plus particle-phase total NO3-), sulfate, ammonium, relative humidity (calculated according to the parameterization of Murphy and Koop (2005), which is critical for upper-tropospheric conditions), and temperature. Total nitrate (inorganic + organic) was input as Nault et al. (2021) found that removing estimated organic nitrate does not impact the pH calculation. This was done to calculate aerosol liquid water and aerosol pH. Model IV was not run with chloride ions as their concentrations were very low, and including chloride limits the model to temperatures ≥ 263 K (Friese and Ebel, 2010), which would greatly limit the analysis of calculated pH for WINTER, ATom-1, and ATom-2. We have added the modifier “calculated” before pH for all situations where we are describing the E-AIM pH and “estimated” when we refer to pH from the empirical estimation methods from AMS measurements, introduced in this study. Also, including chloride precludes running the model under supersaturated-solution conditions, which is a closer approximation of ambient aerosol (Pye et al., 2020). All aerosol mass concentrations were from the University of Colorado at Boulder (CU) AMS. HNO3(g) was measured by the California Institute of Technology chemical ionization mass spectrometer (CIT-CIMS) (Crounse et al., 2006), which was flown in all of these missions (excluding WINTER, where the chemical ionization mass spectrometer of the University of Washington (UW-CIMS) was used for the HNO3 measurements) (Lee et al., 2014, 2018). Results are generally similar when using the soluble acidic gases and aerosols (SAGA) mist chamber measurement for total nitrate (Nault et al., 2020). The forward mode is less sensitive to uncertainties in measurements than the “reverse mode,” which only uses particle composition and T and RH as inputs (Hennigan et al., 2015). Also, due to lack of NH3(g) measurements, the model was run iteratively until convergence in modeled NH3 occurred, similarly to Guo et al. (2016). Performance for calculated pH was investigated by comparing model-calculated HNO3 and NO3- to measurements as the partitioning of nitrate between gas and particle phase is sensitive to calculated pH under acidic conditions (Guo et al., 2016). For all campaigns included herein (DC3, WINTER, SEAC4RS, KORUS-AQ, ATom-1, and ATom-2), the slopes of HNO3 (measured vs. predicted) are within the uncertainty in the measurements and with good correlations (Fig. S4). For NO3-, the slopes are within the measurement uncertainty for five of the six campaigns. For ATom-2, the NO3- slopes were low; however, for this campaign, the measured NO3- mass concentrations were extremely low (mean = 0.02 µg sm-3), and the calculated pH was also very low (mean = -0.5), leading to very little NO3- in the aerosol phase (see Fig. S4).

In addition, other bases present in the atmosphere (such as amines) were examined. Prior studies have shown that amines were less than a maximum concentration of 30 ng m-3 at the ocean surface (Gibb et al., 1999; Facchini et al., 2008; Müller et al., 2009; Frossard et al., 2014; van Pinxteren et al., 2015; Youn et al., 2015). Another study by Sorooshian et al. (2009) found that amine mass concentration dropped off quickly with altitude to concentrations less than 25 ng m-3 at an altitude between 200 and 300 m, which is the approximate minimum altitude flown on the DC-8 during the ATom campaigns. As the 1 min detection limit for the AMS data for amines is typically 10 ng m-3, we expect the amine signal to generally be below the limit of detection and thus outside of our quantification capabilities. This was observed for AMS data from the ATom campaigns, using characteristic ions identified in past studies (Murphy et al., 2007; Ge et al., 2014). It was found that amine ions cannot be distinguished from background for many ATom flights. Only during one flight in ATom-1 did we observe an amine signal (C2H6N+ m/z = 44) above the background (see Fig. S5). During this flight, amines (from the contribution of CH4N, C2H6N, and C3H8N) only accounted for 0.7 ng m-3of aerosol, whereas ammonium accounted for 19 ng m-3. Amines can produce the same fragments as ammonium, but this is only the case for a few percent of the amine fragments (Ge et al., 2014). In this case, the ammonium concentration is 25 times that of the amines. Since amines were even lower during other flights, we assume the effect of amines to the pH calculation is very small and can be ignored for E-AIM calculations.

We used a global chemical transport model (GEOS-Chem 12.6.1; 10.5281/zenodo.3520966; Bey et al., 2001) to investigate modeled global distributions of ammonium nitrate mass fraction (ANf) and calculated aerosol pH across different regions. GEOS-Chem was driven by assimilated meteorological fields from the Modern-Era Retrospective analysis for Research and Applications version 2 (MERRA2) (Gelaro et al., 2017) for the year of 2010. The simulation was conducted at 2∘ (latitude) × 2.5∘ (longitude) with 47 vertical layers up to 0.01 hPa and ∼ 30 layers under 200 hPa. We used the Community Emissions Data System (CEDS) inventory for global anthropogenic emissions (Hoesly et al., 2018) and the Global Fire Emissions Database version 4 (GFED4) for biomass burning emissions (Giglio et al., 2013). Aerosol pH and gas-particle partitioning of inorganic aerosols were calculated online using the ISORROPIA-II model within GEOS-Chem (Fountoukis and Nenes, 2007; Pye et al., 2020). Similarly to Jo et al. (2019), sea salt aerosol was excluded from pH calculations based on a better agreement with the observationally constrained calculated-pH values as suggested by Nault et al. (2020). Oceanic NHx emissions were also included in this model based on recent work (Paulot et al., 2015; Nault et al., 2020).

Application of the one-dimensional Chen method to laboratory data is shown in Fig. 1. Data are expected to lie inside the triangular region and be apportioned depending on the relative distance to the three vertices. For example, data lying at [0.5,0.5] on the line between the OS and AS points would represent a sample with ∼ 50 % OS and ∼ 50 % AS. If data cluster around the [1,1] point, where pure AS resides, all of the sulfate is attributed to AS. From applying this method, it is clear that none of the campaign averages or laboratory data fall between the [0,0] and [1,1] points, suggesting that there may be additional factors (other than sulfate composition) impacting the location of data in this triangular region.

The effect of internally mixed ammonium nitrate (AN) is shown in Fig. 1a. For mixtures containing ANf < 50 %, data center around the pure-AS point in the Chen triangle. When ANf is increased past 0.50, there is an increase in both nfHySOx+ ions, even when all of the particulate sulfate is inorganic. As the particle ANf increases up to ANf = 0.95, the OSf estimation becomes increasingly inaccurate. The method may estimate OSf = 0 % in the latter situation, when OSf is actually 50 %. While OSf = 0 % may be reasonable in some parts of the atmosphere, and one may be inclined to accept this result as it is non-negative, it is actually incorrect due to the effect of particulate AN. Thus for laboratory data, the Chen method should not be used on mixtures containing ANf > 0.50.

The effect of OA internally mixed with AS on the sulfate fragmentation pattern was also explored with toluene, alkanol, and monoterpene SOA (Figs. 1b and S6). For the alkanol SOA experiments we found that the presence of even a small coating of alkanol SOA (which is thought to be liquid; Liu et al., 2019) shifts the normalized AS [1,1] point to ∼ [1.08,1.08], but increases in the fraction of OA (OAf) from 0.1 to 0.3 lead to no further changes in nfHySOx+ (Fig. 1b). This means that for a sample containing a mixture of AS and alkanol SOA, the calculated OSf would be -15 % (Chen et al., 2019). In contrast, toluene SOA, which spans 0 < OAf < 0.5, shows no clear change in the nfHySOx+ ions, indicating that OAf would not bias the Chen method for this example. The monoterpene SOA, from two different experimental datasets (2014 and 2015) using different AMSs, show more varied results than the previous two studies. Overall, the 2014 data show a very small increase in the “pure” AS value in the OAf range 0–0.50, whereas the 2015 monoterpene data show a consistent and constant 10 %–20 % increase in nfHySOx+ compared to the pure-AS calibration point (similarly to the alkanol SOA). However, when OAf is in the range of 0.50 < OAf < 0.70, 30 %–40 % increases are observed for the 2014 and 2015 data. This result is only applicable to a few of the experiments (see Fig. S6), potentially due to very high SOA loadings (up to 300 µg m-3). These high OA concentrations could potentially lead to a change in the particle phase due to condensation of more volatile and liquid species, potentially altering the interactions of the particles and the vaporizer surfaces. These experiments collectively suggest that a “pure” AS calibration point of [1.15,1.15] may be more appropriate when applying the Chen et al. (2019) method to some mixed aerosol at typical OA concentrations observed in the atmosphere; this is discussed further in Sect. 3.2.

Chen et al. (2019) briefly discussed the potential impact of acidity on their OS quantification method. This is explored here with pure-sulfuric-acid lab calibrations (Fig. 1c). Pure sulfuric acid shows a large deviation from the pure-AS triangle point (similar to increasing ANf), nearly doubling the values for the nfHySOx+ ions. This implies that a particle containing sulfuric acid would produce a strong negative bias in the estimate of OS by the Chen method.

The results of applying the Chen et al. (2019) method to five aircraft campaigns are shown in Fig. 1. The effect of internally mixed ammonium nitrate (AN) was explored in Fig. 1a and Sect. 3.1 (for laboratory studies). Here we explore the effect for field data from KORUS-AQ (near Seoul, South Korea), where AN was often a major aerosol component (average ANf ∼ 0.18). As discussed in Sect. 3.1, as the percent of AN in laboratory mixtures of AS–AN increases, so do the nfHySOx+ ions. The same effect is observed for the KORUS-AQ campaign, although the departure from the AS vertex is observed at substantially lower AN fractions for the field data (ANf ∼ 0.30). When field data are affected by AN, the Chen method might be applicable for situations with ANf < 0.30. At higher fractions, a correction could potentially be developed but with increased resulting uncertainty.

The effect of OA (shown in Fig. 1b for laboratory data) on sulfate fragmentation in ambient data is less clear due to the lack of data that have a lower ANf, higher pH, and little or no OS (see Table S1 for average campaign OAf). In the presence of any one of those factors, the sulfate fragmentation will be affected. It is especially challenging to confirm the absence of OS due to the lack of direct total OS measurements available. In Fig. S7, we isolate a subset of the KORUS-AQ dataset (where ANf < 0.3 and pH > 0, defined as “regime II” and discussed in detail in Sect. 3.4) to see if there is an offset in the AS under these chemical conditions as observed in the laboratory data shown in Fig. 1b. Similarly to the lab data, there appears to be a ∼ 10 % offset between the pure-AS fHySOx+ values from calibrations and the KORUS-AQ data that occupy regime II (average OAf ∼ 43 %). This offset is smaller than some of the offsets observed in the laboratory data (Figs. 1b and S6) but may hinder the ability of the Chen OSf quantification method to estimate [OS] even in conditions where the pH > 0 and the ANf < 0.3.

In Fig. 1d, average values for each campaign in regime II, defined as ANf < 0.3 and calculated pH > 0, are shown. For less acidic aerosols and in the absence of OS or ANf effects, it is expected that the data would fall on top of the [1,1] pure-AS point in the 1D triangle plot, but this is not observed. This shift suggests that there are other factors (such as the presence of organics) that affect the location of the pure-AS point. In addition, the average values for the different campaigns vary substantially, so it is unlikely that a “corrected” pure-AS point can be used for all campaign and/or lab data.

To further look into the potential effect of acidity, we consider the ATom campaigns in Fig. 1c. ATom focused on remote oceanic air, with very low ANf (< 0.01). This is expected as AN is semivolatile (DeCarlo et al., 2008; Hennigan et al., 2008; Nault et al., 2018), and for the very-low-calculated-pH conditions during ATom (∼ -1 to 1, average of -0.6), most of the nitrate will be in the form of HNO3(g) (Guo et al., 2016). The Particle Analysis by Laser Mass Spectrometry (PALMS) instrument independently reports OSf ∼ 0.3 %–0.7 % for ATom (depending on the pH). The results for ATom span the range between pure AS and pure H2SO4, following a monotonic trend as acidity increases, consistent with the laboratory results and the results from the WINTER campaign in Chen et al. (2019). We hypothesize that high acidity is leading to the observed departure from the Chen triangle. Hence, the ATom results suggest that all of the sulfate sampled is inorganic, and if the Chen method is applied, then OSf = -26 % to +4 %. Thus the Chen method is insufficient to describe the trends observed for very acidic aerosols until calculated pH increases to ∼ 0 (where the ATom data start to converge onto the pure-AS data point). For campaigns containing particles of calculated pH > 0, the Chen method might be applicable.

To further illustrate that the ATom and KORUS-AQ campaigns are representative of the range of air masses in the troposphere, Fig. 1d shows results for two additional campaigns that focused on the continental US. SEAC4RS and WINTER represent chemical regimes that are not extremely acidic (average calculated-pH SEAC4RS ∼ -0.2, WINTER calculated pH ∼ 1.2). SEAC4RS had low ANf (∼ 0.04), while WINTER had high ANf (∼ 0.25). It is observed that every single campaign average falls outside of the triangle (for the full campaign and non-acidic, low ANf), indicating that the Chen et al. (2019) method, as proposed, is not applicable to many regions of the atmosphere. Average ANf, OAf, and calculated-pH values for different campaigns are shown in Table S1.

We note that this section (Sect. 3.3) should be of most interest for AMS and/or ACSM users and can probably be skipped by others. It is useful to provide a physical interpretation of the trends that are likely driving the observed sulfate fragmentation changes based on the physicochemical details of the AMS detection and those of the particles being sampled. In Fig. 2a, a simplified diagram of the AMS detection process is shown, highlighting important details that are thought to give rise to the observed trends.

Ambient particles containing AS, OS, and other species are sampled into the AMS through a focusing lens. Following a series of differential pumping steps through the instrument, the particles impact on a porous-tungsten standard vaporizer. The time spent under vacuum from sampling to detection is of the order of 15 ms. A fraction of the more viscous particles may bounce from the vaporizer without detection. Non-refractory species in the particles that stick to the vaporizer (such as OS and AS) are heated by heat transfer from the vaporizer surface. Some species may evaporate in the form in which they are present in the particle, while others may thermally decompose to other species, which then evaporate. For example, ammonium sulfate may evaporate to H2SO4(g) and NH3(g), but it may also thermally decompose to SO2(g), SO3(g), and H2O(g) (Hu et al., 2017b). Finally, these gaseous thermal-decomposition products undergo electron ionization to become positively charged species. Since the electrons used in electron impact (EI) have far more energy (70 eV) than typical bonds in a molecule (∼ 6 eV for S=O), the initial ions may fragment into smaller ions if the ionization process results in absorption of > 6 eV of internal energy by the molecule, beyond the ionization energy (Lambert, 1998). Some of the evaporated H2SO4(g) may remain as H2SO4+ after ionization, or it may fragment to HSO3+ or SOx+ ions. SO2(g) can only produce SOx+ ions. Thus the mixture of fragments observed will retain some memory of the species that evaporated from the particles. If the mixture of evaporating species is influenced by the particle composition (e.g., pH, AN, OA, or OSf), then it may be possible to calibrate the observed relationship to estimate an intensive chemical property of the particle.

Figure 2a also shows a schematic close-up of the SV surface, which is the main point in the instrument that controls ammonium sulfate fragmentation. In this diagram, we show a non-smooth surface with pores, consistent with the fabrication of the vaporizer by sintering 50 µm tungsten spheres. The interaction of a particle with this porous surface is dependent on the particle phase and/or viscosity. The red particles represent rigid (more solid-like) particles. These rigid particles can simply bounce off of the vaporizer, leading to no detection. AS-dominated particles are likely to be rigid (due to the solid phase of pure AS), thus increasing bounce and lowering the AMS CE (Matthew et al., 2008; Middlebrook et al., 2012). AS particles can also become trapped in the porous surface. When trapped, they are heated by conduction from the vaporizer surface and by radiation from surrounding surfaces. They reach higher temperatures that lead to more thermal decomposition and a lower H2SO4(g) / SOx(g) ratio. Consistent with this interpretation, it was shown that the H2SO4+ / SO+ fragment ratio increased as the vaporizer temperature was reduced while sampling ambient air, while the SO2+ / SO+ ratio did not change (Fig. S5 in Docherty et al., 2015). In addition, molecules that evaporate as H2SO4(g) from these trapped particles are likely to collide with tungsten surfaces on their way out to the ionization region, leading to additional thermal decomposition (Hu et al., 2017b) and further reducing the H2SO4(g) / SOx(g) ratio for the gases reaching the EI region and thus the HySOx+ / SOx+ ion ratio.

The second case (blue particle) represents the situation where the particle is less rigid and/or viscous or liquid. Acidic sulfate particles (with a lower fraction of the sulfate ions neutralized by NH4+), particles with high ANf, or particles coated with a large water or liquid organic layer are more likely to deform upon impact and not bounce. This leads to an increased CE (Matthew et al., 2008; Middlebrook et al., 2012; Hu et al., 2017a). There are several effects that will lead to a higher H2SO4(g) / SOx(g) ratio reaching the ionization region in this situation: (a) evaporated H2SO4(g) from particles that impact the front of the vaporizer and do not bounce can now escape without further collisions with the tungsten surface; (b) the increased surface area from impact deformation and the lower viscosity allow more H2SO4(g) molecules to escape the particle before those molecules are heated to temperatures that would lead to thermal decomposition.

In Fig. 2b, we show a conceptual model of the impact of these phenomena on the Chen triangle. For very acidic sulfate (approximately a calculated pH < 0), the liquid character of the particles leads to less bounce in the vaporizer. It also leads to faster evaporation, which reduces the internal temperature for the particles and that of the evaporated molecules, leading to less fragmentation. In this part of the atmosphere, OSf cannot be estimated, but pH may be as long as it can be assumed (or shown by additional measurements from the AMS or other instruments) that OSf and non-volatile cations are small. As an air mass becomes more neutralized by NH4+, the particles become less acidic and more rigid and/or viscous, leading to more thermal decomposition of the evaporated species, and the fragmentation of ammonium sulfate occurs at the upper vertex of the triangle. In this part of the atmosphere, methods such as Chen et al. (2019) may be applicable to estimate OSf as long as there are no other effects that interfere with the sulfate fragments detected (such as substantial non-volatile cations or variations in possible OA effects). As more ammonia is added to an air mass, the acidity of the particles decreases, and the higher pH favors the partitioning of HNO3(g) to the particle phase, forming ammonium nitrate. If ANf becomes high enough (> 0.3), the particles again become less rigid and/or viscous, and the fragmentation shifts again outside the Chen triangle for the same reasons discussed for the acidic particles. Finally, Fig. 2c shows the differences in the detection process and the fragments produced in the AMS for OS, AS, and H2SO4.

In Fig. 3a, we introduce a plot of ANf vs. calculated pH that can be used to evaluate the applicability of the OSf methods to different datasets. Data for five different campaigns (those with AS calibrations, labeled “C” in Table 1) are shown, along with the campaign averages. Regime I (“highly acidic, low AN”) occupies the bottom left quadrant, where ANf < 0.3 and calculated pH < 0. Campaigns sampling the more remote atmosphere (e.g., ATom-1, 89 % of data points; ATom-2, 80 %) and a fraction of the data from continental campaigns (SEAC4RS, 13 %; DC3, 40 %) fall in this regime. For remote regions, emissions (such as NH3 and NOx) are generally low. Remote oceanic regions are relatively isolated from the major continental ammonia sources (Paulot et al., 2015). Therefore, less ammonia is available to balance the hydronium ions from H2SO4, leading to high acidity (Quinn et al., 1988; Keene, 2002; Nault et al., 2020). Highly acidic aerosols and lack of NH3 shift HNO3 to the gas phase, so low ANf is observed. In contrast, for sampling in polluted source regions with strong HNO3 formation and substantial NH3 emissions, a much smaller fraction of the data fall in this regime (e.g., only 4 % for KORUS-AQ). In Sect. 3.5 we discuss the potential to estimate pH from AMS data in regime I.

Regime II (lower right) involves less acidic conditions (calculated pH > 0) and lower ANf (< 0.3). In this region sulfate fragmentation in the AMS is not strongly impacted by either ANf or acidity. In principle, in this regime the recently proposed sulfate deconvolution methods could be applicable. The geographical regions studied in Chen et al. (2019) and Song et al. (2019) generally fall in this regime, and this might explain the lack of large negative OSf values in those studies in contrast to our observations for other regions. About half of our campaign data are located in this regime, more so for the continental campaigns and much less so for the remote campaigns. Specifically, 65 % of KORUS-AQ, 60 % of DC3, 87 % of SEAC4RS, 11 % of ATom-1, and 20 % of ATom-2 fall in this regime. We have applied the 1D version of the Chen method to each field campaign after filtering it by the ANf and calculated-pH constraints for regime II. OSf is nominally slightly greater than 0 for ATom-1, OSf ∼ 3 %, of the order of the 0.3 % estimate in regime II from PALMS (for ATom-1 and ATom-2, estimated by only considering the sulfate moiety from the isoprene-derived epoxydiol (IEPOX) or glycolic acid sulfate (GAS) OS, neither of which was detected in the supermicron aerosol; Froyd et al., 2009, 2019; Liao et al., 2015) (see Fig. S8). However, OSf is much less than 0 for ATom-2 (OSf ∼ -23 %) and KORUS-AQ (OSf ∼ -26 %). These unreasonable results may be due to the effect of OA on sulfate fragmentation in the AMS (discussed in Sect. 3.2). For this reason, strong caution is advised in applying OSf estimation methods to ambient data, even in regime II. In addition, estimating OS with sulfate ions may be susceptible to errors due to inaccuracies in AS calibrations, noise present in the ambient data, or other factors.

We also show results from applying the Song et al. (2019) method in regime II (which is based on similar principles to the Chen method) in Fig. S9. Similarly to the Chen method, we see that most OSf values are predicted to be less than 0. For the entire atmosphere, shown in Fig. S10, the distribution for OSf looks similar to Fig. S9.

Regime III is characterized by high ANf (> 0.3) and lower acidity (calculated pH > 0). This chemical regime primarily exists in polluted continental regions near large source regions such as megacities and agricultural regions as high NOx and NH3 emissions can lead to increased particulate AN and an increase in aerosol pH (Pye et al., 2020). In this regime, there are strong variations in the AMS sulfate fragments that are driven by ANf. OSf cannot be estimated with the AMS sulfate fragmentation methods proposed so far unless they are further modified to account for the ANf effect. Around 31 % of KORUS-AQ data fall in this regime, but almost none of the data from the rural and/or remote campaigns fall in this region as AN typically evaporates as the air is diluted during advection away from polluted regions (DeCarlo et al., 2008).

Finally, regime IV in the top left quadrant has high AN (ANf  > 0.3) and high acidity (calculated pH < 0). This chemical regime is unlikely to be observed in the real atmosphere, and indeed there are very few points in that region for our campaigns. Sulfate is ubiquitous (Zhang et al., 2007b; Hodzic et al., 2020), and nitrate is not thermodynamically stable in the aerosol phase together with acidic sulfate for calculated pH < 0 (Guo et al., 2016). For all campaigns we observe ∼ 0 % of points occupying this regime. Very unusual data points can be observed when ammonium-nitrate-containing particles are externally mixed with acidic-sulfate-containing particles in an air mass.

Since the field studies analyzed here targeted large regions but did not sample many others, it is of interest to evaluate the fraction of the troposphere located in each one of the chemical regimes. The results of the GEOS-Chem v12 model are used for this purpose in Fig. 3b and shown as a global map in Figs. 4 and S11. About 67 % of the model troposphere exists in regime I (calculated pH < 0). In addition, ∼ 33 % of the global troposphere exists in regime II, where it may be feasible to estimate OSf from AMS fragments. Less than 1 % of the modeled atmosphere exists in regime III (upper right quadrant), where ammonium nitrate strongly influences sulfate fragmentation, consistent with the relatively small, very polluted geographical regions with very large ANf. Finally, none of the data fell in regime IV, consistent with aerosols being assumed to be internally mixed in GEOS-Chem. At the surface during December, January, and February (DJF) (Fig. 4a), most of the remote oceans fall in regime I (calculated pH < 0 and ANf < 0.3), while regime II (calculated pH > 0 and ANf < 0.3) is dominant over continental regions. At the surface in June, July, and August (JJA) (Fig. 4c), most of the globe is in regime II. Very little of the data fall in regime III, except parts of Asia, regardless of season. A similar pattern is observed in the free troposphere (Fig. 4b and d), with some geographical differences. Regime III (calculated pH > 0 and ANf > 0.3), which represents pollution hotspots, is observed in a large region in Asia during the summer months, whereas the winter months are dominated by regime I (low pH). The summer months in the free troposphere are also mostly in regime II, especially over continental regions. Due to averaging of an entire year as well as the limited spatial resolution of the GEOS-Chem model, locations and periods of high-ANf hotspots are not as prominent in these results, even when the data are divided by season.

From the previous discussion it is clear that sulfate fragmentation changes due to some of the same factors (acidity, ANf) that influence ambient AMS CE. It is of interest to explore whether a quantitative estimate of ambient-particle CE could be derived from the measured sulfate fragments, at least under some conditions, as it could provide a complementary characterization to the CE estimates from the Middlebrook et al. (2012) parameterization. In Fig. 8 we show the CE estimated from Middlebrook et al. (2012) vs. HySOx+ / SOx+ for ATom and KORUS-AQ. CE does show some relationship with HySOx+ / SOx+, with most sensitivity around CE ∼ 0.8–0.9. A substantial level of noise is observed in the high-time-resolution data, and the trend varies between the two campaigns (where variations in CE are controlled by two different effects, acidity vs. ANf). Further research would be necessary to evaluate whether this method could be used to estimate CE.