ion equivalent ratio to enhance computational efficiency by identifying major ionic species and compositional domains (e.g., Pilinis and Seinfeld, 1987; Kim et al., 1993b; Nenes et al., 1998; Fountoukis and Nenes, 2007). However, thermodynamic models do not use charge balance from input data as a proxy for pH. Thermodynamic models (either manually, or automatically) evaluate inputs, in terms of a charge balance, to ensure that the solution obtained is atmospherically relevant – as an excess of nonvolatile cations may imply a strongly alkaline solution that is not found in the atmosphere. This aspect is discussed in more detail in Sect. 4.
Operationally, Hair+ from charge balance is subject to errors associated with measuring aerosol-phase composition which are likely to be large and affect interpretation of ambient conditions. These are the same challenges that arise in thermodynamic calculations based on particulate-only inputs where biases or uncertainty in the measured species can propagate to errors in acidity (Hennigan et al., 2015; Song et al., 2018). When Hair+ is small in concentration or species contributing to the charge balance are incompletely characterized, the proxy may return a value of zero or negative (indicating a surplus of cations) – neither physically possible – due to limited precision and accuracy in the measurements. Using measured aerosol composition, Murphy et al. (2017) and Hennigan et al. (2015) typically found negative values (indicating no H+, theoretically impossible) of H+ from charge balance and an error range large enough to span both positive and negative Hair+ estimates at almost all times. State-of-the-art measurements are not sufficiently precise to overcome this limitation (Murphy et al., 2017). The problems associated with this proxy are highlighted in Sect. 4, where charge balance estimates near zero show no correlation with pH.
In the 1980s–1990s, experimental methods were developed to estimate the apparent net fine-particle (<2.5 µm) strong acidity (Koutrakis et al., 1988, 1992; Purdue, 1993). These methods, synthesized in a workshop report (EPA, 1999; Purdue, 1993), resulted in an officially documented method for estimating Hair+ from measurements. EPA Method IO-4.1 used filter extracts in combination with measurements from a commercially available pH probe (titration methods are another option) to calculate an estimate of Hair+ or H+ as equivalent mass of sulfuric acid. The method relies on efficient particle collection with minimal filter artifacts and low amounts of nitrate compared to sulfate (EPA, 1999). For example, ammonia could displace H+ and neutralize acidic particles during collection without an efficient denuder (Koutrakis et al., 1988). Extraction and dilution of ambient samples modify their chemical environment such that the conditions during measurement are different from those in the ambient atmosphere, potentially affecting gas–particle partitioning of total ammonium and dissociation of weak acids including bisulfate (Purdue, 1993). Variations of this method were developed to limit the extent of dilution by measuring the pH of droplets on the surface of a hydrophobic filter using microelectrodes (Winkler, 1986; Keene et al., 2004). However, the extent of dilution is still enough to shift the sulfate–bisulfate equilibrium outside of conditions present in many atmospheric particles. The use of a strong acidity proxy in many past health studies complicates their interpretation regarding the role of acidity since Hair+ is only a proxy for pH.
Proxies for acidity have been used in a variety of applications. In the past, proxies were specifically applied in the context of acid-catalyzed SOA. Evidence for this phenomenon was sought in ambient data based upon landmark studies that demonstrated an important role of acid-catalyzed reactions in forming SOA in laboratory systems (Jang et al., 2002; Paulot et al., 2009; Surratt et al., 2010). However, due to a lack of direct particle acidity measurements (see Sect. 7.1 for details and discussion), researchers used different acidity proxies to characterize the impacts on SOA formation in the atmosphere. The NH4+/SO42- molar ratio was used in several studies (Zhang et al., 2007; Peltier et al., 2007; Tanner et al., 2009) to infer that more acidic conditions did not enhance SOA concentrations. Froyd et al. (2010) used airborne measurements of the NH4+/SO42- ratio to classify acidic and neutral particle regimes, and they inferred a causal effect of acidity on isoprene organosulfate formation at low NOx in the eastern US. Strong associations between SOA concentrations or SOA marker compounds and H+ derived from the charge balance were inferred in multiple locations (Pathak et al., 2011; Feng et al., 2012; Budisulistiorini et al., 2013; Nguyen et al., 2014). Several other studies investigated the relationship between particle acidity and atmospheric SOA using different predicted or derived measures of acidity. Hair+ estimates based on operational extraction methods were used extensively in the literature to link SOA formation to acidity (Surratt et al., 2007; Offenberg et al., 2009; Zhang et al., 2012). In Beijing, Guo et al. (2012b) found evidence of acid-catalyzed SOA based upon correlations between secondary organic carbon (SOC) concentrations and H+ concentrations (nmol m−3) from ISORROPIA, run without gaseous inputs. Li et al. (2013) also observed correlations between SOA markers and acidity in China using pH predictions from E-AIM with aerosol inputs only. No evidence for acid-catalyzed SOA formation was found in a separate study in Pittsburgh, PA, that analyzed correlations between modeled H+ and measured SOA concentrations (Takahama et al., 2006). Takahama et al. (2006) used gas and particle phase inputs for predictions with the GFEMN model and also observed no correlations between pHc (with γH+c set to unity) and SOA. The studies employing proxies likely suffered from problems with the proxies; themselves (as discussed above); and confounding factors such as correlations between organic aerosol and sulfate, a major source of acidity, that often occur in regional pollution (Sun et al., 2011; Nguyen et al., 2015). These seemingly contradictory results were resolved once pHF was used, and the conclusions reached in these prior studies have been revisited based upon detailed understanding of the underlying chemical mechanisms and additional insight suggesting that the aerosol acidity is frequently not a limiting factor in catalyzing SOA formation (Surratt et al., 2010; Xu et al., 2015; Weber et al., 2016). Acid-catalyzed isoprene SOA has now been implemented in a wide variety of box model and chemical transport model applications that now rely exclusively on thermodynamic models for acidity estimates (Pye et al., 2013; Marais et al., 2016; Riedel et al., 2016; Budisulistiorini et al., 2017). So, while proxies can provide some information on the PM system, they should not be overinterpreted as a measure of pH.
and uses total ammonia (NH3+NH4+) and total nitrate (HNO3+NO3-). The numerator of the GR is sometimes referred to as free ammonia, because it is the amount of TNH3 that would be available to form NH4NO3 under the simplistic assumption that appreciable NH4NO3 does not form when the molar ratio of TNH4 to TSO4 is less than two (i.e., the stoichiometric ratio of (NH4)2SO4). The concept of free ammonia is discussed in greater detail below (Sect. 4.2.3). The GR has not been used explicitly as a proxy for aerosol pH, but it has been used extensively to define aerosol and composition regimes that relate to acidity.
Ansari and Pandis (1998) characterized inorganic PM response for changes in TNH4, TNO3, and TSO4 as functions of the GR, temperature, RH, and system concentrations. Their analysis determined critical values of the GR that defined boundaries of the PM response regimes. As West et al. (1999) showed, the GR still requires complementary thermodynamic modeling to robustly explore the PM response for large sulfate reductions. Other applications of the GR include calculation of the GR as a function of altitude (Adams et al., 1999); characterization of the sulfate–nitrate–ammonia–water aerosol system in the context of natural and transboundary pollution over the US (Park et al., 2004); and exploration of the sensitivity of aerosol nitrate to changes in temperature, RH, TNH4, TNO3, and sulfate for Pittsburgh (Takahama et al., 2004). In addition, Blanchard and Hidy (2003) considered the GR in a study of the response of nitrate to changes in TNH4, TNO3, and sulfate in the southeastern US. A relationship was demonstrated between the GR and an excess-NH3 indicator that resembles free ammonia but accounts for chloride and nonvolatile cations. Pun and Seigneur (2001) used box model simulations to demonstrate that nitrate concentrations in California's San Joaquin Valley would be sensitive to HNO3 levels but not NH3.
where DSN is the degree of sulfate neutralization. Using a chemical transport model, Pinder et al. (2008a) demonstrated that the response of nitrate concentrations to changes in SO2 and NH3 emissions could be reasonably represented as a function of the adjGR and GR, but the adjGR provided a better fit for cases where DSN differs significantly from a value of two. In a separate study, Pinder et al. (2008b) found a strong relationship between the adjGR and the sensitivity of inorganic PM concentrations to NH3 levels at sites in the eastern