Fine-particle water and pH in the southeastern United States

Abstract. Particle water and pH are predicted using meteorological observations (relative humidity (RH), temperature (T)), gas/particle composition, and thermodynamic modeling (ISORROPIA-II). A comprehensive uncertainty analysis is included, and the model is validated. We investigate mass concentrations of particle water and related particle pH for ambient fine-mode aerosols sampled in a relatively remote Alabama forest during the Southern Oxidant and Aerosol Study (SOAS) in summer and at various sites in the southeastern US during different seasons, as part of the Southeastern Center for Air Pollution and Epidemiology (SCAPE) study. Particle water and pH are closely linked; pH is a measure of the particle H+ aqueous concentration and depends on both the presence of ions and amount of particle liquid water. Levels of particle water, in turn, are determined through water uptake by both the ionic species and organic compounds. Thermodynamic calculations based on measured ion concentrations can predict both pH and liquid water but may be biased since contributions of organic species to liquid water are not considered. In this study, contributions of both the inorganic and organic fractions to aerosol liquid water were considered, and predictions were in good agreement with measured liquid water based on differences in ambient and dry light scattering coefficients (prediction vs. measurement: slope = 0.91, intercept = 0.5 μg m−3, R2 = 0.75). ISORROPIA-II predictions were confirmed by good agreement between predicted and measured ammonia concentrations (slope = 1.07, intercept = −0.12 μg m−3, R2 = 0.76). Based on this study, organic species on average contributed 35% to the total water, with a substantially higher contribution (50%) at night. However, not including contributions of organic water had a minor effect on pH (changes pH by 0.15 to 0.23 units), suggesting that predicted pH without consideration of organic water could be sufficient for the purposes of aqueous secondary organic aerosol (SOA) chemistry. The mean pH predicted in the Alabama forest (SOAS) was 0.94 ± 0.59 (median 0.93). pH diurnal trends followed liquid water and were driven mainly by variability in RH; during SOAS nighttime pH was near 1.5, while daytime pH was near 0.5. pH ranged from 0.5 to 2 in summer and 1 to 3 in the winter at other sites. The systematically low pH levels in the southeast may have important ramifications, such as significantly influencing acid-catalyzed reactions, gas–aerosol partitioning, and mobilization of redox metals and minerals. Particle ion balances or molar ratios, often used to infer pH, do not consider the dissociation state of individual ions or particle liquid water levels and do not correlate with particle pH.

and Aerosol Study (SOAS) in summer and at various sites in the southeastern US during different seasons, 23 as part of the Southeastern Center for Air Pollution and Epidemiology (SCAPE) study. Particle water and 24 pH are closely linked; pH is a measure of the particle + aqueous concentration and depends on both the 25 presence of ions and amount of particle liquid water. Levels of particle water, in-turn, are determined 26 through water uptake by both the ionic species and organic compounds. Thermodynamic calculations 27 based on measured ion concentrations can predict both pH and liquid water but may be biased since 28 contributions of organic species to liquid water are not considered. In this study, contributions of both the 29 inorganic and organic fractions to aerosol liquid water were considered and predictions were in good 30 agreement with measured liquid water based on differences in ambient and dry light scattering 31 coefficients (prediction vs. measurement: slope = 0.91, intercept = 0.5 µg m -3 , R 2 = 0.75).  predictions were confirmed by good agreement between predicted and measured ammonia concentrations 33 (slope = 1.07, intercept = -0.12 µg m -3 , R 2 = 0.76). Based on this study, organic species on average 34 contributed 35% to the total water, with a substantially higher contribution (50%) at night. However, not 35 including contributions of organic water had a minor effect on pH (changes pH by 0.15 to 0.23 units), 36 suggesting that predicted pH without consideration of organic water could be sufficient for the purposes 37 48 1 Introduction 49 The concentration of the hydronium ion ( + ) in aqueous aerosols, or pH, is an important aerosol property 50 that drives many processes related to particle composition and gas-aerosol partitioning (Jang et  ion balance cannot be used as a measure of the aerosol concentration of + in air (i.e., moles + per 58 volume of air, denoted hereafter as + ). This is due to two factors, first, an ion balance assumes all ions 59 are completely dissociated, but multiple forms are possible, depending on pH (e.g., sulfate can be in the 60 form of H 2 SO 4 , HSO 4 -, or SO 4 2-). Secondly, pH depends on the particle liquid water content (LWC), as 61 pH is the concentration of + in an aqueous solution. LWC can vary considerably over the course of a 62 day and between seasons significantly influencing pH (Seinfeld and Pandis, 2006). Aerosol 63 thermodynamic models, such as ISORROPIA-II (Nenes et al., 1998;Fountoukis and Nenes, 2007) and 64 AIM (Clegg et al., 1998), are able to calculate LWC and particle pH, based on concentrations of various 65 aerosol species, temperature (T), and relative humidity (RH) and offer a more rigorous approach to obtain 66 aerosol pH (Pye et al., 2013). ISORROPIA-II calculates the composition and phase state of an NH 4 + -SO 4 2-

67
-NO 3 --Cl --Na + -Ca 2+ -K + -Mg 2+ -water inorganic aerosol in thermodynamic equilibrium with water vapor and 68 gas phase precursors. The model has been tested with ambient data to predict acidic or basic compounds, 69 such as NH 3(g) , NH 4 + , and NO 3 - (Meskhidze et al., 2003;Nowak et al., 2006;Fountoukis et al., 2009;70 suggested that the potential for organic gases to partition to LWC is greater than the potential to partition 82 to particle-phase organic matter (Carlton and Turpin, 2013), and partitioning of water soluble organic 83 carbon (WSOC) into the particle phase becomes stronger as RH (i.e., LWC) increases (Hennigan et al., 84 2008). Thus LWC enhances particle scattering effects directly by increasing particle cross sections 85 More information on the SEARCH sites can be found elsewhere (Hansen et al., 2003;Hansen et al., 135 2006). We first focus on the SOAS campaign data, where a wide range of instrumentation was deployed 136 (http://soas2013.rutgers.edu) to develop a comprehensive method of predicting LWC and pH, as well as 137 assessing their uncertainties. The approach is then applied to the SCAPE site data to provide a broader 138 spatial and temporal assessment of PM 2.5 pH in the southeastern US.  Canagaratna et al., 2007). In brief, particles 160 were first dried (RH < 20%) and then immediately sampled through an aerodynamic lens into the high 161 vacuum region of the mass spectrometer, then transmitted into a detection chamber where particles 162 impact on a hot surface (600°C). Non-refractory species are flash vaporized and then ionized by 70 eV 163 electron impact ionization. The generated ions are extracted into the time-of-flight mass spectrometer. 164

Instrumentation
Further details on the AMS setup and data processing can be found in Xu et al. (2015). 165

2.2c CCNc 166
The particle hygroscopic parameter, (Petters and Kreidenweis, 2007) Particle dry scattering was measured with a nephelometer located in the air-conditioned sampling trailer 180 operated with a nafion dryer upstream that maintained an RH of 32 ± 2 % (study mean ± SD, n = 12,464 181 based on 5-min averages). The other was situated in a small white 3-sided wooden shelter (one side 182 covered by a loose tarp) located a distance away from all buildings to provide a scattering measurement at 183 ambient T and RH. Both PM 2.5 cut cyclones were located in ambient conditions, and both nephelometers 184 were calibrated by CO 2 prior to the SOAS field campaign. Typical uncertainty is 3% for scattering 185 coefficients (Mitchell et al., 2009). In addition, the nephelometer RH sensors were calibrated by placing 186 the sensors in a closed container above aqueous saturated salt solutions that had reached equilibrium 187 (measurements made in a thermally insulated container after a period of a few hours). Solution 188 temperatures were monitored. Details on the calibration results are provided in the Supplementary 189 Material Section 1. Recorded RH was corrected by the calibration results. 190

Determining LWC from nephelometers 191
Particle water was inferred from the ratio of ambient and dry PM 2.5 scattering coefficients ( ) measured 192 by the two nephelometers (defined here as aerosol hygroscopic growth factor, ( ) = (1) , ̅̅̅̅̅̅̅̅̅̅̅̅̅ , , ̅̅̅̅̅̅̅̅̅̅̅̅̅ are the average scattering efficiency and average particle diameter under ambient 201 conditions, while , ̅̅̅̅̅̅̅̅ , , ̅̅̅̅̅̅̅̅ represent dry conditions. The method is based on fine particle light 202 scattering being mostly due to particles in the accumulation mode and can be related to scattering 203 efficiencies and the diameter of average surface, for both ambient and dry particle size distributions. 204 Assuming that , ̅̅̅̅̅̅̅̅̅̅̅̅̅ = , ̅̅̅̅̅̅̅̅ (see Supplementary Material Section 2 for justification and 205 uncertainty analysis), it follows then that; 206 Since the LWC is equal to the difference between ambient and dry particle volume, we get; 207 where and are dry particle mass and density, respectively; is water density (constant 1 g cm -3 is 208 applied). For SOAS, dry PM 2.5 mass concentrations were measured continuously by a TEOM (tapered 209 element oscillating microbalance, 1400a, Thermo Fisher Scientific Inc., operated by Atmospheric 210 Research & Analysis Inc., referred to hereafter as ARA). Particle density, , was computed from the 211 particle composition, including AMS total organics, ammonium, and sulfate, which accounted for 90% of 212 the measured PM 2.5 (TEOM) dry mass (SOAS study mean). A typical organic density 1.
The time-resolved composition data shows that dry particle density did not have a significant diurnal 217 variability (± 2.7%, SD/mean, Supplementary Material Figure S2). In the following we refer to the 218 particle water calculated by this method as ( )_water. The uncertainty of ( )_water is estimated to 219 be 15%, mainly caused by the calculation of , ̅̅̅̅̅̅̅̅̅̅̅̅̅ / , ̅̅̅̅̅̅̅̅ (LWC error of 10% from assuming 220  Figure S6). 224

Modeling Methods: Predicting LWC and pH from aerosol composition 225
In most studies, such as SCAPE, particle water was not measured and must be determined based on 226 aerosol composition. Both inorganic and organic components contribute to uptake of water vapor, 227 establishing equilibrium for the ambient RH and T conditions. Thus, LWC is controlled by meteorological conditions and also by aerosol concentration and composition. Thermodynamic models, 229 such as ISORROPIA-II, have been extensively used to predict LWC due to inorganic aerosol components 230 (Fountoukis and Nenes, 2007). Contributions to LWC by organic components are typically based on an 231 aerosol hygroscopicity parameter, , which is determined by CCN data. Here we refer to particle water 232 associated with inorganics and organics as and , respectively. Total particle water ( + ) is 233 taken as the sum of water associated with individual aerosol chemical components (sum of ions and 234 lumped organics) based on Zdanovskii-Stokes-Robinson (ZSR) relationship (Zdanovskii, 1936;Stokes 235 and Robinson, 1966), with the assumption that the particles are internally mixed. The assumptions made 236 in our analysis were discussed in Section 3.4. 237

LWC from inorganic species 238
Particle water associated with inorganic species ( ) were predicted by ISORROPIA-II ( nephelometer, and temperature from the SEARCH site (ARA) meteorological data. 244

LWC from organic fraction 245
To determine the contributions to particle water by , in SOAS the organic hygroscopicity parameter 246 ( ) was calculated based on the observed CCN activities of the organic fraction . 247 In the following analysis diurnal three-hour running averages are used in the calculation. (Diurnal plot is 248 included in the Supplementary Material as Figure S7).

pH prediction 254
The thermodynamic model, ISORROPIA-II (Fountoukis and Nenes, 2007), calculates the equilibrium 255 particle hydronium ion concentration per volume air ( + ), which along with the LWC is then used to predict particle pH. To correct for the LWC associated with the organic aerosol (not considered in 257 ISORROPIA-II), we recalculate pH by considering + and total predicted water ( and ). 258 The modeled concentrations are µg m -3 air for + and LWC. The pH is then, 259 = − log 10 + = − log 10 1000 + + where + (mol L -1 ) is hydronium concentration in an aqueous solution. + and are the output of 260 ISORROPIA-II based on input of water soluble ions, RH, and T. + is + divided by the LWC, and so 261 including decreases + by a factor of /( + ), relative to only considering . 262 ISORROPIA-II has been tested in previous field campaigns where a suite of both gas and particle approach is used. Gas phase input does have an important impact on the + calculation.  was tested with ammonia partitioning, which is discussed in more detail below. Here it is noted that we 275 found that further constraining ISORROPIA-II with measured NH 3(g) (You et al., 2014) resulted in a pH 276 increase of 0.8 at CTR and that the predicted NH 3(g) matched the measured NH 3(g) well (slope = 1.07, 277 intercept = -0.12 µg m -3 , R 2 = 0.76). This also confirms that ISORROPIA-II predicts the pH in the 278 ambient aerosol with reasonable accuracy, as inputting the total (gas + aerosol) ammonium results in 279 predictions that agree with those observed. This is also in agreement with findings of Hennigan et al.

Assumptions 283
In the following analysis we use bulk properties and do not consider variability in parameters with 284 particle size. Particulate organic and inorganic species are assumed to be internally mixed in the liquid 285 phase due to the high RH (74 ± 16%) typical of this study and because a large fraction of the ambient it is not possible to have phase separation, which is the case for our sampling sites. Based on our basic 294 assumption of no liquid-liquid phase separation, pH is considered to be homogeneous in a single particle. 295 However, separated phases would likely have different pHs if liquid-liquid phase separation occurs. In 296 that case, pH should be calculated based on the amounts of water and + in each phase. Gas-particle 297 phase partitioning will change accordingly, due to these separated phases. There are models that are set up 298 to calculate these thermodynamics (e.g., AIOMFAC), but none is yet able to address the compositional 299 complexity of ambient SOA. (Zuend et al., 2010;Zuend and Seinfeld, 2012) Although it is often true that 300 non-ideal interactions between organic and inorganic species exist, good agreement between measured 301 particle water and ammonia partitioning to predictions using the bulk properties (discussed below) 302 suggests these assumptions are reasonable. 303 4 Results 304

Overall summary of meteorology and PM composition at SOAS and SCAPE sites 305
For the SOAS study period, mean T and RH were 25 ± 3 ℃ and 74 ± 16 % (mean ± SD), respectively. 306 This resulted in a ( )_water level of 4.5 ± 3.8 µg m -3 , with a maximum value of 28.4 µg m -3 . In 307 comparison, SOAS mean dry PM 2.5 mass was 7.7 ± 4.6 µg m -3 , implying that the fine aerosols were 308 roughly composed of 37% water, on average. Mean T and RH for SCAPE sites are listed in Table 3. 309 Summer T means were all above 21℃, including CTR. RH means were all high (> 60%) for summer and 310 winter, which is typical for the southeastern US. A more comprehensive suite of ions will provide a better prediction of . However, in the southeastern 317 US, inorganic ions are currently dominated by sulfate and ammonium. During SOAS, the PILS-IC 318 provided a more comprehensive and accurate measurement of water-soluble ions than AMS, which 319 measured only non-refractory sulfate, ammonium, nitrate, and chloride. Refractory, but water soluble ions, 320 such as sodium and associated chloride, and crustal elements including calcium, potassium, and 321 magnesium were present in PM 1 , but in very low concentrations. Contributions of these ions are more 322 important in PM 2.5 than for PM 1 , which tend to reduce aerosol acidity. For instance, Na + has a 323 significantly higher mean in PM 2.5 at 0.056 µg m -3 (1 st half of SOAS study) than 0.001 µg m -3 in PM 1 (2 nd 324 half of SOAS study). Four, one day-long, dust events (06/12, 06/13, 06/16, and 06/21) in the SOAS data 325 set have been excluded from this analysis as assumptions relating to internal mixing of PM 2.5 components 326 are less valid in these cases. Excluding these days, the mean Na + in PM 2.5 drops to 0.024 µg m -3 . 327 If the fraction of the refractory ions (e.g., Na + , K + , Ca 2+ , Mg 2+ ) is negligible compared to the SO 4 (Note, 328 SO 4 stands for sulfate in all its possible forms, from free to completely dissociated), NH 4 + , and NO 3 -, the 329 AMS data sufficiently constrains particle composition for thermodynamic calculations; this apparently is

4.2a LWC, pH and ion balances at Centreville 340
The diurnal variation of LWC contributed by and , along with total measured water, ambient T, RH, 341 and solar radiation at CTR is shown in Figure 3. Predicted and measured LWC trends were in good 342 overall agreement, although the largest discrepancy was observed during the daytime when the LWC 343 level was low and more difficult to measure and accurately predict. Nighttime RH median values were 344 between 85% and 90% and resulted in significant water uptake that reached a peak just after sunrise near 345 7:30 am (local time). The dramatic peak in LWC starting at roughly 5:00 am, reaching a maximum 346 between 7:30 and 8:00 am is likely due to RH increasing above 90%, at which point uptake of water 347 rapidly increases with increasing RH. The similar rapid hygroscopic growth before sunrise was also observed at GIT, RS, and JST (Nov) (Figure 11). After sunrise, rising temperatures led to a rapid drop in 349 RH, resulting in rapid loss of particle water. LWC reached lowest levels (~2 µg m -3 ) in the afternoon, 350 only 20% of the peak value. varied more than diurnally; max/min ratio was 13.1 compared to 351 4.1 for . 352 At CTR, the aerosol was highly acidic, with predicted mean pH = 0.94 ± 0.59 (± SD). The minimum and 353 maximum pH were -0.94 and 2.23 respectively, and pH varied by approximately 1 on average throughout 354 the day (Figure 4a). That is, the + /LWC ratio increased by a factor of 10 from night to day. LWC 355 max/min ratio was 5, whereas + diurnal variation was significantly less (Figure 4b), indicating that the 356 diurnal pattern in pH was mainly driven by particle water dilution. This is further demonstrated in Figure  357 4d, which shows the diurnal variation in the NH 4 + /SO 4 2molar ratio (the main ions driving pH), with only 358 slightly lower ratios during the day. The study mean (± SD) NH 4 + /SO 4 2molar ratio was 1.4 (± 0.5). As 359 LWC is mainly controlled by RH and temperature, the pH diurnal variation was thus largely driven by 360 meteorological conditions, not aerosol composition. 361 In part, because of the diurnal variation of LWC, a simple ion balance or NH 4 + /SO 4 2molar ratio or per 362 volume air concentration of aerosol hydronium ion ( + ) alone cannot be used as a proxy for pH in the 363 particle. Figure 5a shows a weak inverse correlation (R 2 = 0.36) between ion balance and pH. An ion 364 balance of an aerosol is usually calculated as follows (in unit of nmol equivalence m -3 ), for a NH 4 + -Na + -365  (Table 2). Na + is 377 excluded because it is not measured by the AMS. PILS-IC instrumental uncertainty is estimated to be 15% from the variability in standards (variability is calibration slopes), blanks, sample airflow rate, and liquid 379 flow rate (one SD). The total ion uncertainties are listed in Table 2. SO 4 has a higher uncertainty, at 25%, 380 than the rest, which are at 15%. These combined uncertainties lead to an uncertainty of 25% (Figure 6), 381 which is the same as the SO 4 uncertainty. SO 4 , one of the most hygroscopic ions (Petters and Kreidenweis,  382 2007), controls uptake. 383 For the SOAS study, the RH probe in the ambient nephelometer (Humitter 50U, VAISALA Inc.) has a 384 stated maximum uncertainty of 5% at RH = 90%. RH biases with respect to environment conditions can 385 also occur due to placement of the probe. Based on RH comparisons between ARA, Rutgers (Nguyen et 386 al., 2014), and the Georgia Tech instrumentation, a systematic bias as large as 10% is found. Given this, 387 we consider an RH probe factory uncertainty (5%) as a typical value and inter-comparison difference 388 (10%) as an extreme condition. In this analysis, RH was adjusted by ±5% and ±10% and recalculated 389 ( Figure 7). A ±5% perturbation in RH leads to a 91% (slope -1) error for 5% perturbation above the 390 measured value (1.05RH) and 29% error for a perturbation below the measured value (0.95RH). We take 391 60% as average uncertainty. Higher uncertainty is introduced with increasing RH, owing to the 392 exponential growth of LWC with RH and results in the asymmetric LWC uncertainty. Combining 393 uncertainty from ions (25%) and RH (60%), the overall uncertainty is calculated as 65%. 394 The uncertainty sources for are , , , and RH (Equation 5). The uncertainties of these 395 parameters are estimated to be 26% (details can be found in Supplementary Material Section 3), 10%, 396 20%, and 5% (from above), respectively. In summary, the overall uncertainty of is 35%. 397 The total uncertainty of LWC can be expressed as a sum of and uncertainties, where is the mass 398 fraction.
was found to be 36% and was 64%. 399 Given the above, is 43%. This method of assessing predicted LWC uncertainty can be applied to 400 SCAPE sites as well. The specific predicted LWC at SCAPE sites were calculated and are listed in Table  401 3.
uncertainty associated with ions is the same as noted above, 25%, because it is estimated by  IC and AMS differences. Similar uncertainties in at the SCAPE sites are expected if RH uncertainties 403 are similar at all sites. 404

pH uncertainty: 405
As pH is based on + and LWC, the uncertainty of pH can be estimated from these two parameters. We 406 applied the adjoint model of ISORROPIA, ANISORROPIA (Capps et al., 2012), to quantify the 407 sensitivity of predicted + to the input aerosol species at the conditions of the thermodynamic 408 calculations. pH uncertainty resulting from aerosol composition is then determined by propagating the 409 input parameter uncertainties, using ANISORROPIA sensitivities, to the corresponding + and pH 410 uncertainty. 411 We now assess how pH of PM 2.5 is affected by using an incomplete measurement of ionic species by 412 comparing the pH predicted based on the more complete suite of ions measured by the PILS-IC versus the 413 AMS, during SOAS. Sensitivities of aerosol species to + were calculated by ANISORROPIA with 414 PILS-IC data and presented as partial derivatives (Table 2). Higher sensitivity values imply the inorganic 415 ion is more important for ion balance. In the SOAS study, + is most sensitive to SO 4 , and then NH 4 + , 416 as they were the major ions. Uncertainties of ions were estimated by the difference between IC-ions and 417 AMS-ions, as well as PILS-IC measurement uncertainty. Since Na + is not measured by AMS, we cannot 418 estimate the difference between PILS-IC and AMS. The loadings and sensitivities of NO 3 and Clwere 419 very low, so they are assumed not to contribute much to + + . Given this, Based on the input for Equation 9 (Table 2), + + is estimated as 14%. LWC is most sensitive to RH 421 fluctuations, so it is considered the main driver of LWC uncertainty in the pH calculation. As discussed, 422 we artificially adjusted RH by ±5% and ±10% (10% is considered an extreme condition). + , , , as 423 well as pH were all recalculated using 90%, 95%, 105%, and 110% of the actual measured RH. RH+5% 424 and RH-5% lead to 12% and 6% variation in pH based on orthogonal regression slopes, respectively 425 ( Figure 8). RH Figure S8), 442 similar sensitivities of + to ions are expected. However, actual uncertainty for each sampling period is 443 possibly higher due to higher loadings of refractory ions at SCAPE sites due to contributions from urban 444 emissions. Refractory ions not measured by the AMS (i.e. Na + , K + , Ca 2+ , Mg 2+ ), have a minor effect on 445 predicting LWC, but may have an important effect on pH (e.g., result in higher pH) in locations where 446 they could substantially contribute to the overall ion balance. 447

4.2b Model validation: Prediction of liquid water 448
Several LWC measurements were made at CTR during SOAS. In addition to ( )_water (4.5 ± 3.8 µg 449 m -3 ), particle water was quantified with a Semi-volatile Differential Mobility Analyzer (SVDMA). With 450 this method, a SOAS study mean particle water concentration of 4.3 ± 3.7 µg m -3 (± STD) was obtained 451 (Nguyen et al., 2014). The orthogonal regression between these two measurements (SVDMA water vs 452 ( )_water) has slope = 0.91, intercept = -0.0 µg m -3 , R 2 = 0.35. Differences could be caused by 453 differences in size-resolved composition (particle composition beyond PM 1 that contributes LWC; 454 SVDMA scans up to 1.1 µm, while ( )_water is based on PM 2.5 ), instrument sample heating (i.e., the 455 degree to which the instrument was close to ambient conditions, especially when ambient RH was high, 456 and most sensitive to slight T differences), and differences in RH probe calibrations. CTR predicted total LWC, ( + ), was 5.1 ± 3.8 µg m -3 and agreed well with ( )_water. The total 458 predicted water was highly correlated and on average within 10% of the measured water, with slope = 459 0.91, intercept = 0.5 µg m -3 , R 2 = 0.75 (see Figure 9). Since excluding refractory ions (Section 4.1) and 460 not considering gas phase species in the ISORROPIA-II calculations do not significantly affect the LWC 461 prediction, its comparison across sites is less uncertain than pH. 462

4.2c Model validation: Prediction of pH 463
ISORROPIA-II calculations of pH at CTR for the SOAS study were evaluated by comparing measured 464 and predicted NH 3(g) . Although NH 4 + and NH 3(g) , along with other aerosol components, are input into the 465 model, comparing ambient NH 4 + and NH 3(g) to model predictions is not a circular analyses. For each 466 observed data point, the model calculates total ammonia from the NH 4 + and NH 3(g) input, and then 467 calculates the gas-particle ammonia partitioning assuming equilibrium. There are also other various 468 assumptions/limitations associated with the model. Figure 10 shows the SOAS study time series of 469 measured and predicted NH 3(g) and the fraction of ammonia in the gas phase (NH 3(g) / (NH 3(g) + NH 4 + ). 470 Measured and predicted NH 3(g) are in good agreement. Periods when almost all ammonia was in the gas 471 phase (ratio near 1) are related to precipitation events (06/10, 06/24, 06/28, 07/03, 07/04) when aerosol 472 concentrations were very low. Not including these events, the study mean (± SD) fraction ammonia in the 473 gas phase was 0.41 (± 0.16) (median value is also 0.41). These results provide confidence in 474 ISORROPIA-II calculations of particle pH, and demonstrate the utility of including both measurements of 475 particle and gas phases in these types of studies. 476 When gas data are not available, pH predictions are not as accurate (Hennigan et al., 2014). Running 477 ISORROPIA-II in the forward mode, but with only aerosol concentrations as input, may result in a bias in 478 predicted pH due to repartitioning of ammonia in the model. In the southeast, where pH is largely driven 479 by SO 4 and NH 4 + , the aerosol NH 4 + input will be partitioned in the model between gas and particle phases 480 to establish equilibrium. Sulfate repartitioning does not occur since it is non-volatile. Thus, NH 4 + will be 481 lost from the particle and a lower pH predicted. At CTR ammonia partitioning has been included in all 482 model runs, but as no NH 3(g) was available for SCAPE. Assuming the average NH 3(g) /NH 4 + ratio from 483 CTR applies to all SCAPE sites to estimate NH 3(g) , along with measured particle composition at each site, 484 we got pH increases ranging from 0.87 to 1.38. In the following, all pHs reported for SCAPE are 485 corrected for this bias (i.e., pHs are increased by 1 to simplify the correction). Note that ammonia 486 partitioning does not significantly affect the LWC prediction ( predicted without NH 3(g) vs 487 predicted with NH 3(g) : slope = 1.00, intercept = -0.01 µg m -3 , R 2 = 0.98).

4.3a Seasonal trends 490
The methods developed and verified at CTR are now applied to the SCAPE study where fewer species 491 were measured. LWC predictions at all SCAPE sites are shown in Table 3, providing insights on seasonal 492 trends of LWC in the southeast. The overall summer LWC mean was 5.0 µg m -3 and winter mean 2.2 µg 493 m -3 . 494 At the SCAPE sites, JST, YRK, GIT, and RS, summer mean pHs were between 1 and 1.3, similar to CTR 495 (mean of 0.94). In winter the pHs (mean between 1.8 and 2.2) were higher by ~ 1 unit. Although LWC 496 was higher in summer, which tends to dilute + and increase pH, summer pH was lower due to higher 497 ion (i.e., sulfate) concentrations (Table 3). Similar diurnal pH patterns were seen at all sites in all seasons 498 and follow the diurnal variations of particle water (Figure 11). Overall the pH in the southeast is very low, 499 between 1 and 2 (mean), in both rural and urban environments. pH values in summer at various sites were 500 similar (1 to 1.3), suggesting a fairly homogeneous distribution of acidity due to spatially uniform sulfate 501 in the southeastern US . In winter the diurnal range in pH was roughly 2 units, while 502 the diurnal range in summer was smaller, with pH varying by roughly 1. 503 Recall at CTR, 10% RH uncertainty can result in a pH prediction error of up to 45% due to the high RHs 504 observed during the study. We estimated pH uncertainty from and by + 10% RH for each SCAPE 505 site. As Table 3 shows, the pH uncertainty associated with RH is much lower in winter (only 1-3%) than 506 summer (20-40%), although RH averages were similar, e.g., JST in May (67 ± 19%) and Nov (63 ± 19%), 507 with even higher RH in winter at YRK. Total pH uncertainty at all SCAPE sites are calculated by the 508 same method as CTR. Table 3 shows that higher RH and T result in larger pH uncertainty. In summer, pH 509 uncertainty is mainly caused by RH; while in winter, it can be attributed mostly to uncertainty in ion 510 concentrations. 511

4.3b The role of 512
was significant, accounting for on average 29-39% of the total PM 2.5 particle water for all our sites 513 ( Figure 12 and Table 3). Note that, at SCAPE sites were calculated by in-situ AMS measurements at 514 each SCAPE site and the mean (0.126) measured at CTR, due to lack of CCNc. Note that could 515 be higher or lower at each site depending on the type of organics presented and the related . Figure  516 12 shows that is related to the organic mass fraction. is comparable to at night. In contrast, it 517 was only 33% of during the daytime (Figure 3). The significant fraction, even during daytime, 518 indicates organic aerosol components will have a considerable contribution to aerosol radiative forcing. 519 Although organics are less hygroscopic than ammonium sulfate, a large fraction of the PM 2.5 (~70%) was 520 organic, making contributions important. Of the organic factors associated with , Cerully et al. 521 (2014) showed that MO-OOA (more-oxidized oxygenated organic aerosol, also referred to as LVOOA, 522 low-volatile oxygenated organic aerosol) and Isoprene-OA (isoprene derived organic aerosol) were twice 523 as hygroscopic as LO-OOA (less-oxidized oxygenated organic aerosol, also referred to as SVOOA, semi-524 volatile oxygenated organic aerosol). The LWC associated with MO-OOA and Isoprene-OA account for 525 ~60% and ~30% of total in the daytime, respectively. 526 The effect of particle water on pH can also be delineated. pH calculated just by alone will be affected 527 by an underestimation of particle water, resulting in a slightly lower pH (Figure 13).
is on average 29% 528 to 39% of total water at all sites, as a result pH increases by 0.15 to 0.23 units when is included. 529 Independent of the pH range, a 29% to 39% fraction always increases pH by 0.15 to 0.23 due to the 530 logarithmic nature of pH. The effect of on pH can be simply denoted as log 10 (1 − ). For example, 531 when is 90%, it shifts pH up by 1 unit. pH based on is highly correlated with pH for total water 532 ( + ) (Slope = 0.94, intercept = -0.14, R 2 = 0.97). This indicates that if organic mass and are 533 not available, ISORROPIA-II run with only ion data will give a reasonable estimate of pH, since both 534 + and are outputs of ISORROPIA-II, while is predicted based on organic mass and . 535 Accurate temperature and RH are still necessary inputs, especially when RH is high. 536

Overall implications of low pH 537
Highly acidic aerosols throughout the southeast during all seasons will affect a variety of processes. For 538 example, aerosol acidity strongly shifts the partitioning of HNO 3(g) to the gas phase resulting in low 539 nitrate aerosol levels in the southeast during summer (the higher summertime temperature also plays a 540 secondary role). Aerosol acidity also impacts the gas-particle partitioning of semi-volatile organic acids. 541 Note, organic acids are not considered in our model, under these acidic conditions (pH = 1) their 542 contributions to the + (hence pH) are expected to be negligible. Because the pK a (pK a = -log 10 K a , K a 543 referred as acid dissociation constant) of trace organic acids are > 2 (e.g., pK a of formic acid, one of the 544 strongest organic acids, is 3.75, Bacarella et al. (1955)), low pH prevents dissociation of the organic acids. 545 Since + is involved in aqueous phase reactions, low pH can affect reaction rates by providing protons. 546 Investigators have found that Isoprene-OA formation is acid-catalyzed and sulfuric acid participates in the 547 reaction as a proton donor in chamber studies (Surratt et al., 2007). However, aerosol acidity appears not 548 to be a limiting factor for Isoprene-OA formation in the southeastern US, owing to the consistently very 549

Conclusions 554
Particle pH is important and difficult to measure directly. However, the commonly used pH proxies of ion 555 balances and NH 4 + /SO 4 2molar ratios do not necessarily correlate with pH. Therefore, predicting pH is the 556 best method to analyze particle acidity. By combining several models we present a comprehensive 557 prediction method to calculate pH and include an uncertainty analysis. ISORROPIA-II is applied to 558 calculate the concentration of + and from inorganic aerosol measurements, and CCN activity is 559 used to predict . The adjoint model of ISORROPIA, ANISORROPIA, is applied to determine 560 sensitivities, which are used for propagating the measurement uncertainties to pH. We find that should 561 be included when predicting particle LWC when organic loadings are high (such as in the southeastern 562 US). However, the pH prediction is not highly sensitive to , unless mass fraction to the total 563 particle water is close to 1. Thus, in most cases particle pH can be predicted fairly accurately with just 564 measurements of inorganic species and ISORROPIA-II. However, constraining ISORROPIA-II with gas 565 phase species, such as NH 3(g) , as done in this work (or HNO 3(g) ), is highly recommended, along with 566 running ISORROPIA-II in the forward mode. ISORROPIA-II does not consider organic acids, but at the 567 low pHs of this study, they do not contribute protons (Bacarella et al., 1955). However, when pH 568 approaches 7, the dissociation of organic acids cannot be neglected. Finally, the model was validated 569 through comparing predicted to measured liquid water ( + to ( )_water) and predicted to 570 measured NH 3(g) concentrations. 571 On average, for the SOAS and SCAPE field studies, particle water associated with the PM 2.5 organic 572 species ( ) accounted for a significant fraction of total LWC, with a mean of 35% (± 3% SD) indicating 573 the importance of organic hygroscopic properties to aqueous phase chemistry and radiative forcing in the 574 southeast US. Although organics are less hygroscopic than sulfate and ammonium, the larger mass 575 fraction of organics than inorganics promotes uptake. Predicted LWC was compared to LWC 576 determined from ambient versus dry light scattering coefficients and a TEOM measurement of dry PM 2.5 577 mass. In SOAS, the sum of and was highly correlated and in close agreement with the measured 578 LWC (slope = 0.91, R 2 = 0.75). LWC showed a clear diurnal pattern, with a continuous increase at night 579 (median of 10 µg m -3 at 7:30 am) reaching a distinct peak when RH reached a maximum near 90% just 580 after sunrise during the period of lowest daily temperature, followed by a rapid decrease and lower values 581 during the day (median of 2 µg m -3 at 2:30 pm).
In the southeastern US, pH normally varied from 0.5 to 2 in the summer and 1 to 3 in the winter, 583 indicating that the aerosol was highly acidic throughout the year. The minimum and maximum pH were -584 0.94 and 2.2 at CTR, respectively and varied from a nighttime average of 1.5 to daytime average of 0.6, 585 mostly attributable to diurnal variation in RH and temperature. Mean NH 4 + /SO 4 2molar ratios were 1.4 ± 586 0.5 (SD) and roughly half the ammonia was in the gas phase (NH 3(g) / (NH 3(g) + NH 4 + ) = 41 ± 16 %, mean 587 ± SD). pH at other sites in the southeast (SCAPE study) was estimated based on a limited data set at an 588 estimated uncertainty of 9-49% and a systematic bias of -1 since NH 3(g) is not included in the 589 thermodynamic model run in the forward mode. pH can still be predicted with only aerosol measurements, 590 but an adjustment of 1-unit pH increase is recommended for the southeastern US. pH has a diurnal trend 591 that follows LWC, higher (less acidic) at night and lower (more acidic) during the day. pH was also 592 generally higher in the winter (~2) than summer (~1). These low pHs have significant implications for 593 gas-aerosol partitioning, acid-catalyzed reactions including isoprene-OA formation, and trace metal 594 mobilization.   recalculated based on ± 5% and ± 10% original RH to investigate pH uncertainty. The slopes and R 2 947 indicate pH uncertainty caused by RH. 948 Fig. 9. Comparison between total predicted and measured water by nephelometers based on hourly 951 averaged data at CTR (SOAS). An ODR fit was applied. Error bars for selected points are shown. 952 Fig. 10. CTR (SOAS) time series of hourly averaged measured NH 3(g) , predicted NH 3(g) , NH 3(g) fraction 955 (i.e., measured NH 3(g) /(NH 3(g) +NH 4 + )) and precipitation. 956