Aerosol and gas measurements were conducted at the Yorkville, Georgia (33.929∘ N, 85.046∘ W) SouthEastern Aerosol Research and Characterization (SEARCH) field site from mid-August to mid-October 2016. This is one of the sampling sites for the Southeastern Center for Air Pollution and Epidemiology (SCAPE) study in which aerosol characterization measurements were conducted in the summer and winter of 2012 (Xu et al., 2015a, b). A detailed description of the field site can be found in Hansen et al. (2003). This rural site is situated in a mixed forest–agriculture area approximately 55 km northwest and generally upwind of Atlanta. The immediate surrounding area is used for cattle grazing and poultry concentrated animal feeding operations (CAFOs) (Fig. S1 in the Supplement). There are no major roads near the field site and nearby traffic emissions were negligible. A large coal-fired power plant (Plant Bowen) is situated approximately 25 km north of the site. Hence, the field site is impacted mainly by BVOC and NH3 emissions, with occasional spikes in SO2 and minimal influence from urban anthropogenic pollutants such as HNO3, O3, NOx, and CO (Fig. S2). The sampling period was characterized by moderate temperatures (24.0 ∘C average, 32.6 ∘C maximum, 9.5 ∘C minimum) and high relative humidities (RHs) (68.9 % RH average, 100 % RH maximum, 21.6 % RH minimum). Meteorological data are shown in Fig. S3. Data reported are displayed in eastern daylight time (EDT).

Instruments were housed in a temperature-controlled (∼20 ∘C) trailer during the field study. Gas-phase HNO3, SO2, and organic acids (formic, acetic, oxalic, butyric, glycolic, propionic, valeric, malonic, and succinic acids) were measured with a custom-built chemical ionization mass spectrometer (CIMS) using sulfur hexafluoride ions (SF6-) as reagent ions. SO2 and HNO3 were detected as fluoride adducts (F2SO2- and NO3-⚫HF, respectively) while the organic acids (HX) were detected primarily as conjugated anions (X-) using the quadrupole mass spectrometer (Huey et al., 1995, 2004; Nah et al., 2018). This CIMS is referred to hereafter as the SF6-CIMS. Gas-phase NH3 was measured with an additional custom-built CIMS using protonated ethanol clusters ((C2H5OH)n+) as reagent ions. NH3 was detected primarily as NH4+ ions with the quadrupole mass spectrometer (Nowak et al., 2002; Yu and Lee, 2012; You et al., 2014a). This CIMS is referred to hereafter as the NH3-CIMS.

Since HNO3, NH3, and organic acids may condense on surfaces, both SF6-CIMS and NH3-CIMS used inlet configurations that minimized wall interactions (Huey et al., 2004; Nowak et al., 2006). Each CIMS was connected to an inlet (a 7.6 cm ID aluminum pipe) that protruded beyond the trailer's wall by ∼40 cm into the ambient air. Both inlets were ∼2 m above the ground. A donut-shaped ring was attached to the ambient sampling port of each pipe to curtail the influence of crosswinds on the pipe's flow dynamics. Both rings were wrapped with a fine wire mesh to prevent ingestion of insects. A flow of ∼2800 Lmin-1 was maintained in each pipe using regenerative blowers (Ametek Windjammer 116637-03). Part of this flow (7 Lmin-1 for the SF6-CIMS and 4.6 Lmin-1 for the NH3-CIMS) was sampled through a custom-made three-way PFA Teflon valve, which connected the pipe's center to the CIMS sampling orifice and could be switched automatically between ambient and background measurements.

Background measurements were performed every 25 min for 4 min for both the SF6-CIMS and NH3-CIMS. During each background measurement, the sampled air flow was passed through an activated charcoal scrubber (Sigma Aldrich) that removed SO2, HNO3, and organic acids prior to delivery into the SF6-CIMS, and through a silicon phosphate scrubber (Perma Pure LLC) that removed NH3 prior to delivery into the NH3-CIMS. More than 99 % of the targeted species were removed during background measurements for both the SF6-CIMS and NH3-CIMS. Standard addition calibrations were performed every 5 h for the SF6-CIMS using the outputs of a 1.12 ppm 34SO2 gas cylinder (Scott Marrin Inc.) and a formic or acetic acid permeation device (VICI Metronics). Calibrations for the other gases measured by the SF6-CIMS were performed in post-field laboratory work, details of which can be found in Nah et al. (2018) and Supplement Sect. S1. Standard addition calibrations were performed hourly for the NH3-CIMS using the output of a NH3 permeation device (KIN-TEK). The outputs of the formic and acetic acid permeation devices were measured periodically by scrubbing the output of the permeation tube in deionized water, followed by ion chromatography analysis for formate and acetate. The emission rate of the NH3 permeation device was measured using UV optical absorption (Neuman et al., 2003).

The detection limits for species measured by the SF6-CIMS and NH3-CIMS were approximated from 3 times the standard deviation values (3σ) of the ion signals measured during background mode. The detection limits for HNO3, SO2, and the various organic acids measured by the SF6-CIMS ranged from 1 to 60 ppt for 2.5 min integration periods, which corresponded to the length of a background measurement with a ∼4 % duty cycle for each m/z (Table S1 in the Supplement). Measurement uncertainties for the concentrations of HNO3, SO2, and the various organic acids originate mainly from calibration measurements and were between 12 % and 25 % (Table S1). The detection limit for NH3 measured by the NH3-CIMS was 1 ppb for 2.3 min integration periods, which corresponded to the length of a background measurement with a ∼29 % duty cycle for the NH4+ ion. Measurement uncertainties for NH3 concentrations were 13 %.

A high-resolution time-of-flight aerosol mass spectrometer (HR-ToF-AMS, Aerodyne Research Inc.) was used to measure the elemental composition of ambient non-refractory PM1 (particles with aerodynamic diameters <1 µm). Ambient air was sampled at 16.7 Lmin-1 through a URG PM1 cyclone and then through a Nafion dryer prior to delivery into the HR-ToF-AMS. Aerosols were dried to RH <20 % to eliminate the influence of RH on the HR-ToF-AMS's particle collection efficiency. A detailed description of the HR-ToF-AMS can be found in the literature (DeCarlo et al., 2006; Canagaratna et al., 2007, 2015). Briefly, the aerodynamic lens of the HR-ToF-AMS focused the dried submicron aerosols into a narrow beam. The aerosols were then impacted onto a heated tungsten surface (∼600 ∘C) on which they were flash vaporized. The resulting vapors were ionized by electron impact ionization (70 eV), and the ions were detected by a time-of-flight mass spectrometer. Gas-phase interferences were accounted for by subtracting the signals obtained during daily measurements of filtered, particle-free sampling air. Ionization efficiency calibrations were performed weekly using 300 nm ammonium nitrate and ammonium sulfate particles. Composition-dependent collection efficiency (CDCE) values of 0.44 to 0.55 were determined using the procedure detailed by Middlebrook et al. (2012), in which CDCE values are derived based largely on aerosol inorganic species concentrations and the RH in the sampling line. In addition, a constant collection efficiency (CE) value of 0.9 was determined from the comparison of raw HR-ToF-AMS SO42- data with other particulate SO42- measurements performed during the study. Comparisons of aerosol mass concentrations obtained from the application of CDCE values (i.e., 0.44 to 0.55) vs. a constant CE value (i.e., 0.9) to the raw HR-ToF-AMS data are discussed in Sect. 3.2. Uncertainties in HR-ToF-AMS measurements were estimated to be approximately 25 % (Canagaratna et al., 2007).

Particle-phase water-soluble organic acids and inorganic cations and anions were measured using two particle-into-liquid sampler (PILS) systems coupled to ion chromatographs (ICs) (Orsini et al., 2003). Each PILS sampled ambient air at nominally 16.7 Lmin-1 through a URG PM1 cyclone. Before PILS1, which was used to measure water-soluble inorganic cation and anions, two long (24 cm) URG glass annular denuders coated with sodium carbonate and phosphorous acid were used to remove acidic and basic gases. Before PILS2, which measured water-soluble organic acids, a 28 cm parallel plate carbon denuder (Sunset Lab) was used to remove organic gases (Eatough et al., 1993). In each PILS, aerosols were mixed with water vapor at ∼100 ∘C generated from heated ultrapure deionized water (Weber et al., 2001; Orsini et al., 2003). The resulting droplets were impacted onto a plate, with the resulting liquid sample analyzed using the ICs. Each IC system was calibrated at the beginning and end of the study using five multi-compound standards in order to create calibration curves. Periodically, a HEPA filter (Pall Life Sciences) was placed on the inlet to determine the background in near real time. The measurement uncertainty for each IC system was about 10 %.

PILS1 was connected to two Dionex ICS-1500 ICs (Thermo Fisher Scientific) to measure the water-soluble inorganic ions. These two IC systems include an isocratic pump, self-regenerating anion or cation suppressor, and conductivity detector. This system will be referred to hereafter as the PILS–IC. Anions were separated using a Dionex IonPac AS15 guard and analytical column (4×250 mm, Thermo Fisher Scientific) employing an eluent of 38 mM sodium hydroxide at a flow rate of 1.5 mLmin-1. Cations were separated using a Dionex IonPac CS12A guard and analytical column (4×250 mm, Thermo Fisher Scientific) employing an eluent of 18 mM methanesulfonic acid at a flow rate of 1 mLmin-1. A new chromatogram was obtained every 30 min with a sample loop fill time (i.e., ambient sample integration time) of 20 min. The limit of detection for the various anions and cations was approximately 0.01 µgm-3.

PILS2 was coupled to a Dionex ICS-4000 capillary high-pressure ion chromatography (HPIC) system to measure the water-soluble organic acids. The HPIC includes an eluent generator, isocratic pump, degausser, suppressor, carbonate removal device, and conductivity detector. This system will be referred to hereafter as the PILS–HPIC. The organic acids were separated using a Dionex AS11-HC-4 µm capillary guard and analytical column (0.4×250 mm, Thermo Fisher Scientific), which used a potassium hydroxide gradient separation method at a flow rate of 0.015 mLmin-1. A new chromatogram was obtained every 60 min with a sample loop fill time of 2 min. The limit of detection for the various organic acids was approximately 0.001 µgm-3.

Particle- and gas-phase water-soluble organic carbon (WSOCp and WSOCg, respectively) were measured using two Sievers 900 series total organic carbon (TOC) analyzers (GE Analytical Instruments), as described by Sullivan et al. (2004). For WSOCp measurements, ambient air was sampled at 15.2 Lmin-1 through a URG PM1 cyclone and a parallel plate carbon denuder into a PILS coupled to the first TOC analyzer. For WSOCg measurements, ambient air was sampled at 20 Lmin-1 through a Teflon filter (45 mm diameter, 2.0 µm pore size, Pall Life Sciences) to remove particles in the air stream. This filter was changed every 3 to 4 days. The particle-free air was then directed to a MIST chamber filled with ultrapure deionized water, which scrubbed the soluble gases at an air flow rate of 20 Lmin-1. Soluble gases with Henry's law constants greater than 103 moleL-1atm-1 were scrubbed into deionized water in the MIST chamber (Spaulding et al., 2002). The resulting MIST chamber liquid sample was analyzed by the second TOC analyzer. The TOC analyzers converted the organic carbon in the liquid samples to carbon dioxide using UV radiation and chemical oxidation. The carbon dioxide formed was then measured by conductivity. The amount of organic carbon in the liquid samples is proportional to the measured increase in conductivity of the dissolved carbon dioxide. Each WSOCp and WSOCg measurement lasted 4 min. Background WSOCp and WSOCg measurements were performed for 45 min every 12 h by stopping the sample air flow and rinsing the system with deionized water. Both TOC analyzers were calibrated at the beginning and end of the study using varying concentrations of sucrose solutions to create calibration curves (as specified by the instrument manual). The limit of detections for WSOCp and WSOCg were 0.2 and 0.4 µgCm-3, respectively. The measurement uncertainties for WSOCp and WSOCg were estimated to be 10 % based on uncertainties in the TOC analyzer, sample air, and liquid flows.

A suite of instruments operated by the SEARCH network provided supporting gas and aerosol measurements (Hansen et al., 2003; Edgerton et al., 2005, 2006, 2007). O3 was measured with a UV absorption instrument (Thermo Fisher Scientific) with a temporal resolution of 1 min. NO and NOx were measured using a chemiluminescence instrument (Thermo Fisher Scientific) with a temporal resolution of 1 min. NO2 was obtained from the difference between NO and NOx. CO was measured using a nondispersive infrared absorption instrument (Thermo Fisher Scientific) with a temporal resolution of 1 min. NH3 was measured by a denuder-based instrument (ARA) with a temporal resolution of 5 min. Comparisons of measurements by the NH3-CIMS and denuder-based instrument will be presented in Sect. 3.1. A filter-based particle composition monitor (ARA) provided 24 h-integrated PM2.5 measurements of particle mass and major inorganic ions measured offline by ion chromatography. Organic carbon (OC) and elemental carbon (EC) in PM2.5 were measured by an OC–EC analyzer (Sunset Labs) with a temporal resolution of 1 h. This analyzer determined OC by thermal optical transmittance. VOCs were measured by a gas chromatography–flame ionization detector (GC-FID, Agilent Technologies) with a temporal resolution of 1 h.

The thermodynamic equilibrium model ISORROPIA II was used to determine the phase state and composition of an NH4+–SO42-–NO3-–Cl-–Na+–Ca2+–K+–Mg2+–water inorganic aerosol in equilibrium with its corresponding gas-phase species (Fountoukis and Nenes, 2007; Nenes et al., 1998). This approach was used in previous studies to determine particle water and pH in different parts of the world (Guo et al., 2015, 2016, 2017a, c; Bougiatioti et al., 2016; Weber et al., 2016; Shi et al., 2017). The pH of an aqueous solution is defined as the negative logarithm of the hydronium ion (H3O+) activity on a molality basis (http://www.goldbook.iupac.org/html/P/P04524.html, last access: 6 July 2018): pH=-log⁡10a(H+)=-log⁡10m(H+)γm(H+)/mθ, where a(H+) is the hydronium ion activity in an aqueous solution, m(H+) is the hydronium ion molality, γm(H+) is the molality-based hydronium ion activity coefficient, and mθ is the standard molality (1 molkg-1). For simplicity, H3O+ is denoted here as H+ even though we recognize that the un-hydrated hydrogen ion is rare in aqueous solutions. Since most thermodynamic equilibrium models (e.g., ISORROPIA II, E-AIM) do not report liquid concentrations, but instead report species in terms of concentration per volume of air (e.g., µgm-3, µmolm-3), we have calculated the particle pH by pH=-log⁡10γH+Haq+=-log⁡101000γH+Hair+Wi+Wo≅-log⁡101000γH+Hair+Wi, where γH+ is the hydronium ion activity coefficient (assumed to be 1), Haq+ is the concentration of hydronium ions in particle water in moles per liter (i.e., the density of water is assumed to be 1000 kgm-3, and so pH is calculated in terms of molality), Hair+ (µgm-3) is the hydronium ion concentration per volume of air, and Wi and Wo (µgm-3) are the bulk particle water concentrations associated with inorganic and organic species per volume of air, respectively. In Eq. (1b), the molecular weight of H+ is taken as 1 gmole-1, and 1000 is the factor needed for unit conversion of grams per liter to micrograms per cubic meter. Hair+ and Wi are outputs of the ISORROPIA II model. Previous studies have shown that particle pH values predicted using only Wi are reasonably accurate since the sensitivity of particle pH to the effects of Wo is small (Guo et al., 2015). For the southeastern US, Guo et al. (2015) reported that particle pH values predicted using only Wi were systematically 0.15 to 0.23 units lower than those predicted using Wi+Wo during the 2013 Southern Oxidant Aerosol Study (SOAS) and SCAPE campaigns. Given this small deviation and that organic aerosol hygroscopicity was not measured in this field study, we report particle pH only considering Wi.

ISORROPIA II was run in “forward” mode, which assumes that aerosols are “metastable” with no solid precipitates, to predict particle pH and the partitioning of semi-volatile compounds. In forward mode, the model calculates the gas–particle equilibrium partitioning concentrations based on the input of the total concentration of a species (i.e., gas + particle). In reverse mode, the model calculates the gas–particle equilibrium partitioning concentrations based on the input of only the particle-phase concentration of a species. We used forward mode because the reverse mode is sensitive to measurement errors, which often result in large model biases in the predicted particle pH (Hennigan et al., 2015). The measured particle-phase inorganic NH4+, SO42-, and NO3- concentrations and gas-phase HNO3 and NH3 concentrations were used as model inputs. The metastable assumption is reasonable since the high RH (average RH 68.9 %) observed during the study indicated that the aerosols had likely deliquesced. We excluded data for periods when the RH was above 95 % since the exponential growth in particle liquid water with RH introduces large pH uncertainties (Malm and Day, 2001; Guo et al., 2015).

In using ISORROPIA II to predict particle pH and the partitioning of semi-volatile compounds, we also assumed that the aerosols are internally mixed and that the particle pH does not change with particle size (i.e., the overall particle pH is characterized by the particle's bulk properties). As long as some small fraction of sulfate is mixed with various aerosol components, (e.g., non-volatile cations), the assumption that aerosols are completely internally mixed has a small effect on the predicted pH (Guo et al., 2017b). However, the presence of multiple organic and inorganic species in ambient aerosols may lead to multiple phases within the particle (i.e., phase separation). Consequently, this may result in the unequal distribution of inorganic species among different phases, each with its own water activity and inorganic concentration. Previous studies have shown that liquid–liquid and solid–liquid phase separations may occur for mixed organic and inorganic aerosols at low RH and organic aerosol oxygen-to-carbon atomic ratios (O/C) (Bertram et al., 2011; Song et al., 2012; You et al., 2013, 2014b; You and Bertram, 2015). Phase separations were always observed at O/C≤0.5, while no phase separation was observed at O/C≥0.8. The probability for the occurrence of phase separation decreased at higher RH for 0.5<O/C<0.8. The average O/C for this field study is 0.69±0.06. Organic acids were not included in the calculation of particle pH. This is reasonable since their total mass concentration was small compared to the total inorganic mass concentration. The average ratio of the organic acid mass concentration to the inorganic mass concentration is 0.25. Furthermore, Song et al. (2018) showed that including organic acid mass concentrations in thermodynamic model calculations had minor effects on particle pH if the system is in equilibrium. The validity of these assumptions and the resulting thermodynamic model predictions will be evaluated by comparing the predicted gas–particle partitioning ratios of semi-volatile inorganic compounds with measured values in Sect. 3.3.

Continuous measurements of NH3 were made using the NH3-CIMS from 13 September to 12 October. Figure 1a and b show the time series and average diurnal profile of NH3, respectively. NH3 concentrations ranged from 0.7 to 39.0 ppb (0.5 to 28.5 µgm-3) and exhibited consistent diurnal cycles. NH3 was generally higher in the late mornings and early afternoons. Concentrations started to increase at 07:30, which coincided with an increase in temperature at sunrise (Fig. S3). Possible reasons for the morning increase include volatilization of particulate ammonium and animal waste, entrainment from the residual layer where NH3 may not have been depleted, evaporation of dew or fog that contained dissolved NH3, and emission from plant stomata (Ellis et al., 2011). NH3 decreased at 14:30, approximately 1 h before temperature decreased, and may be due to changes in the boundary layer height. However, this hypothesis cannot be tested since the boundary layer height was not measured during the study. The diurnal plot does not account for dilution as the boundary layer expanded and only indicates that if emissions were solely from the surface and lower concentrations aloft, these NH3 sources were of significant magnitude.

The average NH3 concentration measured by the NH3-CIMS is 8.1±5.2 ppb. This is approximately 2 times higher than the average NH3 concentration (3.8±2.9 ppb) measured by the denuder-based instrument operated by the SEARCH network over the same time period (Fig. S4). Differences in NH3 concentrations measured by the two instruments may be due to positive and negative sampling artifacts caused by differences in sampling inlets (e.g., inlet length and location), frequency of calibration and background measurements, and (in the case of the denuder-based instrument) possible sample contamination during chemical analysis. Discussions on how differences in measured NH3 concentrations affect PM1 pH predictions will be presented in Sect. 3.3. Nevertheless, there is a record of NH3 concentrations measured by the denuder-based instrument at this site since 2008. Just prior to and during this study, NH3 concentrations are generally the highest observed since 2011 (Fig. S5). These elevated NH3 concentrations may be due to sporadic biomass burning episodes caused by elevated temperatures and widespread drought across the southeastern US in 2016 (Park Williams et al., 2017; Case and Zavodsky, 2018).

The NH3-CIMS measurements are examined with the meteorological data to gain insights into the primary NH3 sources during the sampling period. To account for wind speed, the 1 h averaged NH3 concentrations are first multiplied by their corresponding 1 h averaged wind speeds. These normalized NH3 concentrations are then used to construct a wind direction polar plot showing the average normalized NH3 concentration per 10∘ bin (Fig. 1c). The wind direction polar plot shows that the normalized NH3 is approximately 2 times greater than the average when air masses are transported from the southeast, the general direction of the poultry CAFOs located approximately 2 km from the field site (Fig. S1), which are known for having high NH3 emissions. This conclusion is reaffirmed by NH3 measurements from the SEARCH network's denuder-based instrument.

NH3 concentrations measured by the two instruments in this study are substantially higher than those measured in three recent field studies conducted in the continental US: the 2010 California Nexus (CalNex) study, 2013 Southeast Nexus (SENEX) study, and 2013 SOAS study (see Table 1). The differences in NH3 may be attributed to differences in land use, proximity to CAFOs, and meteorological conditions. The high NH3 concentrations in this study allow us to make ambient observations of the effect of NH3 on particle acidity and the gas–particle partitioning of semi-volatile inorganic and organic compounds, and compare them with previous studies.

The aerosol inorganic chemical composition was measured by several instruments during this study. The HR-ToF-AMS, PILS–IC and PILS–HPIC measured the composition of PM1, while a filter-based particle composition monitor measured the composition of PM2.5. Comparisons of aerosol SO42-, NO3-, and NH4+ mass concentrations obtained from the application of CDCE values to the raw HR-ToF-AMS data are compared to those measured by the other three instruments in Fig. S6. NH4+ measurements by the PILS–IC are not available for comparison due to denuder breakthrough that occurred during the study.

SO42- measurements by the various instruments are generally well correlated with each other, with R2 values ranging from 0.64 to 0.92. Although PM1 SO42- measurements by the two PILS systems show good agreement with each other, HR-ToF-AMS CDCE-applied SO42- measurements are approximately 2 times higher than the PILS and filter measurements. Similar systematic differences are also observed for NO3- and NH4+ measurements. NO3- and NH4+ measurements from the four instruments are moderately correlated (R2=0.54 to 0.79 and R2=0.94, respectively). NO3- measurements from the PILS and filter systems are mostly similar; however, HR-ToF-AMS CDCE-applied PM1 NO3- and NH4+ measurements are approximately 3 times and 2 times higher than the PILS and filter measurements. One possible reason is that the calculated CDCE is lower due to organics dominating the aerosol composition during the study (average of 74.2±7.9 % of the non-refractory PM1 mass concentration). Lee et al. (2015) suggested that a high organic mass fraction may impede the complete efflorescence of aerosols when they are passed through the drier prior to delivery into the HR-ToF-AMS, thus reducing the particle bounce and increasing the CE value. Hence, we estimated HR-ToF-AMS PM1 mass concentrations that would be consistent with PILS and filter measurements by multiplying all the raw HR-ToF-AMS data by a constant CE value of 0.9, which was obtained from comparisons of the raw HR-ToF-AMS SO42- data with PILS–IC and PILS–HPIC SO42- measurements. The constant CE-applied HR-ToF-AMS data are used in all our subsequent analyses.

Figure 2 shows the time series and average diurnal profiles of non-refractory PM1 species. The average non-refractory PM1 organics, SO42-, NO3-, and NH4+ mass concentrations are 5.0±2.3, 1.6±0.4, 0.2±0.1, and 0.4±0.2 µgm-3, respectively. Organics are the dominant non-refractory PM1 species, accounting for 74.2±7.9 % of the non-refractory PM1 mass concentration during the field study. Organic aerosol mass concentration was slightly higher at night, which is likely caused by changes in the boundary layer height, emission sources, and SOA formation processes (Xu et al., 2015b). Previous studies have shown that nighttime SOA production in the southeastern US is largely attributed to nitrate radical oxidation and ozonolysis of monoterpenes, which are abundant at night (Pye et al., 2015; Xu et al., 2015a, b; Lee et al., 2016; Zhang et al., 2018). Specifically, the nitrate radical oxidation of some monoterpenes (e.g., β-pinene) could form low-volatility organic nitrates that are condensable and could contribute substantially to the nocturnal organic aerosol mass (Boyd et al., 2015, 2017; Ng et al., 2017). Apportionment of organic aerosol sources will be discussed in an upcoming publication. SO42- is the second most abundant non-refractory PM1 species (16.3±5.7 % mass fraction), followed by NH4+ (5.9±2 % mass fraction) and NO3- (3.6±2.2 % mass fraction). SO42- mass concentration peaked in the afternoon due to enhanced SO2 photooxidation (Weber et al., 2003). The NO3- mass concentration measured by the HR-ToF-AMS is the nitrate functional group (-ONO2) present on organic and inorganic nitrates. Hence, the diurnal profile of the NO3- mass concentration in Fig. 2 has contributions from both organic and inorganic nitrates. The mass concentrations of organic and inorganic nitrates increased after sunset and peaked at sunrise (Fig. S7), likely due to the formation of organic nitrates from nighttime NO3 chemistry and increased gas-to-particle partitioning of organic and inorganic nitrates as temperature decreased (Xu et al., 2015a, b). Quantification and characterization of organic nitrates based on HR-ToF-AMS and PILS–IC PM1 NO3- measurements will be discussed in a future publication. NH4+ mass concentration has moderate diurnal variations with marginally higher concentrations in the afternoon, likely due to the contrasting day–night phases of ammonium sulfate and ammonium nitrate formation. SO42-, NO3-, and NH4+ molar concentrations indicated that NH4+ is mainly associated with SO42- in PM1.

CIMS HNO3 and NH3 data, HR-ToF-AMS PM1 SO42- and NH4+ data, PILS–IC PM1 NO3- and non-volatile cation (Cl-, Na+, Ca2+, K+, and Mg2+) data, measured temperature, and RH are used as ISORROPIA II model inputs to predict PM1 Wi and pH from 13 September to 6 October. Figure 3 shows the time series and average diurnal profiles of ISORROPIA-predicted PM1 Wi and pH. PM1 is highly acidic with pH values ranging from 0.9 to 3.8 and an average pH of 2.2±0.6. The average PM1 pH is 2.5±0.6 during periods when the NH3 concentration is higher than 13.3 ppb (i.e., average NH3 concentration +1 standard deviation = 8.1+5.2=13.3 ppb). The PM1 pH values in this study are generally similar to those reported by Guo et al. (2015) at the same field site during winter 2012. Our observation that PM1 is acidic despite the high NH3 concentrations in this study is consistent with previous studies showing that particle pH has weak sensitivities to wide NH3 and SO42- mass concentration ranges due to pH buffering caused by the partitioning of NH3 between the gas and particle phases (Weber et al., 2016; Guo et al., 2017c). This weak particle pH sensitivity also explains the small changes in PM1 pH values (about 10 % lower, Fig. S8) when NH3 measurements by the SEARCH network denuder-based instrument are used in ISORROPIA II calculations (instead of NH3-CIMS measurements).

PM1 pH varied by approximately 1.4 units throughout the day. Wi has an average value of 1.6±1.7 µgm-3. PM1 Wi and pH showed similar diurnal profiles, with both peaking in the midmorning and reaching their minima in the midafternoon. These diurnal trends are consistent with those previously reported by Guo et al. (2015) for PM1 measured during the summer and winter in different parts of the southeastern US. Also shown in Fig. 3b is the diurnal profile of Hair+, which peaked in the midafternoon. The Wi and Hair+ maximum / minimum ratios are comparable (6.5 and 5.3, respectively), thus indicating that the diurnal variation in particle pH is driven by both Wi and Hair+.

The average PM1 pH for this study is about 1 unit higher than that for the SENEX and SOAS campaigns (Table 1) and is likely due to the much higher abundance of NH3 in this study. The average NH3 mass concentration in this study is approximately 49 times and 15 times higher than that in the SENEX and SOAS campaigns, respectively. The average PM1 pH for this study is similar to that for the CalNex campaign even though the average NH3 mass concentration in this study is only approximately 4 times higher than that in the CalNex campaign (Guo et al., 2017a). This may be due, in part, to PM1 SO42- and NO3- mass concentrations at CalNex being approximately 2 times and 18 times larger than those of this study, respectively. Aerosol inorganic SO42- and NO3- species are hygroscopic species. The much higher NO3- mass concentrations in the CalNex campaign (due, in part, to high NOx emissions) increased particle Wi substantially, which diluted H+ and raised particle pH, resulting in more gas-to-particle partitioning of NO3-, and eventually leading to pH levels similar to those observed in this study. This type of feedback does not happen in the southeastern US, where non-volatile SO42- dominates the uptake of particle water. It is also possible that the higher RH and lower temperatures during the CalNex campaign (relative to this study) contributed to high particle Wi, which diluted H+ and raised particle pH levels similar to those observed in this study.

The validity of this study's thermodynamic model predictions is evaluated by comparing the predicted gas–particle partitioning ratios of semi-volatile inorganic compounds (i.e., NO3- and NH4+) with measured values (Fig. S9). CIMS HNO3 and NH3 data, PILS–IC NO3-, and HR-ToF-AMS NH4+ data are used in this comparison. ε(NO3-) and ε(NH4+) are defined as the particle-phase molar concentration divided by the total molar concentration (gas + particle), i.e., ε(NO3-)=NO3-/(HNO3+NO3-) and ε(NH4+)=NH4+/(NH3+NH4+). Predicted NH3, NH4+, and ε(NH4+) values are generally within 10 % of and are highly correlated (R2=0.96 to 0.99) with measured values (Fig. S9). While predicted HNO3 values generally agreed with measurements, substantial scatter can be seen between the predicted and measured values for NO3- and ε(NO3-). This scatter can be attributed, at least in part, to uncertainties brought about by the low PM1 NO3- mass concentrations and effects of coarse-mode cations (e.g., Na+, Ca2+, K+, and Mg2+) on fine-mode HNO3–NO3- gas–particle equilibrium (i.e., HNO3 can partition to both fine and coarse modes, thereby affecting fine-mode NO3- concentrations; no such effect occurs for NH3–NH4+ gas–particle equilibrium). In general, the overall good agreement between model predictions and measurements indicated that our assumptions that aerosols are metastable (i.e., aerosols are supersaturated aqueous droplets) with no phase separation for the thermodynamic calculations are reasonable for the conditions of this study and do not affect model predictions.

The molar fractions of NO3- and NH4+ in the particle phase (i.e., ε(NO3-) and ε(NH4+)) measured in this study are compared with those measured during the CalNex, SENEX, and SOAS campaigns. Figure 4 shows the measured ε(NO3-) and ε(NH4+) values as a function of their ISORROPIA-predicted particle pH for the various field studies. For each field study, only a subset of the data are chosen for this comparison (1≤Wi≤4 µgm-3 and 15 ∘C ≤ temperature ≤ 25 ∘C) to reduce the effects of variability in Wi and temperature on gas–particle partitioning for comparison with the calculated S (or sigmoidal) curves, which are calculated based on Wi=2.5 µgm-3 and temperature = 20 ∘C. The S curves for HNO3–NO3- and NH3–NH4+ partitioning as a function of particle pH are also plotted as solid lines. The S curves are calculated based on the solubility and dissociation of NO3- and NH4+ species in water: εNO3-=HHNO3∗RTWi×0.987×10-14γH+γNO3-10-pH+HHNO3∗RTWi×0.987×10-14,εNH4+=γH+10-pHγNH4+HNH3∗RTWi×0.987×10-141+γH+10-pHγNH4+HNH3∗RTWi×0.987×10-14, where HHNO3∗ and HNH3∗ (mole2kg-2atm-1) are equilibrium constants and are the products of the Henry's law constant and the dissociation constant of HNO3 and NH3, respectively; R is the gas constant (8.314 m3PaK-1mol-1); T is temperature (K); and γi's are activity coefficients. HHNO3∗ and HNH3∗ values at 20 ∘C are calculated using equations found in Clegg and Brimblecombe (1990) and Clegg et al. (1998), respectively. Activity coefficients predicted by ISORROPIA II are γH+-NO3-=γH+γNO3-=0.28, γH+=1 and γNH4+=1. Derivations of the analytically calculated S curves for ε(NO3-) and ε(NH4+) in Eqs. (2) and (3) can be found in Guo et al. (2017a). As shown in Fig. 4, the measured ε(NO3-) and ε(NH4+) values for the four field studies all generally converged on the calculated S curves. The higher particle pH values in this study and the CalNex campaign relative to those for the SENEX and SOAS campaigns resulted in less NH3 and more HNO3 partitioned to the particle phase, as predicted by these simple analytical expressions. A similar analysis will be performed for the organic acids in Sect. 3.5.

The time series and average diurnal profiles of WSOCg and WSOCp are shown in Fig. S10. The average WSOCg mass concentration (3.6±2.7 µgCm-3) is roughly 4 times higher than that of WSOCp (1.0±0.6 µgCm-3). The diurnal profile of WSOCp is somewhat flat, likely due to various organic aerosol sources having different water solubility and diurnal cycles and compensating for each other throughout the day (Xu et al., 2015b, 2017). In contrast, WSOCg displayed strong diurnal variations. WSOCg increased at 07:30, which coincided with the sharp increase in solar irradiance (Fig. S3). WSOCg decreased at 21:30, approximately 2 h after sunset. Also shown in Fig. S10 are the time series and average diurnal profile of the mass fraction of total WSOC in the particle phase, i.e., Fp=WSOCp/(WSOCp+WSOCg). The peak Fp coincided with the minima of WSOCg at 07:30.

The average WSOCg and WSOCp (3.6±2.7 µgCm-3 and 1.0±0.6 µgCm-3) are slightly lower than those measured during the SOAS campaign (SOAS WSOCg=4.9 µgCm-3 and WSOCp=1.7 µgCm-3) (Xu et al., 2017). While the diurnal profiles of WSOCp in both studies are flat, the diurnal profiles of WSOCg measured in the two studies are different. WSOCg measured in the SOAS study decreased at sunset, while WSOCg measured in this study decreased 2 h after sunset. Differences in WSOCg diurnal profiles in the two studies are likely due to differences in emission sources as a result of different sampling periods (SOAS was in early summer and this study was in early fall), land use, and/or land cover. The ratio of WSOCp to OC for this study was estimated at 30 %, but this comparison is imprecise because WSOCp was PM1 and OC was PM2.5 (refer to Fig. S11 and Supplement Sect. S2).

Figure 5 shows the time series of particle- and gas-phase concentrations of formic, acetic, oxalic, malonic, succinic, glutaric, and maleic acids. Their diurnal profiles are shown in Fig. 6. Gas-phase measurements of glutaric and maleic acids are not available. Gas-phase measurements of butyric, glycolic, propionic, and valeric acids were also measured during the study and have been presented in Nah et al. (2018), but will not be discussed here since their particle-phase measurements are not available.

Assuming that all the measured organic acids are completely water soluble, 30 % of the WSOCg is comprised of these organic acids (Nah et al., 2018). Formic and acetic acids are the most abundant gas-phase organic acids, with averages of 2.2±1.6 and 1.9±1.3 µgm-3, respectively. The average carbon mass fraction of WSOCg comprised of formic and acetic acids is 7 % and 13 %, respectively. All the gas-phase organic acids displayed strong and consistent diurnal cycles, with higher concentrations being measured during warm and sunny days. Their concentrations start to increase at sunrise (at 07:30), building to a peak between 15:30 and 19:30, then decrease overnight.

Nah et al. (2018) previously showed that the measured gas-phase organic acids during the study, including oxalic acid, likely have the same or similar sources. Poor correlations between gas-phase organic acid concentrations and those of anthropogenic pollutants (HNO3, SO2, CO, and O3) indicated that these organic acids are not due to anthropogenic emissions and are likely biogenic in nature. Biogenic emissions of gas-phase organic acids and/or their BVOC precursors are elevated at high temperatures, resulting in higher organic acid concentrations during warm and sunny days. For example, isoprene, which is the dominant BVOC in Yorkville, has a somewhat similar diurnal profile to the organic acids. In addition, the concentration of isoprene is moderately correlated with those of formic and acetic acids (Fig. S10 of Nah et al., 2018), which are known products of isoprene photooxidation. Some of these gas-phase organic acids may also be formed in the particle phase during organic aerosol photochemical aging, with subsequent volatilization into the gas phase. The gas–particle partitioning of organic acids likely depends on thermodynamic conditions, which are controlled by particle pH and Wi and meteorological conditions, as will be shown in Sect. 3.5.

The measured particle-phase water-soluble organic acids contributed on average 6 % to the HR-ToF-AMS-measured organic aerosol mass concentration. The average carbon mass fraction of WSOCp comprised of these organic acids is 4 %. Previous studies have shown that particle-phase organic acids found in rural environments are oxidation products of gas-phase aliphatic monocarboxylic acids, which are formed in the photochemical oxidation of biogenic unsaturated fatty acids and other BVOC precursors (Kawamura and Gagosian, 1987; Kawamura and Ikushima, 1993; Kerminen et al., 2000; Kawamura and Bikkina, 2016). These particle-phase organic acids can also be produced during the multiphase photochemical aging of ambient organic aerosols (Ervens et al., 2004; Lim et al., 2005; Sorooshian et al., 2007, 2010).

Oxalate is the most abundant measured particle-phase water-soluble organic acid anion (contributing on average 26 % to the total particle-phase organic acid mass concentration), with mass concentrations ranging from 0.01 to 0.34 µgm-3 and an average of 0.07±0.05 µgm-3. Acetate (average of 0.06±0.03 µgm-3) and formate (average of 0.05±0.03 µgm-3) are the second and third most abundant measured particle-phase water-soluble organic acid anions, respectively. Particle-phase formate, acetate, and maleate showed weak diurnal variations, and may be due, in part, to various emission sources having different diurnal cycles and compensating for each other throughout the day. Particle-phase oxalate, malonate, and succinate peaked in the middle to late afternoon, while glutarate generally peaked in the midmorning. This suggests that while the production of these organic acids is photochemically driven, they may have different BVOC precursors and/or different photochemical production pathways. In addition, since oxalic (C2), malonic (C3), succinic (C4), and glutaric (C5) acids belong to the same homologous series of organic diacids, it is possible that the photochemical aging of particle-phase glutaric acid resulted in the formation of its successive homologues via the cleavage of C–C bonds. Hence, organic aerosol photochemical aging may also have contributed to the diurnal profiles of particle-phase oxalate, malonate, succinate, and glutarate.

The online and simultaneous measurements of gas- and particle-phase organic acid mass concentrations provided the opportunity to study gas–particle partitioning behavior of semi-volatile organic compounds with respect to particle pH, as is more commonly done with semi-volatile inorganic species (see Sect. 3.3). Since formic, acetic, and oxalic acids are the three most abundant measured organic acids present in the gas and particle phases, we focus on the gas–particle partitioning behaviors of these three organic acids. The average molar fractions (±1 standard deviation) of formic, acetic, and oxalic acid in the particle phase (i.e., ε(HCOO-), ε(CH3CO2-), and ε(C2O42-)) are 3.6±3.6 %, 5.8±5.0 %, and 73.7±9.8 %, respectively. The uncertainties of these ratios for formic, acetic, and oxalic acids are 16 %, 16 %, and 17 %, respectively, which are obtained from the propagation of their SF6-CIMS and PILS–HPIC measurement uncertainties.