Atmospheric aerosol organic matter (OM) composition, sources, and formation processes have been a focus of research for many decades (Haagen-Smit, 1952; Went, 1960). However, because the organic fraction of aerosol particles contains thousands of individual chemical compounds (Schum et al., 2018a), it is a difficult task to characterize the total OM composition of an aerosol sample. Typical molecular-level analytical techniques quantify up to 30 % of OM concentration (Hallar et al., 2013). Chromatography techniques suffer from needing to have sufficient molecular selectivity and sensitivity for each chemical, requiring calibration of each species. As an alternative, rather than quantifying each chemical, the total OM concentration can be measured.

Some analytical techniques such as aerosol mass spectrometry can quantify OM concentrations in real time (Aiken et al., 2008). Other methods with involved chemical analyses of discrete filter samples have been used to estimate OM concentration. These include multiple linear regression of aerosol constituents using various analytical techniques (Hand et al., 2019; Malm and Hand, 2007; Simon et al., 2011), extrapolation from gas chromatography–mass spectrometry of extracts (Turpin and Lim, 2001), infrared absorption spectrometry of extracts (Polidori et al., 2008), or thermal–optical and gravimetric analyses of extracts (El-Zanan et al., 2009). However, each of these methods is subject to specific limitations. Aerosol mass spectrometry OM concentrations, for example, are subject to uncertainties resulting from fragmentation and high heat exposure (Canagaratna et al., 2015). Filter extraction procedures can result in the loss of organic species (Kawamura and Bikkina, 2016) and render a sample unusable for further analysis, while multiple linear regression and mass balance techniques require accurate estimation of all inorganic species concentrations, which can involve large uncertainties (e.g., ignoring particle water mass or losses of volatile ammonium and nitrate during NH4NO3 collection from different filter media; Chow et al., 2015; Yu et al., 2006).

The methods of estimating OM concentrations listed above are either not feasible or have substantial uncertainty for measurements that are remote, resource-limited, or long-term (e.g., multi-year). Analyses of OM for routine monitoring networks have specific requirements. Because of the large number of samples, collection must be simple, and the cost of analysis must be low. Nondestructive, filter-based techniques are also desirable for networks because they allow for multiple chemical analyses to be performed on one sample.

In air monitoring networks, OM concentrations are typically estimated indirectly from organic carbon (OC) concentrations (Edgerton et al., 2005; Pitchford et al., 2007). While OM includes other atoms such as O and H associated with C (sometimes also N, S, and P; Russell, 2003), OC accounts for only the C atoms. Sample OM concentration is typically determined from thermal optical reflectance (TOR) OC by multiplying the OC concentration by a static ratio of OM/OC. An OM/OC value of 1.4 for urban samples (White et al., 1977) or 1.8 for rural samples (Pitchford et al., 2007) is typically used, although a value 2.1 for rural areas (Turpin and Lim, 2001) has been broadly cited. However, OM/OC varies widely amongst ambient samples. For example, Ruthenburg et al. (2014) estimated values varying between 1.46 and 2.01 (10th and 90th percentiles) in 1 year of samples at seven rural US locations. This and other observed OM/OC variability suggests that a static value of OM/OC is not adequate to capture the spatial and temporal variations in OM. A technique for routine OM concentration measurement in ambient aerosol at network sites is therefore needed.

Fourier transform infrared absorption (FT-IR) spectrometry can be used to quantify most of the organic aerosol concentration in a given sample by functional groups (Coury and Dillner, 2009; Faber et al., 2017; George et al., 2015; Reff et al., 2005; Russell et al., 2011; Ruthenburg et al., 2014). Measuring functional group concentrations in ambient aerosol samples is useful to (1) accurately estimate the total OM concentration, (2) further characterize the OM composition by functional groups, (3) monitor organic composition and sources of aerosol over time, and (4) estimate the degree of oxidation. The FT-IR spectrometry approach is particularly useful for routine and network OM measurements because it can be applied to filter samples that are routinely collected for other purposes (e.g., particulate matter mass), is nondestructive, and is inexpensive.

The principle of organic characterization through FT-IR spectrometry is as follows: chemical bonds with appropriate vibrational symmetries and frequencies absorb light at specific mid-infrared wavelength ranges, allowing the determination of the bond type and, in some cases, even molecular environment. The magnitude of the light absorption is proportional to the number of bonds present, allowing the direct quantification of bonds within an aerosol sample (Allen et al., 1994).

Infrared absorption spectrometry has been used to quantify functional groups using a peak-fitting approach (Takahama et al., 2013), but factor-based calibration of spectra can more readily determine interferents and is strengthened by using multiple spectral bands at once (Naes et al., 2002). Specifically, partial least-squares (PLS) regression has been used in factor-based work. A comparison of the peak fitting and PLS calibration methods has been recently discussed (Reggente et al., 2019). In a PLS functional group calibration, concentrations of pure chemical standards are regressed onto their corresponding FT-IR spectra to reduce the number of variables describing the data. These new variables, sometimes called “factors”, are identified to explain the covariance between the chemical standard concentrations and spectra. Each functional group is quantified (typically by mole) as a weighted sum of the extracted factors, resulting in a unique calibration model for each functional group (see Sect. 2.5, Supplement Sect. S10, and Naes et al., 2002). Examples of PLS calibration of functional groups in atmospheric OM include the work of Reff et al. (2007), Coury and Dillner (2009), Ruthenburg et al. (2014), and Kamruzzaman et al. (2018).

Calibration curves are developed from “laboratory standards”: pure chemicals collected onto fresh polytetrafluoroethylene (PTFE) filters. The chemical mass collected is varied to capture the relationship between infrared absorption and number of bonds (Coury and Dillner, 2008). Ruthenburg et al. (2014) built a set of FT-IR–PLS calibration models using nine organic chemicals and one inorganic salt interferent (ammonium sulfate) to quantify four functional groups: aliphatic C-H, carbonyl (C=O), carboxylic acid O-H, and alcoholic O-H. The concentrations of these functional groups (and OM concentrations as weighted sums of these functional groups) were predicted in ambient filter samples collected from seven IMPROVE network sites in 2011. The same measurements were made, adding an amine functional group model, for a larger group of IMPROVE network sites from 2013 (Kamruzzaman et al., 2018). However, the relatively short list of chemicals to represent atmospheric composition likely limited the ability of these models to characterize the aerosol composition fully. Previous work was also done with a more comprehensive list of chemical standards; unfortunately, the particular measurement technique damaged the filter samples, which is not desirable for air monitoring network data (Coury and Dillner, 2008).

Efforts to improve FT-IR functional group concentration measurements involve addressing the following challenges: (1) approximating atmospheric composition by selecting appropriate lists of chemicals and functional groups for calibration, (2) considering ambient aerosol molecular environments, including particle water content, (3) selecting appropriate model parameters based on the current understanding of atmospheric composition, (4) validating models when methods for direct comparison are lacking, and (5) quantifying as much of the OM mass as possible given that most, but not all, relevant molecular bonds absorb in the mid-infrared spectral range. The following paragraphs discuss these challenges in more detail.

The selection of chemicals is nontrivial: atmospherically representative bonds must be selected to enable the calibration to capture the variation in ambient samples. It is not possible to generate standards of the thousands of individual molecules that exist within aerosol samples, many of which have not yet been identified (Schum et al., 2018). An appropriate starting point for the list of chemical standards used in the calibration models is the atmospheric speciation reported in previous studies. The molecular bonds (or functional groups) included in the calibration must represent the majority of the OM. In addition, efforts to measure subgroups of functional groups within a broad functional group category such as carbonyl groups are made (e.g., inclusion of dicarboxylic acids and amino acids), while recognizing the limitations of subdividing groups given overlapping spectral features. In addition, inorganic species that absorb infrared light must be included as “interferents” in a robust calibration model.

Laboratory standards are prepared with the goal of capturing the molecular structures and intermolecular interactions most relevant for the atmosphere. The infrared spectrum of a molecule is affected by its chemical environment, including its hydrogen and ionic bonding interactions with other molecules in a sample (Davey et al., 2006; Mayo et al., 2003). Ideally, the variety of interactions between the many molecules in ambient aerosol particles would be modeled by the calibration to capture the variability in infrared spectral features. The bonding structures within particles of single, pure chemicals, and between mixtures of chemicals, may also warrant consideration. Mixtures can probe for interactions between different types of polar organic functional groups (hydrogen bonding), as well as organic with inorganic ions (ionic bonding, such as carboxylates). Water that is chemically or physically bound to collected ambient aerosol particles is also expected to alter ambient samples spectroscopically and could be abundant (Dabek-Zlotorzynska et al., 2011). The presence of water could induce molecular transitions, such as formation of gem-diols from carbonyls (Maroń et al., 2011), or enhance spectral features of particle water: as liquid water associated with particles (Faber et al., 2017) or as hydrate water chemically bound to particle chemical constituents (Cziczo and Abbatt, 2000). Laboratory-generated particles under humid conditions may display these spectral impacts of water, and may be useful as inputs to inform models.

The inputs to PLS models must be carefully selected to minimize measurement uncertainty. Examples of inputs include the concentration range of the chemical standards and the number of PLS factors included in each model. These inputs are selected based on the best available information but may need to be updated over time as understanding of atmospheric composition improves.

Few methods exist for verifying FT-IR spectrometry functional group concentrations. Strong correlations have been found between ratios of FT-IR spectrometry measurements with high-resolution aerosol mass spectrometry tracer ions (e.g., ratioed carboxylic acids and C-H groupings); direct (not ratioed) correlations between measurements were less successful (Faber et al., 2017; Russell et al., 2009a). Ruthenburg et al. (2014) quantitatively evaluated their FT-IR functional group concentrations by comparing OC concentrations from summed functional groups with TOR OC concentrations.

Although comprehensive in that a broad range of molecules in OM are detected, there are some limitations to the sensitivity of FT-IR spectrometry. Some bonds, such as tertiary C-C bonds and C-O bonds, do not absorb in mid-infrared spectral regions or absorb where the filter substrate, PTFE, also absorbs (Weakley et al., 2016). Ongoing work using empirically based simulations aims to quantify this “mass recovery” of FT-IR-spectrometry-resolvable ambient OM (Burki et al., 2019).

The goal of this work is to further develop a method to measure functional group concentrations and calculate OM concentrations in ambient aerosol samples using FT-IR spectrometry and PLS calibration. Samples were collected by the SouthEastern Aerosol Research and Characterization (SEARCH; Hansen et al., 2003) network. There are two main components of achieving the overall study goal. The first is to expand upon previous work (Ruthenburg et al., 2014) to better characterize OM and address other challenges of FT-IR spectrometry and PLS calibration (as described in Sect. 1.3). The second is to evaluate the improved method by quantifying atmospheric functional group concentrations over multiple years at consistent locations.

To address the first component of achieving the study goal, a broader list of atmospherically relevant chemical standards were incorporated, including chemicals specific to the southeastern US. The functional groups included more specific subgroups than in previous work: aliphatic C-H groups, carboxylic acids, oxalates, non-oxalate and nonacid carbonyls, and alcohols. Additional interfering species, including particle water and ammonium nitrate, were accounted for, and molecular interactions expected in ambient samples were considered. Model parameters such as the number of regression factors were selected based in part on current atmospheric composition literature and focused studies using simulation methods.

To address the second component, SEARCH samples from 2009 to 2016 at five sampling sites with varying (urban or rural) emissions were analyzed. The calibration of SEARCH samples was particularly challenging due to interference from the thicker filter material and lower aerial density of particles than the IMPROVE samples used by Ruthenburg et al. (2014). The final models were evaluated qualitatively and semiquantitatively by comparing the ambient SEARCH functional group measurements with atmospheric composition measurements made using multiple analytical methods. For example, resulting OM and OC concentrations were compared with residual OM and TOR OC concentrations, respectively.

Aerosol composition in the southeast was characterized from 1999 to 2016 by the SEARCH network. The SEARCH network was unique in that it focused on one region of the US, with sites in urban and rural pairs (Birmingham and Centreville in Alabama and Atlanta and Yorkville in Georgia). Measurement methods were advanced and comprehensive, including real-time gas-phase measurements, light and mass-based measurements of total particles, a variety of particle-phase composition measurements (trace elements, inorganic salts, OC, and elemental carbon), and supporting meteorological variables.

Filter samples of ambient aerosol collected in the SEARCH network from 2009–2016 were used in the present study. The sampling sites included urban Birmingham (BHM) and rural Centreville (CTR) in Alabama, urban Jefferson Street, Atlanta (JST), rural Yorkville (YRK) in Georgia, and a rural outlying landing field (OLF) near Pensacola in Florida (Edgerton et al., 2005). Samples from colocated samplers at the JST site (cJST) were used to calculate the sampling uncertainty of the functional group measurements (Sect. 2.6). Three additional SEARCH network sites were closed before 2016 and were therefore not included in the current study; sampling in the SEARCH network ended in 2016, on different dates for each site.

Samples analyzed in this work were collected using the Federal Reference Method (U.S. Environmental Protection Agency, 2011). Briefly, Partisol Plus 2025 samplers (Rupprecht & Patashnick, Fisher Scientific, http://www.thermofisher.com/, last access: 9 December 2019) were used to collect ambient particulate matter smaller than 2.5 µm aerodynamic diameter (PM2.5) at 16.7 L min-1 onto MTL 47 mm PTFE filters with 2 µm pore size (Measurement Technology Laboratories, https://mtlcorp.com/filters, last access: 9 December 2019). Gravimetric analysis of PM2.5 mass and X-ray fluorescence of trace metals concentrations were performed using these filters. Additional filter samples were collected and analyzed by the SEARCH network (Edgerton et al., 2005). Quartz filters (37 mm) were used for TOR analysis of OC and elemental carbon concentrations. PTFE filters (47 mm) were used for SO42-, NO3-, and NH4+ analyses. Nylon and cellulose filters (47 mm) were used for negative artifact NO3- and NH4+ analyses, respectively. SEARCH TOR OC measurements are blank-corrected using annual network-wide mean field blank OC concentrations.

One-in-three-days, seasonally representative (January, April, July, and October) samples from 2009 to 2015, as well as daily samples from 2016, were analyzed using FT-IR spectrometry. The one-in-three-days sampling schedule matched the sampling for TOR OC measurements. At each site, ∼30–45 samples were analyzed by FT-IR spectrometry per year from 2009 to 2015; 1474 ambient sample filters were included altogether in this study. A total of 359 field blank filters were used (approximately two field blank filters per month, per site).

In contrast to other networks, there were some advantages and challenges of SEARCH sampling for FT-IR analyses. Unlike IMPROVE samples, filters were shipped and stored at < 4 ∘C (from Aerosol Research and Analysis, Inc., ARA, in Morrisville, NC) to minimize loss of volatile species. Gravimetric filter measurements were made in an environmentally controlled weigh space to minimize uncertainty in water content (Edgerton et al., 2005), a control technique the IMPROVE network has only recently implemented. However, the mass loading of SEARCH network filter samples was generally lower than that of the IMPROVE network. While the IMPROVE network uses 25 mm diameter filters and a flow rate of 22.8 L min-1, the SEARCH network used relatively large filters (47 mm diameter) and a lower flow rate (16.7 L min-1), following the Federal Reference Method (FRM) sampling procedures (Mikhailov et al., 2009). The Chemical Speciation Network (CSN) also uses 47 mm diameter filters for collection, and, similarly to SEARCH, filters are shipped and stored cold; however, the SEARCH aerosol loading was higher than that in the CSN, which uses a flow rate of 6.7 L min-1 and 47 mm diameter filters. In addition, the SEARCH filters were constructed of thicker PTFE material, overlapping some aerosol sample peaks in transmission spectrometry and producing strong, variable FT-IR spectral features related to scattering by PTFE.

Laboratory standards used to measure functional group concentrations were produced by collecting particles of pure chemicals onto 47 mm MTL PTFE filters to mimic ambient SEARCH network samples. The aerosol generation system consisted of an atomizer (model 3076 Constant Output Atomizer, TSI Inc.), a custom-built diffusion dryer, and a Partisol (FRM) aerosol sampler operated at 16.7 L min-1. The atomizer was supplied with pure chemical solutions and filtered house air (Model 3074B Filtered Air Supply, TSI Inc., http://www.TSI.com/, last access: 9 December 2019).

Two types of laboratory blanks were collected. “Chamber blanks” were collected using deionized (DI) water (≥18.2 MΩ purity) for 10–180 min or isopropanol (IPA; Spectrum Spectrasolv grade) for 5–35 min. “Method blanks” were placed in the aerosol generation system and handled identically to laboratory standards, but the pump was not turned on. One method blank was collected while each pure chemical was being collected. Multiple pure chemicals (Table 1) were chosen to represent each of the organic functional groups calibrated (see Sect. 2.5).

For each pure chemical, 10–20 filters of varying masses were collected (for 1–35 min); 315 chemical standards were produced. The mass of functional group deposited onto each laboratory standard filter was calculated as the difference in filter mass (in µg) before and after collection. Each filter was pre- and post-weighed at least three times using a high-precision balance (±2 µg; model XP2U, Mettler–Toledo, https://www.mt.com, last access: 9 December 2019). The total quantity of functional group anticipated in ambient samples, based on literature values, was used to determine the range collected for each chemical. For example, suberic acid standards were generated in the range of 0.04–4 µmol C=O per filter, which is higher than expected for suberic acid itself (Gao et al., 2006) but within the range anticipated for total C=O (Polidori et al., 2008). The range of measured functional group concentrations in ambient samples was also compared to the dynamic range included in the models (Sect. 3.3.2).

Most of the pure chemical solutions were prepared in IPA and/or DI water; a small number were prepared in ethanol (Koptec Pure Grade). Impurities in the solvents were identified by looking at FT-IR spectra of chamber blanks. However, weights of the impurities in the IPA and ethanol were within the uncertainty of the high-precision balance when collected for up to 35 min, and were not predictive in the functional group models. No impurities were discovered in the DI water. Sonication for up to 2 h was used for some solutions. Concentrations and other details of the pure chemical solutions are listed in Sects. S1–S3.

Molecular environments of the laboratory standards were influential on the infrared spectra and were explored qualitatively (observations summarized in Sect. 3.2, and more detail compiled in Supplement). Hydrogen and ionic bonding patterns were interpreted within spectra of collected standards containing single chemicals. In some cases, a chemical was not included in the model due to a variable hydrogen bonding pattern. The influence of humidity on the laboratory standards was assessed by exposing a selection of laboratory standards to a dry and a wet environment (a desiccator with silica beads and a desiccator with water, respectively). Blank filters, as well as laboratory standard filters containing a hydrophobic chemical (squalene), were analyzed as controls. Each filter was exposed to each environment for 1 week.

Analyses of the sample and laboratory standard filters were carried out in transmission mode on a Bruker Tensor II FT-IR spectrometer (Bruker Optics, Inc.; http://www.bruker.com/, last access: 9 December 2019) equipped with a mid-infrared light source and liquid nitrogen cooled mercury cadmium telluride detector. Each filter was placed into a custom-built (see Debus et al., 2019) chamber within the FT-IR spectrometer that was continuously flushed with air scrubbed of H2O and CO2 (model VCDA air purge system, Puregas, LLC, http://www.puregas.com/, last access: 9 December 2019; < 10 % humidity). Additional information about the FT-IR spectrometry analyses can be found elsewhere (Debus et al., 2018; Ruthenburg et al., 2014). Spectra were collected between 4000 and 420 cm-1, but 1500 to 400 cm-1 was excluded due to strong PTFE filter absorption (Weakley et al., 2016) and highly variable absorption between chemicals.

Subsets of ambient SEARCH samples were reanalyzed after differing storage periods to determine whether FT-IR handling and analysis, short-term storage and transport, or long-term storage had substantially affected the spectra. Changes in predicted functional group and OM concentrations over each period were compared to the sampling uncertainty to assess whether a measurable bias could be observed. The results of this reanalysis demonstrated that (1) duplicate analyses via FT-IR spectrometry were reproducible (-3 % median bias in OM concentrations) and FT-IR analysis did not impact filter sample composition, but (2) decreases in some functional group concentrations for some samples were measurable within the first year or two after sampling (e.g., approx. -10 % yr-1 and -5 % yr-1 median bias in aCOH and OM concentrations, respectively); however, (3) samples stabilize in storage and no longer had measurable concentration changes after several years (approx. 5 % median bias measured between 7 years and 5 years after collection). Additional information about the reanalyses is summarized in Sect. S16.

Outlier laboratory standards and blanks were identified, and data were removed or set aside during the calibration process so that models were constructed and evaluated based on data with minimal errors. Laboratory standards and blanks with the following characteristics were explored as potential outliers: (1) unusually strong water vapor absorption bands in the spectra, (2) uncharacteristic and atypical chemical absorption bands in the spectra, (3) atypical molar absorptivities compared to other laboratory standards, or (4) collected material weights that were too high or essentially zero (except for blanks). Spectra with anomalously high leverage values (those which disproportionately impacted the model result; Hoaglin and Welsch, 1978) were also examined.

Ambient samples and field blanks are expected to be occasionally anomalous: for example, filters can be ripped, and field blanks can be swapped with ambient samples. Potential outlier ambient samples and field blanks were identified using a variety of methods. We treated the confirmed sample outliers in two ways. If no explanation for poor data quality could be determined, the spectrum was set aside into the validation set (see Sect. 2.5) and not used in the model construction process. Functional group concentrations of these spectra were measured and reported after model construction. If an explanation for poor data quality was determined, the spectrum was excluded from the analyses entirely.

We identified and further explored ambient samples with the following characteristics as potential outliers: (1) a spectrum that was visibly anomalous (e.g., swapped with a blank, having a hole, or having strong water vapor absorption bands), (2) a spectrum corresponding to a high TOR OC concentration but low infrared absorption, or (3) a high error in prediction after calibration. Principal component analysis (PCA), a technique used to find the patterns describing maximum variance in a dataset (Naes et al., 2002), was additionally used to identify potential outliers. Overall, approximately 8 % (128 of 1656) of the ambient samples were removed from the dataset, and 31 were set aside for later prediction (in the validation set). Samples missing a TOR OC concentration were still included in the results.

Six functional group calibration models were initially constructed: saturated and aliphatic C-H (aCH), unsaturated C-H (unsCH), carboxylic acids (COOH), oxalate C=O (oxOCO), non-oxalate C=O (noxCO), and alcohol C-OH (aCOH). We used a linear regression between COOH and noxCO to differentiate between carboxylic C=O and “naCO” (nonacid, non-oxalate, or other C=O; see Sect. S11 and Takahama et al., 2013). This was necessary because, although the C=O stretching bands of carboxylic acids are theoretically shifted to lower wavenumbers (∼1700–1710 cm-1) than an unperturbed C=O stretching band (∼1725–1740 cm-1; Mayo et al., 2003), there is not a clear separation between these two types of C=O in spectra of particles and this spectral range is not unique to carboxylic acids. A calibration model for unsCH was developed, but we did not include the values in our results because a substantial fraction of the samples was below the detection limit (see Sect. 2.5.3). The five functional groups reported are therefore aCH, COOH, oxOCO, naCO, and aCOH.

Although we used literature values as an initial estimate for the range of functional groups in the ambient samples, we further determined the maximum number of moles of each functional group to include in the models using a randomized energy minimization algorithm called simulating annealing (Ledesma et al., 2012; see Sect. S8–S9 for discussion on this method). The final values determined were 30 µmol aCH and unsCH, 5 µmol COOH, 4 µmol oxOCO, 4 µmol noxCO, and 10 µmol aCOH.

Partial least-squares (PLS) regression was used for calibration and performed in Matlab using the nonlinear iterative partial least-squares (NIPALS) algorithm (Wold and Sjostrom, 2001). A mathematical description of PLS regression for functional group measurement is given in Reggente et al. (2019) and Ruthenburg et al. (2014). Briefly, PLS identifies a set of factors describing the variations in the laboratory standard spectra and known functional group moles, based on the maximal covariance between them. The spectral patterns of these factors (loadings) and the respective contributions of the factors to each standard spectrum (scores) are derived. The spectra and moles of functional groups in the calibration set of laboratory standards are mean-centered prior to use in the PLS model. A set of regression coefficients, similar in concept to the slope of a univariate calibration curve, is calculated from the scores and loadings.

Laboratory and field data were partitioned into subsets for model development and application: (1) a calibration set of standards for training the calibration models, (2) a test set of standards used for testing the model parameters with respect to the response of laboratory standards, (3) a test set of ambient SEARCH samples for testing the model parameters with respect to bulk metrics such as residual OM and TOR OC, and (4) a validation set for evaluating model performance using the final model parameters. The calibration set of standards contained seven laboratory standards of each chemical, two chamber blanks per chemical, one method blank per chemical (56 total laboratory blanks), and 20 % of the available SEARCH network field blanks (52). The test set of standards contained 1 to 14 standards per chemical (depending on the number of available standards) and the rest of the laboratory blanks (20) and field blanks (307). The test of samples set contained 1125 ambient samples and the same 307 test set field blanks. The validation set of samples contained 318 ambient samples, as well as extreme samples that were identified as possible outliers, but no explanation for their removal from the dataset was found (31; Sect. 2.4). The test and validation sets of ambient samples were combined for all figures and metrics.

The calibration set for each functional group model contained chemicals as organic “interferents” if the particular molecule did not contain that functional group, with quantities of functional group set to zero. This accounted for spectral overlap between functional groups. For example, carboxylic acids and alcohols were quantified separately, but both functional groups contain an O-H bond absorbing in a similar mid-infrared range. Changing the number of such organic interferent standards in each model had a negligible impact on prediction.

Each functional group model was tested by applying it to the test set of laboratory standards using Eq. (1). The moles (n) of each functional group (g) in a laboratory standard (j) with spectrum xj are measured as the sum of inner products with regression coefficients b as follows: 1nig=Σijbgjxij. The modeled moles of functional groups in the test set of laboratory standards (Eq. 1) were plotted against the known moles from filter weights. An orthogonal least-squares regression of the moles from the model and filter weights was fitted, and the median error, correlation coefficient, and slope were examined. Model inputs (such as the subset of laboratory standards included in the calibration versus test sets of standards, and the maximum quantity of each chemical in the calibration set laboratory standards) were altered to optimize the modeled test set of standards.

Multiple methods were tested to find the optimal number of factors for each SEARCH functional group model (see Sect. S8). The minimum root-mean-squared error of cross-validation (RMSECV) with a k-fold of 3 was selected because of its speed and simplicity. Overfitting of the COOH functional group was observed (resulting in overestimation of naCO concentrations). To minimize this effect, the maximum number of factors was constrained to 15 for this model. All other functional groups were constrained to 25 factors. The resulting numbers of factors for each functional group calibration model selected by the automated minimum RMSECV method were 21, 25, 15, 24, 20, and 25 for aCH, unsCH, COOH, oxOCO, noxCO, and aCOH, respectively.

The precision of the functional group measurement method was evaluated using two approaches, which attempted to evaluate some of the most substantial potential sources of uncertainty in the method. The first approach was the comparison of functional group concentrations measured from two colocated sampling sites within the SEARCH network (“sampling uncertainty”). The second approach was the calculation of confidence intervals (bootstrapped) around the functional group concentrations measured using a set of 18 model predictions, each of which had one organic chemical standard removed from the models (“chemical selection uncertainty”).

The sampling uncertainty accounted for the sensitivity of the FT-IR spectrometry analysis procedure to differences in filter substrates, FT-IR analysis handling, and SEARCH network sampling and handling procedures. Sampling uncertainty was calculated (Hyslop and White, 2008, 2009) using measured functional group concentrations from the JST site and its colocated site, cJST. The colocated sampler was used to collect PM2.5 for only a subset of dates (2009–2011, October 2015, and 2016). This uncertainty was used throughout the study as the most complete estimate of method uncertainty, since it included most possible sources of uncertainty, aside from those arising from selection of model inputs and parameters.

The chemical selection uncertainty accounted for the possible impact of excluding a particular atmospherically important chemical from our models, within the bounds of our chemical list. We performed this “leave one out” analysis with the expectation that the sensitivity of the models would be similar between chemicals in the current models as well as some hypothetical, atmospherically important chemicals not included in the models. The chemical selection uncertainty was calculated as follows. A total of 18 sets of models were constructed, each excluding one organic chemical. Ambient functional group concentrations were measured using all models. For each functional group, the concentrations measured by all models were aggregated into one vector. The uncertainty over all samples and models was then determined using the sampling uncertainty equations between the “base case” concentrations (calculated with all chemicals included) and the “leave one out” concentrations.

Known atmospheric OM molecules are comprised mainly of a small number of functional groups, which include C-H, alcohol O-H, and various forms of C=O groups. Relevant C=O groups include carboxylic acids and carboxylates, as well as esters, ketones, and lactones. Multiple molecules that contain each of five important functional groups (aCH, COOH, oxOCO, naCO, and aCOH) were included in the calibration models in this work. Selections were made based on the known presence of a molecule in atmospheric OM or because the molecule exemplified the spectra of a functional group (Fig. 1; Table 1). Mass contributions from organic S and N comprise a smaller portion of ambient OM (Liu et al., 2009; Stone et al., 2012) and were not included in this work. Substantial contributions of organosulfates to southeastern aerosol composition are possible (Hettiyadura et al., 2015), and the OM/OC ratios of small organosulfate molecules are high; therefore, future models may consider such chemicals. The following paragraphs outline the atmospheric relevance and spectral features of each functional group reported in the current models.

The C-H bond is ubiquitous in atmospheric organic molecules and is present in nearly all chemicals in the models (Table 1; Fig. 1). Fresh atmospheric emissions often contain abundant C-H bonds (e.g., alkanes from industrial and biogenic sources; Rogge et al., 1993), though C-H as a functional group should not be attributed only to fresh emissions since it is also plentiful in oxidized material (Schum et al., 2018b). Although minor in comparison to C=O or O-H stretching bands, there are some variations in the C-H stretching bands (e.g., -CH2- at 2926 asymmetric and 2853 symmetric ±10 cm-1 for straight-chain alkanes, or 3085–2927 cm-1 asymmetric and 3028–2854 cm-1 symmetric in cyclic molecules; Mayo et al., 2003). A variety of C-H bonds were therefore selected for the models, including ring structures, short-chain and long-chain molecules (additional insight on the variation in C-H bond absorption will be discussed in forthcoming work, Amir Yazdani, personal communication, 2018).

Saturated and unsaturated C-H bonds were quantified separately to distinguish between any differences in sources (e.g., Moretti et al., 2008). However, the concentrations measured using the unsCH model were not reported because a majority of sample concentrations measured were below the unsCH MDL. These measurements are realistic: low unsCH compared to aCH concentrations have also been observed in work using nuclear magnetic resonance (Moretti et al., 2008) as well as in previous FT-IR functional group calibration work (Guo et al., 2015; Liu et al., 2012; Russell et al., 2009b, 2011). Observed absorption coefficients of unsCH bonds were also low, consistent with theory (Mayo et al., 2003).

Carbonyls are a particularly informative functional group in infrared spectra of ambient OM due to their strong absorption coefficients and high abundance in the atmosphere. A strong, broad C=O stretching band at ∼1700–1800 cm-1 is observed in ambient OM spectra (Takahama et al., 2013). In particular, molecules containing carboxylic acids may contribute the majority of OM mass (Decesari et al., 2007), the most abundant of which are typically the C2–C4 dicarboxylic acids (Kawamura and Bikkina, 2016). Six carboxylic acids were included in the calibration models. As in our previous work (Ruthenburg et al., 2014), malonic (C3 dicarboxylic acid) and suberic acids (C8 dicarboxylic acid) were included. The latter represents longer-chain carboxylic acids because it is spectrally similar to C16 and C18 monocarboxylic acids (National Institute of Advanced Industrial Science and Technology, 2018). Oxalic (C2 dicarboxylic) and succinic (C4 dicarboxylic) acids, which are often the most abundant organic species quantified in OM (Kawamura and Bikkina, 2016), were added to the current models. As a representative aromatic carboxylic acid, terephthalic acid was selected, originating from oxidation of burning plastics or other industrial activities (Wang et al., 2012). D-alanine, an amino acid, was also included.

Amines and amino acids have been studied in functional group calibrations (Kamruzzaman et al., 2018; Liu et al., 2009). Amines and amino acids could contribute ∼5 %–10 % of organic aerosol concentrations and come from a variety of anthropogenic and biogenic sources (Russell et al., 2011). D-Alanine was included in the current models, differing from other carbonyl-containing spectra by its down-shifted carboxylic C=O stretching band (due to the electron donating power of the adjacent N atom) and C-N stretching band in the same spectral region. These amino acid bands overlap with those of carboxylate C=O, but multivariate regression factors can account for other features of these functional groups to distinguish between them.

Although southeastern ambient aerosol particles may be acidic (Guo et al., 2015), concentrations of oxalate exceeding those of oxalic acid have been observed in ambient samples (Yang and Yu, 2008). Ammonium and sodium oxalates were therefore included in the models as example carboxylate salts, calibrated separately from the carboxylic acid functional group as oxalate carbonyl (oxOCO). The FT-IR spectra of ammonium and sodium oxalates were different from the spectra of oxalic and most other carboxylic acids, in that the C=O stretching bands of carboxylate salts are below 1700 cm-1 (Fig. 1). Longer chain carboxylates such as succinates could contribute additional OM. The spectrum of ammonium oxalate also contains two N-H stretching bands overlapping with O-H stretching bands and carboxylic sum tones at 3500–3100 cm-1, allowing the models to account for ammonium carboxylate interferences to measured COOH and aCOH concentrations.

Other, nonacid (and non-oxalate) carbonyls including esters, cyclic esters, and ketones could be abundant in atmospheric aerosol. Cyclic esters (lactones) within large, multifunctional molecules have been observed in ambient aerosol (Kahnt et al., 2018), and oxo-carboxylic acids such as cis-pinonic and pyruvic acids are frequently observed in ambient OM (Kawamura and Bikkina, 2016). These nonacid carbonyls were quantified in the models as “naCO”, separate from carboxylic acids and oxalate, as in the work of Russell and co-workers (Frossard and Russell, 2012). The naCO was expanded in the present models to include not only a long-chain ketone and ester but also a lactone (D-glucono-delta-lactone) and a large, conjugated ketone-containing molecule (tannic acid). An aldehyde-containing molecule was also tested in the models, but the solubility of the particular chemical used (divanillin) limited the maximum mass collected onto filters (see also Sect. S4). The lactone was chosen to represent cyclic carbonyl structures such as carbohydrates and furanones (Hamilton et al., 2004). Tannic acid was included in the naCO functional group to represent larger, humic-like molecules. Its spectrum is characterized by a broad C=O stretching band due to the movement of electrons through its multi-ring, oxygenated aromatic structure (Fig. 1; Table 1), similar to spectra of observed atmospheric humic-like material (Chen et al., 2016). The molecule is large relative to atmospheric components observed using typical ion and gas chromatography methods (Gao et al., 2006) and has a known chemical structure (unlike other humic-like candidate molecules). Note that tannic acid contains no COOH moieties but instead contains ester and ketone naCO, unsCH, aCH, and phenolic aCOH.

Along with nonacid carbonyls, alcohol OH (aCOH) is often recognized as an intermediate within oxidation schemes because the C atom is not maximally oxidized (Heald et al., 2010). A variety of alcohol-containing molecules were included in the models, typified by broad hydrogen bonded O-H stretching bands ∼3500–3100 cm-1 (Fig. 1). meso-Erythritol was included as a representative isoprene oxidation product, which is understood to be important in the southeast (Claeys et al., 2004). Phenols were represented by 4-nitrocatechol, which is most often associated with biomass burning and pesticide emissions (Harrison et al., 2005; tannic acid also contains phenol). Along with 4-nitrophenol, levoglucosan is an abundant tracer for biomass burning emissions (Mayol-bracero et al., 2002); it was also included in our previous work (Ruthenburg et al., 2014). Glucose was spectrally similar to levoglucosan but was included to represent carbohydrates from other sources such as fungal spores (Caseiro et al., 2007). Although there is little literature discussing long-chain alcohols in atmospheric aerosol, they are indeed present at low quantities (Rogge and Hildemann, 1994). 1-Docosanol was therefore included, as in the work of Ruthenburg et al. (2014).

Three types of interferent molecules were included in each of the functional group models: inorganic salts, particle water, and interfering organic species. Ammonium nitrate and ammonium sulfate are abundant in atmospheric aerosol, and overlap spectrally (N-H stretching) with strongly absorbing organic molecule features, such as O-H and C-H stretching bands. Therefore, these inorganic salts were included as interferents in the models (ammonium nitrate was not included in the Ruthenburg et al., 2014 models). Water also contributes some O-H stretching to aerosol spectra (Frossard and Russell, 2012), so a hygroscopic inorganic salt with negligible inorganic absorption stretches, magnesium chloride (MgCl2), was also included in the models. To our knowledge, particle water has not been previously accounted for as an interferent in functional group measurements by PLS calibration of FT-IR spectra, although water interference has been discussed and explored in peak fitting calibrations (Faber et al., 2017; Frossard and Russell, 2012). The result of including particle water as an interferent in the calibration models (collected as MgCl2) was the contribution of spectral features to the models associated with particle water (demonstrated in the VIP scores; see Sect. S12). No substantial changes in the measured functional group concentrations (including that of aCOH) or the predicted OM concentrations were observed due to the inclusion of particle water standards (Sect. S6). This is probably because the humidity in the FT-IR spectrometer sample chamber is low (0 %–10 %). Particle water was therefore limited to liquid water in un-effloresced highly hygroscopic particles, hydrate water, or as embedded water under aerosol material layers (Frossard and Russell, 2012).

Aspects of the environment within and around collected standard particles were examined to discern whether the conditions were relevant to simulated ambient aerosol samples. In particular, three types of molecular-level interactions with the particles of the collected laboratory standards were considered: (1) hydrogen bonding patterns within pure chemicals, (2) hydrogen and ionic bonding within mixtures of two different chemicals, and (3) changes of pure chemicals due to exposure to water.

The organization and orientation of polar organic molecules within solid particles is dictated in part by the intermolecular or intramolecular hydrogen bonding interactions between H and O atoms (and possibly other electronegative atoms). These hydrogen bonding patterns can strongly influence infrared spectra, causing splitting, broadening, or frequency shifts in absorption bands (Davey et al., 2006). Dimeric or polymeric hydrogen bonding structures of carboxylic acid standards in the present work were confirmed by the broad O-H stretching band between approximately 3200 and 2600 cm-1 (with overlaid sum tone absorption bands) and the presence of out-of-plane O-H wagging bands between 950 and 850 cm-1 (Mayo et al., 2003). Similar hydrogen bonding O-H stretching bands were observed for most alcohols, at higher frequencies due to their weaker hydrogen bonding than carboxylic acids (Mayo et al., 2003). If O-H bonds are unassociated with other polar groups, free O-H stretching peaks are present in an FT-IR spectrum (Davey et al., 2006; Mikhailov et al., 2009). This was observed in the standards of single, pure chemicals containing multiple polar, oxygenated functional groups, including tartaric acid (not included in models; see discussion and spectra in Sect. S4) and 4-nitrocatechol spectra. Free O-H stretching bands were not clearly observed in the SEARCH ambient sample spectra but could have contributed low absorbance within the sample mixture. Hydrogen bonding within the likely amorphous solid structures of ambient particles (Mikhailov et al., 2009) and the dimeric or polymeric polar protic chemical used in the calibration were generally consistent.

Laboratory standard filters used for (quantitative) calibration included one chemical on each filter, but hydrogen or ionic bonding interactions between the many chemicals in ambient aerosol samples were expected. We therefore generated laboratory standards with mixtures of pure chemicals, including combinations of two carboxylic acids (malonic with terephthalic acid and malonic acid with succinic acid), carboxylic acids with alcohols (succinic or malonic acids with meso-erythritol and malonic acid with levoglucosan), and an inorganic salt with carboxylic acids (ammonium nitrate with terephthalic acid, succinic acid, or malonic acid). Hydrogen bonding interactions were observed (see Sect. S7, Fig. S8) in some mixtures, such as those of meso-erythritol with malonic and succinic acids, which resulted in the splitting or broadening of the O-H stretching band of meso-erythritol (likely due to the formation of additional hydrogen bonding environments). No substantial changes to the C=O stretching bands were observed. No interactions were visible in the FT-IR spectra between inorganic salts and carboxylic acids or between some of the mixed polar protic species, such as malonic acid with terephthalic acid. Oxalate standards, as discussed earlier in Sect. 3.1, accounted for carboxylate salt (ionic bonded OM) contributions to OM concentrations. Based on these observations, models constructed with pure chemical standards could be misattributing some spectral features (adding some error and scatter or bias via overprediction or underprediction) but, seemingly, only for some functional groups and some molecular interactions.

The influence of water exposure on laboratory standards was examined to demonstrate possible differences between ambient and laboratory-generated particles. Although chemical effects were anticipated, including addition of water to nonacid carbonyl groups to form gem-diols or changes in hydrogen bonding structure after deliquescence, there was no spectral evidence of either. Instead, an irreversible decrease in laboratory standard infrared absorption occurred when hygroscopic species were exposed to humid conditions (glucose, ammonium sulfate, and pyruvic acid; see Sect. S6 and Fig. S5). This was likely the result of a redistribution of collected material away from the infrared beam: there was no consistent and significant change in the weight of standard filters, and a similar decrease in infrared absorption was not observed for the hydrophobic species squalene. Some additional water vapor absorption was also observed. The dry (∼0 %–10 % relative humidity) environment of the FT-IR spectrometer sample chamber was also examined by exposing laboratory standards to a dry environment; no effect on the spectra was observed. Particle water laboratory standards (MgCl2) were included in the calibration models, as described earlier in Sect. 3.1, and effectively accounted for the known portion of particle water (Dabek-Zlotorzynska et al., 2011; Faber et al., 2017).

There are scarce measurements of functional groups to validate the FT-IR–PLS method developed here. We address this challenge by instead corroborating our measurements with multiple qualitative and quantitative metrics from separate methods. We evaluate the model results by comparing to bulk measurements including residual OM concentrations; TOR OC concentrations; and ratios of OM/OC, O/C, and H/C from other techniques. Expected trends between urban and rural pairs, seasons, and functional groups, based on previous research, were also used.

The expansion of the list of chemicals included in the current calibration models from previous work was overall successful relative to the techniques and other study results discussed in the previous sections. These improvements suggest that further expanding and refining the calibration standards may make functional group measurements more accurate, increase the number of functional groups that can be measured, and improve OM recovery. Other chemicals suggested for addition to the models include those used for aerosol mass spectrometry calibration (Aiken et al., 2008; Canagaratna et al., 2015). Additionally, several oxygenated chemicals with multiple functional groups proved difficult to collect in relevant chemical form and quantity for atmospheric aerosol (e.g., tartaric acid; see Sect. S4 and Fig. S4) but should be revisited as atmospherically important species and groups. Other potentially important groups to consider include aldehydes and anhydrides (see Sect. S4). Since it was discovered herein that high silicate (dust) concentrations might degrade the quality of functional group predictions, building calibrations of suspended dust particles could be considered in the future.

Although the extended calibration designed in this work captures variation in the OM speciation beyond that of previous work, there are additional functional groups that should be considered in further work. Kamruzzaman et al. (2018) demonstrated the importance of amine N-H and C-N bonds in OM calculations, and organosulfate O-S and O-C bonds are additionally likely to be influential (Stone et al., 2012).

The observed interactions between some polar protic species are acknowledged and should be considered in future work. However, the uncertainties in quantitative multi-chemical laboratory standards prevented us from including them in the current models. The challenges observed in our explorations have included (1) an inability to measure the weight of each chemical collected from particles generated from a solution with both chemicals and (2) volatilization during sequential collection of chemicals. Multicomponent laboratory standards could be a way to include atmospheric chemical interactions in FT-IR spectrometry models if the above challenges can be overcome or sufficiently minimized.

There are additional sources of uncertainty within the model parameters that should be further addressed. Takahama and Ruggeri (2017) demonstrated that the C/functional group ratio (λ) values applied to calculate OM and OC concentrations herein are likely realistic but have some uncertainty and are known to vary for different chemicals. Although the number of standards per chemical, the number of factors in each PLS model, the dynamic range of standards included in each model, and other inputs have been selected carefully, the correct values of these inputs cannot be exactly known. The chemical selection uncertainty addressed in Sect. 3.3.2 cannot entirely capture the variability in model results due to the possible mis-specification of chemicals used in the models and could be further discussed. Despite these challenges, the agreement between our results and many available expected or reference values demonstrates that the results are reasonable (e.g., OM and OC concentrations with previous work, given mass accuracy expectations, realistic trends in urban versus rural concentrations, and the atomic ratios O/C and H/C).