For this work, we use 794 pairs of ambient PM2.5 samples collected in the IMPROVE monitoring network, 250 laboratory standards, and 54 blank samples used previously by , , and for building FG and TOR OC and EC calibration models with canonical PLS regression. A pair of ambient samples consists of particles collected on 25 mm quartz fiber filters and 25 mm PTFE filters. The quartz filters are analyzed by TOR IMROVE_A protocol for OC and EC mass , and the PTFE filters are used for acquisition of infrared spectra, among other properties. Monthly median values of OC loadings in blank samples are subtracted from ambient TOR OC loadings to account for the gas phase adsorption artifact by quartz fiber filters . The ratio of organic mass (OM) to organic carbon estimated in ambient samples span a range of 1.46 and 2.01 between the 10th and 90th percentiles, with a median ratio of 1.69 . The 250 laboratory standards consist of 9 compound types in single, binary, and ternary mixtures, and reference concentrations are obtained by gravimetric analysis of the filters . Four FG calibration models are built for alcohol hydroxyl (aCOH), carboxylic hydroxyl (cCOH), alkane hydrocarbon (aCH), and carbonyl (CO), which comprise these compounds. The blank samples are analytical blanks of PTFE filters analyzed in the laboratory.

The PTFE filters are scanned (without pretreatment) using a Tensor 27 FT-IR spectrometer (Bruker Optics) with liquid-nitrogen-cooled mercury cadmium telluride detector in transmission mode. Each spectrum is acquired over mid-infrared wavenumbers of 4000 to 420 cm-1, and absorbance spectra are calculated with respect to an empty sample chamber as reference. The chamber is purged with air free of water vapor and carbon dioxide using a purge-gas generator (Puregas) for all scans.

Two different versions of the spectra described above are used in building calibration models with each described in Sect. . Unprocessed (“raw”) spectra are unmodified except zero-filled (interpolated) points introduced by the acquisition software are removed such that absorbance values at 2784 wavenumbers at a resolution of 1.3 cm-1 remain. Baseline corrected spectra are modified according to the procedure described by . Absorbances below 1500 cm-1 are removed, and the interferences from PTFE are removed by polynomial and linear interpolation between background regions such that the analyte absorption is isolated for analysis. In this process, spectra are interpolated along a wavenumber grid, which is also spaced at a resolution of 1.3 cm-1, such that this spectra type contains 1563 wavenumbers. Both types of spectra have previously shown comparable results for TOR OC and EC prediction with PLS calibration . Example spectra are shown in Supplement Sect. S1.

Notation for matrices and vectors is provided in Appendix . PLS performs a bilinear decomposition and projection of both X and y onto orthogonal bases P and q, respectively : X=TPT+EX,y=TqT+ey. The score matrix T relates the two sets of variables and is defined by column matrices of loading weight vectors, W=[w1,w2,…,wK], factor loadings P=[p1,p2,…,pK], and direction vectors R=[r1,r2,…,rK] . The direction vectors can be defined by loading weights and factor loadings: R^=W^P^TW^-1. A hat above a symbol denotes the estimator of a variable. From the matrix of direction vectors, we can construct scores and regression coefficients: T^=XR^,b^=R^q^T. y is therefore estimated as y^=XR^q^T. The objective function that is satisfied by solutions for W and R are described in Appendix .

There are two types of variables in our application of PLS regression: the physical variables, or spectral features, corresponding to wavenumbers at which absorbances are measured (columns of X), and LVs which represent the underlying components of the model (columns of T). To avoid ambiguity, we will always refer to the latter as LVs. Solutions obtained using PLS with full wavenumber resolution will be referred to as the “full” (wavenumber) solutions.

We consider four methods for obtaining models that require fewer wavenumbers, which are summarized below and described in more detail in Appendix , and by their respective authors in the cited literature. The underlying principle for wavenumber selection used in this paper is covariance maximization (for PLS regression) or residual minimization (for OLS regression) scaled by a 1-norm penalty (‖⋅‖1) placed on the regression vector (b), weight, or direction vector (w and r, respectively). These penalties lead to (1) shrinkage (vector elements tend toward 0) and (2) selection (some elements become exactly 0). One sparse PLS formulation, which we refer to as SPLSa, effectively imposes the 1-norm penalty on the weight vectors wks of PLS . The second sparse PLS formulation, which we refer to as SPLSb, imposes the penalty on surrogate vectors kept in close alignment with the direction vectors rks (which are closely related to the weight vectors) to target a higher degree of sparsity . Elastic net (EN) regularization is not a variant of PLS but belongs to a separate class of regression algorithms that solve Eq. (). EN generalizes the least absolute shrinkage and selection operator (LASSO; ); the model infidelity with respect to the response variable is penalized not only by the 1-norm but also by the 2-norm applied directly to the regression vector b. The primary advantage for including the 2-norm penalty is that this addition imparts a grouping effect, in that variables which co-vary are often selected together rather than one of its members at random. For spectroscopic applications where absorption bands span over several wavenumbers, selection by groups associated with the same absorption band rather than single wavenumbers from each band is desirable for interpretation. The last method of estimation, EN–PLS, is a hyphenated method that combines EN for variable selection and PLS for finding an alternate solution to Eq. () using the same subset of wavenumbers as selected by EN. In addition to the number of LVs described above, the sparse methods described above introduce an additional free parameter that controls the magnitude of penalty against lack of sparseness, and different models with varying degrees of sparsity are defined by changing this parameter (Table ).

We distinguish between samples used for training and validation of calibration models (the “calibration set”) and the test set used for evaluation (the “test set”, which has no influence on model development or validation). The calibration and test sets are constructed identically to the most accurate class of full wavenumber models described previously . For FG calibration, 158 laboratory standards are used for the calibration set while 80 similar laboratory samples and all 794 ambient samples are reserved for the test set . No blank samples are included in the FG calibration, though samples with particular FG concentrations of 0 (e.g., compounds that only contain other FGs than those for which the calibration model is being built) are included . For TOR OC and EC calibration, the 794 ambient samples are arranged in order of TOR reference concentration and every third sample is selected for the test set and the remaining two-thirds of samples used for the calibration set . Similarly, one-third of blank samples are reserved for the test set while the remaining two-thirds are included in the calibration set. While the division between sets is arbitrary in the TOR OC case, for TOR EC the blanks are first arranged according to their predicted concentrations using a calibration model developed without blank samples and every third selected for the test set as for ambient samples. additionally divided the EC samples into high and low concentration samples to build a hybrid (piecewise) calibration model for improving predictions for the latter group of samples. For the purpose of this work, we only consider a single calibration model that spans the entire range of concentrations for each algorithm and spectra preparation. Full wavenumber calibration models for TOR OC and EC developed using this protocol have demonstrated ability to capture overall variations in concentrations which span a wide range of PM composition and environmental conditions .

The root mean squared error (RMSE) between the observed (y) and estimated values (y^) determined by cross validation (CV) is conventionally used for model selection . The RMSE given θ (a model parameter or a set of parameters) is defined as RMSEθ=1N‖y-yθ^‖22. This estimate is calculated for V model predictions evaluated against V validation sets to arrive at the RMSE of V-fold CV, or RMSECV. To obtain this estimate, the calibration set is divided into V “folds” or subsets; model parameters are trained on V-1 subsets combined together and validated on the remaining subset, with the training and validation sets determined by successive permutation over V repetitions. For this work, samples in the calibration set are arranged in order of increasing concentration for 10-fold venetian blind CV in all methods such that the results are deterministic, and the validation sets are likely to be representative of the training sets for each permutation . However, as RMSECV generally captures the decreasing model bias and underestimates the growing variance, various strategies for avoiding overfitting risk has been proposed. One convention is to select a solution within a specified tolerance of the minimum RMSECV – e.g., a fixed value of 10 % , or within 1 standard deviation of the mean as estimated from the CV folds . For PLS, and present new metrics which weigh decreasing RMSECV against increasing 2-norm magnitude ‖b‖ of the regression vector, which is directly correlated with calibration model variance . We consider an additional solution defined by the minimum of a penalized form of the RMSECV : pRMSECVθ=RMSECVθ-min⁡θ{RMSECVθ}max⁡θ{RMSECVθ}-min⁡θ{RMSECVθ}+‖b^θ‖-min⁡θ{‖b^θ‖}max⁡θ{‖b^θ‖}-min⁡θ{‖b^θ‖}. As ‖b‖ generally increases with the number of LVs, the model selected with this metric is sensitive to the maximum number of LVs over which the metric is evaluated . We evaluate pRMSECVs over the interval of LVs between one and the minimum RMSECV solution in increments of one, leading to selected models generally exceeding 10 % of the minimum RMSECV value and providing a higher degree of parsimony with respect to the number of LVs. Limited justification for this work is provided in Appendix , and a more dedicated discussion on these metrics is provided by .

Selection of the full wavenumber model is described according to the procedure by , whereby an alternate formulation of the pRMSECV metric is evaluated with an ensemble of penalties and selected by consensus scoring . For EN, in addition to the minimum RMSECV solution, we consider a more parsimonious solution within 1 standard error of the minimum RMSECV. For evaluation and selection of sparse PLS methods, we reduce the complete set of models generated by varying the sparsity parameter (except for EN–PLS, which is fixed by the EN solution) and LVs by considering (1) global minimum RMSECV solutions, (2) solutions within 10 % tolerance of the minimum RMSECV model (standard errors of RMSECVs were not readily obtainable), and (3) solutions meeting the minimum pRMSECV criterion. These solutions are described further in Sect. S2. The final solution for each algorithm and spectra type is selected from among candidate models according to the extent of wavenumber reduction and capability to produce estimates which are evaluated favorably against external reference measurements of TOR OC and EC in the test set (when significant differences in predictions exist). We consider our approach sufficient for this exploratory work, but model selection weighing a metric of fidelity (e.g., RMSE) against two dimensions of parsimony (number of wavenumbers and LVs) is a potential area of further research.

Models are evaluated on sparseness and comparison to reference measurements. Reference measurements include FG abundances in laboratory standards and TOR OC and EC concentrations in ambient samples in the test set. For evaluation of FGs in ambient samples, we sum the carbon mass estimated from FG abundances (which we designate as “FG-OC”) and compare against TOR OC. FG-OC is estimated from moles n of FGs as 12.01 µg mole ×(0.5naCH+ncCOH) . We characterize sparseness by the number of selected wavenumbers, or non-zero variables (NZVs). We use the Pearson's correlation coefficient (r) to determine how closely related the predictions are (as characterized by linearity) and the regression slope determined by orthogonal regression (also referred to as major axis regression) to characterize overall bias between two sets of values . The intercept from the regression is not reported to simplify the discussion (it is generally near 0); for detailed evaluation that also considers detection limits and values close to 0, a further study and exposition is recommended. Orthogonal regression is appropriate for our comparisons as it considers that both concentrations being compared are subject to error. However, we do not weigh each observation by the magnitude of their errors, as measurement errors are currently not well characterized for each sample and erroneous weighting can lead to mischaracterization of bias.

We first describe our interpretation of the most parsimonious EN–PLS solution for each FG and extend our interpretation to the SPLSa, SPLSb, and full spectrum solutions. For aCH, CO, and cCOH FGs, the same vibrational modes are used for both baseline corrected and raw spectrum solutions. In the case of aCH, the C–H stretching mode (near 2900 cm-1) and what appears to be spurious correlation with C=O stretching (near 1700 cm-1) in carbonyl compounds are found. In the calibration experiments, carbonyl compounds were included in the set of compounds used as laboratory standards for the calibration of the aCH FG (i.e., malonic acid, adipic acid, suberic acid, arachidyl dodecanoate, and 12-tricosanone; ). For CO, the C=O stretching is used. The C=O stretching vibration is used also in the cCOH calibration, in both the baseline corrected and raw spectrum solutions. Different sections of the spectra in the region of C=O stretching absorption are used for CO and cCOH solutions, though they do not necessarily coincide with wavenumbers expected for their specific chemical environments. Carbonyl in carboxylic acids are nominally centered around a lower vibrational frequency (∼ 1710 cm-1) than in esters (∼ 1735 cm-1), but in our solution the wavenumbers used by the cCOH model in the carbonyl region is higher than that for the CO model which also included esters in the calibration set. While carbonyls have a relatively narrow absorption band compared to O–H stretching used by alcohol (3500–3200 cm-1) or carboxylic hydroxyl groups (3400–2400 cm-1), it is broad enough such that EN–PLS selects different regions of the band that may not correspond to the location of peak absorbance. The high VIP scores and negative coefficients found for the wavenumbers around 2360 cm-1 in both CO and cCOH raw spectrum solutions can be associated with the background (PTFE) correction which can interfere with carbonyl quantification, which lies at the shoulder of the C–F stretching mode of PTFE. Additional wavenumbers associated with high VIP scores found in the cCOH in the raw solution are also attributed to background correction. In the case of aCOH, different vibration modes are used by the baseline corrected and the raw spectrum solutions. While the baseline corrected solution uses the alcohol O–H stretching mode (near 3300 cm-1), the raw spectrum solution uses C–O–H bending (680–620 cm-1) and C–O stretching vibrational modes (1200–1015 cm-1). In the baseline corrected solution for aCOH, the high VIP score at 1707 cm-1 is interpreted as a spurious correlation with CO, present in compounds in the calibration set. The high VIP scores in the aCOH raw spectrum solution are attributed to background correction.

SPLSa, SPLSb, and full spectrum solutions use the same vibrational modes of the EN–PLS solution for the quantification of cCOH, aCH, and CO. The additional peaks in the raw spectrum solutions are interpreted as being associated with background correction. For aCOH, the less parsimonious methods use the O–H stretching in both the baseline corrected and the raw spectrum solutions in contrast to the EN–PLS solution, which uses two different vibrational modes for different spectra types.

Similarity in predicted abundances is not necessarily anticipated by the number of wavenumbers used. An illustration is provided in Fig. , where a group of similar baseline corrected ambient spectra is overlaid on VIP scores for the full model, SPLSa, and EN–PLS. While the EN–PLS solutions have a higher degree of sparsity than the SPLSa (2–6 % of original wavenumbers EN–PLS compared to 6–93 % for SPLSa) for every FG except baseline corrected CO (Table ), EN–PLS estimates are more closely aligned with the full wavenumber predictions. The aCOH abundance of sparse solutions are an anomaly in that they are correlated with each other and overpredict the full wavenumber estimates by a significant amount (which is true for all sparse solutions; Sect. ). This pattern may be the result of selecting narrow bands of wavenumbers for the estimation of this FG, when O–H stretching from hydroxyl groups in alcohol compounds exhibit a broad absorption band . Even for this similar group of spectra which presumably share similar chemical composition, the varied patterns in predicted concentrations across sparse models indicate that the features selected for quantification by laboratory standard calibrations may not be consistent with additional features present in ambient samples. We anticipate that this analysis of such sensitivity can further guide the selection of laboratory standard mixtures for calibration, in addition to measurement intercomparisons.

For both the prediction of TOR OC and EC, different sets of wavenumbers (i.e., absorption bands) are used between the raw (Fig. ) and baseline corrected (Fig. ) spectrum solutions. In the raw solution for TOR OC and TOR EC prediction, large VIP scores with negative coefficients near 2000 and 1200 cm-1 constitute a means for the correction of the PTFE absorption and scattering. For instance, this correction compensates for the positive artifact near 4000 cm-1, where the PTFE scattering is the only contributor to the infrared signal, but PTFE contributions are also present in regions of analyte absorption. As the largest VIP scores are associated with PTFE correction and smaller VIP scores associated with wavenumbers in absorption bands of target analytes, we primarily consider absorption bands above a low VIP threshold of approximately 0.5 in this work.

Even by excluding wavenumbers with extremely small VIP scores and PTFE contributions, many interpretations for contributing FGs still exist on account of the large number of overlapping absorption bands at each wavenumber used by the two spectra types. In this first analysis of relevant wavenumbers for TOR OC and EC calibration, we present our interpretation through a “common FG hypothesis” in which we assume it most likely that predictions by the raw and baseline corrected spectra models are primarily enabled by a common set of FGs. This framework leads to the possibility that the same FG may be used by the two solutions by means of different vibrational modes (at different wavenumbers), and the inference that these comprise essential FGs necessary for prediction. We cannot exclude the possibility that there exists a suite of FGs with approximately similar capability to provide, in some combination, quantitative prediction of TOR OC and EC, leading to two models that require less than maximal overlap in FGs. If we consider an extreme case, which we denote as the “divergent FG hypothesis,” a pair of models may use a minimally redundant set. This approach to band assignment can lead to an intractable number of possibilities and is also considered less plausible given the similar level of accuracy and robustness attained by the two models. Table  presents our findings of bonds found in each model; additional possibilities for each wavenumber are documented in Sect. S3. We limit our discussion below to main FGs found by both models through the perspective of the common FG hypothesis.

We preface our interpretations by stating that, at this time, we make no claim regarding the relative contributions of each FG to TOR OC or EC mass, as our VIP analysis considers the importance of spectra absorbances (and not FG abundance) to the mass concentrations. Knowledge regarding molar absorption coefficients and the relationship of FG to carbon abundance are additionally necessary to relate absorbance with the mass concentrations to which the models are calibrated; this information is unavailable and not possible to estimate unambiguously from the set of regression coefficients for these complex mixtures.

The wavenumbers used by the TOR OC calibration models correspond to vibrational modes associated with major FGs of organic PM. Carbonyls associated with carboxylic acids, ketones, aldehydes, and esters are used by both models through the C=O stretch (1700–1750 cm-1). Carboxylic acid groups are inferred through O–H and C=O stretch by the baseline corrected model and O–C=O bending in the raw spectra model. The alcohol FG is used by both baseline corrected and raw solutions but by means of different vibrational modes (i.e., O–H stretch in baseline corrected spectrum solution and C–O–H bending in the raw spectrum solution), as in the case of the EN–PLS solution for aCOH FG. N–H bending associated with amide and amines (1640–1550 cm-1) is used by both models, with a strong N–C=O (630–570 cm-1) and C=O out-of-plane bending absorption in amides (615–535 cm-1) additionally used by the raw spectrum solution. Given the additional support for assignment of the N–H bending mode to amide in the raw spectrum solution, our common FG hypothesis favors the interpretation that this mode in the baseline corrected spectra mode may also be more strongly linked with amides. While not currently reported in measurements of organic aerosol by FT-IR e.g.,, amide-containing compounds have been suggested to partition to the aerosol phase as well as formed through condensed phase reactions . Various vibrational modes associated with aromatic and alkene species have medium or weak absorption in regions used by both raw and baseline corrected spectrum solutions. The modes associated with conjugation of C=O with phenyl and alkenes absorb in regions used by both baseline corrected and raw solutions. Alkane chains are used by the baseline corrected solution by means of the C–H stretching mode in the wavenumber range 2913–2921 cm-1. In the raw solution, the assignment is less clear, but the region of 1505–1517 cm-1 used by the model (with high VIP scores and positive coefficients) overlaps with the shoulder of CH2 bending vibrations of alkane chains near 1475 cm-1. Given the large contribution of alkane C–H groups to the overall organic aerosol mass estimated as estimated by FG calibrations (60–70 %; ), the lack of a more obvious correspondence between regression coefficients and vibrational models of saturated CH groups is unexpected.

The baseline corrected TOR EC calibration model appears to rely on similar absorption bands and FGs as TOR OC; this can be partly explained by the restricted range of wavenumbers used. However, as the regression coefficients are different we note that the bands are weighted differently in arriving at their respective predictions, possibly indicating their use for OC artifacts in quantification of TOR EC. Many similarities in the structure of VIP scores with the raw solutions of TOR OC can be accounted to the PTFE corrections previously described, though the main spectral features used by the raw spectra TOR EC model appears to be vibrational modes in the molecular fingerprint region that overlaps with the absorbance from the C–F stretching of PTFE (∼ 1200 cm-1) and the adjacent region between 1497 and 1531 cm-1, which is at the lower boundary of the baseline corrected solution.

Both TOR EC models may use four FGs used by the TOR OC solutions: aromatic and ring structures, amines and amides, and esters. The C–C ring stretch is present in the baseline corrected solution at ∼ 1600 and ∼ 1500 cm-1 for the raw spectrum solution. In the former case, there may also be indication for the conjugation of phenyl rings with carbonyl compounds in ketones, aldehydes, and esters and weak absorption due to overtones in substituted benzene rings. Amines and amides may be incorporated through the N–H bending absorption by the baseline corrected solution (1587–1601 cm-1) and the C–N stretching in aromatic amines in the raw solution. Additionally, given the positive regression coefficients, it is possible that the TOR EC raw spectra model uses the fingerprint region (1100–1300 cm-1) associated with vibrational modes of amines and ethers, using not only this region to compensate for the possible artifacts due to PTFE absorption as for TOR OC. The C=O stretching vibration (1722–1739 cm-1) in the baseline corrected solution can be attributed to ketones, aldehydes, or esters, but when harmonizing with the raw spectrum solution according to the common FG hypothesis, the ester assignment through the C–O–C antisymmetric stretch (1275–1279 cm-1) is considered possible. Ester formation has been associated with aqueous phase processing of biogenic organic compounds in atmospheric PM , so its association with EC is unexpected and tentative.

The band assignments for TOR OC are perhaps not surprising given that many of the FGs have been used previously for quantification of organic PM, but it is worth considering our interpretation for TOR EC in context as FT-IR is not commonly employed for the study of elemental carbon or similar substances. “Elemental carbon” strictly refers to sp2 carbon not bound to other elements and has the property of thermal stability with respect to vaporization up to 4000 K in an inert atmosphere, or 340 ∘C in an oxidizing environment . EC by TOR is therefore quantified by heating PM samples at these high temperatures in the presence of oxygen, and its quantity separated from the preceding OC vaporized anoxically by an operationally defined protocol based on evolving filter optical properties . Atmospheric elemental carbon as reported by this method is likely to represent a set of strongly light-absorbing, low-volatility compounds that characterize carbonaceous material formed or emitted from combustion processes rather than in one of the chemically pure allotropic forms (e.g., graphite and diamond) .

Direct measurements of elemental carbon and associated substances by infrared spectroscopy are not numerous, but recorded infrared spectra of ground graphite and coal; reporting strong, broad absorption bands centered near 1600 cm-1 superposed on a wider band between 1800 and 900 cm-1 in both substances. While 1600 cm-1 is near reported lattice frequencies for crystalline graphite , the band becomes visible only with extensive grounding of this material in which crystalline structure is lost . Therefore, attribute these bands to non-crystalline graphite structure, presumably carbon–carbon bonds which occur in exposed edges of the ground graphite . The 1600 cm-1 band has in the past been attributed to aromatic or carbonyl structures as their resonances overlap in this region, but the absorption line shapes of these two structures are not accompanied by the broader band spanning a range of 900 cm-1 . The absorption band around 1600 cm-1 can also be found in spectra of polycyclic aromatic hydrocarbons such as anthanthrene and benzo[ghi]perylene and has been attributed to the stretching of the aromatic C=C bonds .

The absorption band around 1600 cm-1 is required by our baseline corrected solution and the raw solution appears to use a shoulder of the same band at lower wavenumbers (range 1497–1531 cm-1). The relevance of this band to both solutions for the prediction of TOR EC is consistent with the presence of sp2 bonds in ring-structured substances (as discussed above) known to be emitted from combustion sources . We attribute the absorption around 1700 cm-1 in the baseline corrected solution to (the shoulder of the) ester C=O stretch for harmony in interpretation with the ester C–O–C antisymmetric stretch at 1275 cm-1 in the raw solution, as described previously. Because of the complexity of the PM mixture captured by the infrared spectra, we are unable to identify the broader feature of 1800–900 cm-1 associated with graphitic structure reported by . However, as the baseline corrected spectrum solution does not use information below 1500 cm-1, it appears that accurate calibration models of TOR EC can be constructed even by omission of a large portion of this broad band. Amines have been associated with anthropogenic emissions and strong partitioning behavior to the aerosol phase e.g.,, so identification of this FG is plausible given our understanding of EC sources.

We explicitly remark that while the absorption bands discussed in relation to VIP scores are all observed in the overall infrared spectra used for building calibration models, they are associated with the PM mixture and do not correspond to direct observations of bands in physically or chemically isolated specimens of TOR EC. The bands are selected mathematically, based on strength of covariance (in combination with other bands) with TOR EC for selection in quantitative prediction. Similar approaches based on covariance analysis methods have reported acetyl, aromatic, and phenol structures or alkane C–H to predict the abundance of recalcitrant or black carbon in soils. For predicting TOR EC in atmospheric samples, it is possible that our calibration models not only use graphitic structure of EC but also rely on fragments of co-emitted OC, or artifact from the partitioning of total carbon between OC and EC by TOR. Based on our analysis of FGs in Sect. , we cannot rule out at present time that some of these organic FG assignments may arise from spurious correlations. While surface FGs of soot particles sampled at source have been detected by FT-IR , we consider that their potential mass contribution is insignificant with respect to the overall mass of accompanying organic PM such that the possibility of extracting this surface FG contribution to the overall organic signal is unlikely. We anticipate that plausibility of these hypotheses can be further constrained in future studies.

There are additional bands which appear to be relevant for one spectra type but not the other for both TOR OC and EC (and also other analytes discussed in Sect. ) and, as described in the following section (Sect. ), more models can be constructed that include a larger number of wavenumbers. It is unclear whether these additional FGs are superfluous, complementary, or spurious in their relation to groups discussed above, but the value of their absorbances was not ruled out in the model selection process. The most reasonable interpretation of relevant FG lies somewhere between the extremes of the common FG and divergent FG hypothesis, and further investigation on this topic is also left for future work.

SPLSa and SPLSb solutions for TOR OC and EC calibration models developed with baseline corrected spectra use wavenumbers similar to EN–PLS, which are described above. In both TOR OC and EC models, additional wavenumbers in the range 2200–2500 cm-1 and above 3300 cm-1 are used by SPLSa and SPLSb solutions. The former set of wavenumbers may correspond to vibrational modes from isocyanates, nitriles, and phosphines and usually have very low absorbance in ambient samples. This may explain why the most parsimonious solutions from EN–PLS do not use this range of wavenumbers. The wavenumbers above 3300 cm-1 may correspond the absorption of alcohol and amine FGs, whose contribution to TOR OC and EC prediction is taken into account in other parts of the spectrum by the EN–PLS solution. SPLSa, SPLSb, and EN–PLS raw spectrum solutions for TOR OC and EC use the range near 1700 cm-1 attributed to C=O absorption, and the PTFE C–F stretching region to account for removing the PTFE contribution to the overall signal.

The full spectrum solutions include features that have been previously described in the EN–PLS solutions, though more specific interpretation is more difficult for lack of sparsity. In the baseline corrected solution we can see that for both TOR OC and EC high VIP scores correspond to the regions around 1700, 3000, and 3400 cm-1 associated with C=O, C–H, and O–H stretching, respectively. For TOR EC, the high VIP scores in the region of C–H stretching are associated with negative coefficients, as in the EN–PLS solution. For the raw spectra models of TOR OC and EC, the PTFE C–F stretching region is also used for background subtraction. The most distinguishing features with highest VIP scores associated with analytes are the C=O stretching (near 1700 cm-1) for the TOR OC and benzene ring stretch (near 1500 cm-1) for the TOR EC.