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## Russelllm090124supplement.doc

**Appendix 1. Revised FTIR Algorithm for Functional Group Identification**
FTIR spectra were analyzed using a revised algorithm for baselining and spectral smoothing,
fitting overlapping peaks, and integrating absorbance before converting to mass with standard
calibrations. Table S-1 summarizes the regions and parameters used in the algorithm.

Baselining and spectral smoothing. A third-order polynomial is used to baseline each spectra, in
order to reduce both bias (with respect to zero) and variance in baselines of blank filter spectra
over a linear baseline. CO interference is removed with an interpolated spline, and interference
from H O is minimized with wavelet de-noising methods.

Spectral resolution of carboxylic acid absorption. The O-H stretching band in carboxyl groups is
very broad and span between 3100-2400 cm-1 [Lambert et al., 1998]; overlapping with a
significant number of peaks that we quantify. To resolve the shape of peaks within this type of
spectra, we retrieved a series of carboxylic acids with varying quantities of aliphatic C-H and
COOH groups (adipic, glutaric, malonic, azelaic, decanoic, stearic, and succinic acids) from the
NIST Chemistry Webbook (http://webbook.nist.gov/chemistry/) and searched for a two-factor
solutions using Positive Matrix Factorization as our factor analysis technique. A sum of Gaussian
peaks were selected to represent the COOH component such that when fitted to adipic acid
reference spectra produced in our laboratory, quantitatively reproduced the saturated aliphatic C-
H absorptivity observed in non-carboxylic acid species (docosanol and docosene).

Band-fitting. Fixed carboxylic C-OH and ammonium spectra are subtracted from each spectrum
based on a simple scaling algorithm. Absorption peaks for the remaining groups are fitted using
box constraints primarily determined from reference spectra analyzed in the laboratory
[Gilardoni et al. 2007]; multiple sets of initial values are provided to the least-squares fitting
routine and the final set of parameters is selected based upon the analysis of residuals.

Oxygenated groups. The quantity of carboxylic COOH (“acid groups”) is determined from
examining mole ratios of carboxylic C=O and carboxylic C-OH. The acid group is quantified by
averaging moles of carbonyl and carboxylic C-OH when they are approximately equal, or the
minimum of either group when their molar quantities significantly differ. Non-carboxylic
carbonyl is determined as the carbonyl in significant excess of carboxylic C-OH, and this is
interpreted to be carbonyls associated with aldehyde and ketonic species. “Excess Acid” is
defined as carboxylic C-OH in excess of reported carbonyl, as can occur when we miss
quantification of amino acid and conjugated carbonyls because of significant shifts in peak
absorption, and is included in the reported carboxylic acid group fraction.

“Excess Alcohol” is determined by area of unidentified residuals in the region approximately
between 3400 and 2900 cm-1. While alcohol and phenolic absorbance generally occurs in the
region 3600-3200 cm-1 [Lambert et al., 1998], we report the total absorbance in this region in
mass units of alcohol C-OH to provide an upper bound to the concentration.

Detection Limits. Detection limits are determined as the minimum area statistically
distinguishable (2σ) above errors estimated from baselining and ammonium subtraction for each

**Appendix 2. Positive Matrix Factorization for FTIR Spectra and Correlation to Elemental**
**Concentrations**
Positive Matrix Factorization [Paatero and Tapper, 1994] was implemented as our multivariate
curve resolution technique to statistically reduce our 128 ambient spectra into a few
“components” that share significant co-variation in absorbance across wavenumbers. Baselined
and smoothed sample spectra were provided to PMF as the data matrix. The scaling coefficient is
the reciprocal of variance in analytical error (1/σ2), as determined by variability in baselining of
blank sample spectra determined at each wavenumber. The scaling factor is estimated from
possible baselining error at each wavenumber. A set of field blanks was collected with each
sample, and spectra from these were baselined similarly to the sample spectra. On average, the
baselining errors are zero at each wavenumber, but the variability about the mean is used to
estimate the baselining error for each sample.

We systematically explored the solution space of two parameters: number of factors (

*p*) and
rotation parameter (FPEAK). We applied singular value decomposition to the entire data set and
also sectionally, by fixed-size moving window analysis (Keller and Massart, 1991). The trace of
eigenvalues in each case was used to constrain the value of

*p* to those values which provided
sufficient data reconstruction (approximately 90% data recovery). FPEAK was restricted to the
domain in which the

*Q* value (value of the least squares) objective function was comparable to or
below the theoretical expected value defined by

*E*(

*Qm*) = (

*n*×

*m)*-

*p*(

*n*+

*m*).

*E*(

*Qm*) is the expected
value of the portion of

*Q* (the objective function) that arises from the data-fitting (excluding
penalty terms) and

*n*x

*m* are the dimensions of the data matrix.

Table S-1. Absorbance frequencies, quantified peak ranges, absorptivity coefficients anddetection limits used in quantifying organic functional groups from FTIR spectra.

Functional Group

Source: http://aerosols.ucsd.edu/supplement/RussellLM090124supplement.pdf

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