Analyzing experimental data and model parameters: implications for predictions of SOA using chemical transport models

Despite critical importance for air quality and climate predictions, accurate representation of secondary organic aerosol (SOA) formation remains elusive. An essential addition to the ongoing discussion of improving model predictions is an acknowledgement of the linkages between experimental conditions, parameter optimization and model output, as well as the linkage between empirically-derived partitioning parameters and the physicochemical properties of SOA they represent in models. In this work, a “best available” set of SOA modeling parameters is selected by comparing predicted SOA yields and mass concentrations with observed yields and mass concentrations from a comprehensive list of published smog chamber studies. Evaluated SOA model parameters include existing parameters for two product (2p) and volatility basis set (VBS) modeling frameworks, and new 2p-VBS parameters; 2p-VBS parameters are developed to exploit advantages of the VBS approach within the computationally-economical and widely-used 2p framework. Fine particulate matter (PM 2.5) and SOA mass concentrations are simulated for the continental United States using CMAQv.4.7.1; results are compared for a base case (with default CMAQ parameters) and two best available parameter cases to illustrate the highand low-NO x limits of biogenic SOA formation from monoterpenes. Results are discussed in terms of implications for current chemical transport model simulations and recommendations are provided for future modeling and measurement efforts. The comparisons of SOA yield predictions with data from 22 published chamber studies illustrate that: (1) SOA yields for naphthalene, and cyclic and > C5 straight-chain/branched alkanes are not well represented using either the newly developed or existing parameters for low-yield aromatics and lumped alkanes, respectively; and (2) for four of seven volatile organic compound +oxidant systems, the 2p-VBS parameters better represent chamber data than do the default CMAQ v.4.7.1 parameters. Using the “best available” parameters (combination of published 2p and newly derived 2p-VBS), predicted SOA mass and PM 2.5 concentrations increase by up to 15 % and 7 %, respectively, for the high-NO x case and up to 215 % ( ∼ 3 μg m−3) and 55 %, respectively, for the low-NOx case. Percent bias between model-based and observationally-based secondary organic carbon (SOC) improved from−63 % for the base case to −15 % for the lowNOx case. The ability to robustly assign “best available” parameters in all volatile organic compound +oxidant systems, however, is critically limited due to insufficient data; particuarly for photo-oxidation of diverse monoterpenes, sesquiterpenes, and alkanes under a range of atmospherically relevant conditions.


Introduction
Atmospheric fine particulate matter (PM 2.5 ) has long been linked to direct climate forcing, with estimates of radiative forcing due to the sulfate fraction surpassing that due to the organic carbon fraction (Haywood and Boucher, 2000 and references therein). However, more recently, Goldstein et al. (2009) reported that for the southeastern United States (US) the spatial and temporal distributions of aerosol optical thickness (AOT) are most consistent with biogenic organic aerosol precursors (e.g., α-pinene), suggesting secondary K. C. Barsanti et al.: Implications for predictions of SOA using chemical transport models organic aerosol (SOA) can dominate AOT in the summer, affecting negative radiative forcing or cooling in the region. A modeling study by Myhre et al. (2009) also suggests that SOA is a significant contributor to negative radiative forcing, on a global scale. Additional radiative forcing (Park et al., 2010), though positive in sign, may be possible if one considers the production of brown carbon from SOA constituents (Updyke et al., 2012). SOA, by virtue of its contribution to PM 2.5 (20-50 % globally, Hallquist et al., 2009), also plays a role in adversely affecting health (e.g., Pope, 2007). It is thus of critical importance that a quantitative and predictive understanding of SOA be achieved. To that end, much effort has been directed at developing, improving, and testing SOA models that are sufficiently comprehensive yet not computationally burdensome.
Accurate representation of SOA is elusive, even at the process-level, and becomes increasingly so as attempts are made to simplify and parameterize systems that are not fully understood. While the focus of this work is on bottom-up SOA modeling approaches, top-down approaches exist as well (e.g., Spracklen et al., 2011). One bottom-up approach to simulating SOA in three-dimensional chemical transport models (CTMs) proceeds by combining anthropogenic and biogenic emissions estimates with smog chamber data on SOA formation from individual volatile organic compound (VOC) precursors to generate regional and/or global SOA fields (Hallquist et al., 2009). Representation of SOA formation is based on gas/particle (G/P) partitioning theory (Pankow, 1994a, b) and historically parameterized using the two-product (2p) approach of Odum et al. (1996), in which up to two lumped products are assumed to represent the condensable oxidation products of each VOC+oxidant system. For each such system, products are assigned empiricallyderived partitioning parameters (K p or C*) and stoichiometric product yields (α) using a least-squares fitting approach, typically such that one product has a relatively lower α value and lower volatility (product 1) and the other has a relatively higher α value and higher volatility (product 2). An alternative, more recent approach is the volatility basis set (VBS) approach Lane et al., 2008b), in which C* values are defined by fixed logarithmicallyspaced bins and least-squares fitting is used to assign α values (e.g., Pathak et al., 2007a). In addition to SOA formation from oxidation of volatile precursors ("traditional" SOA), the VBS approach has been used to parameterize SOA formation based on smog chamber studies of intermediate to low volatility precursors (Grieshop et al., 2009;Presto et al., 2010), including those precursors produced from the evaporation of primary organic aerosol (POA) (Grieshop et al., 2009).
While there are a variety of limitations associated with using smog chamber data to derive model parameters to represent SOA formation in the real atmosphere (e.g., Kroll and Seinfeld, 2008), and more detailed modeling approaches are being developed (e.g., GECKO-A, Aumont et al., 2005;Lee-Taylor et al., 2011;and CNPG, Pankow and Barsanti, 2009;Barsanti et al., 2011), most widely-used approaches for predicting SOA in CTMs rely on parameterizations of chamber experiments. These CTMs include CAM-Chem (Lack et al., 2004;Heald et al., 2008), CMAQ (Carlton et al., 2010), GEOS-Chem (Henze and Seinfeld, 2006;Pye et al., 2010), GISS GCM (Chung and Seinfeld, 2002) and PM-CAMx (Lane et al., 2008b;Tsimpidi et al., 2011). The default implementation of the 2p and VBS approaches in these CTMs, as well as the fitting of 2p and VBS parameters, assumes instantaneous G/P equilibrium. Recent work suggests that this assumption is appropriate in CTMs (Saleh et al., 2013), though other recent studies (Virtanen et al., 2010;Cappa and Wilson, 2011;Vaden et al., 2011;Perraud et al., 2012;Shiraiwa and Seinfeld, 2012) suggest that this assumption may not be appropriate under all conditions; changes in the physicochemical properties of particles due to ambient condition changes and/or condensed-phase chemistry may lead to circumstances where partitioning kinetics are controlled by particle-phase diffusion. In this work, the default assumption of instantaneous equilibrium is retained.
Chamber studies conducted with very high initial precursor concentrations (and subsequently high reacted hydrocarbon levels, HC), lead to very high organic aerosol mass concentrations (M o ) relative to ambient values. Because high M o values favor SOA condensation, even relatively volatile compounds can contribute significantly to the SOA that forms. In dark α-pinene ozonolysis experiments by Yu et al. (1999) ∼ 50-95 % of the SOA mass formed can be attributed to identified and hypothesized oxidation products that are relatively volatile, with K p values on the order of 10 −6 to 10 −1 m 3 µg −1 (C* ≈ 10 5 to 10 µg m −3 ). In more recent dark α-pinene ozonolysis experiments by Camredon et al. (2010), also at high M o , all of the proposed and identified major monomeric oxidation products in the condensed phase have K p values on the order of 10 −5 to 10 −1 m 3 µg −1 (C* ≈ 10 4 to 10 µg m −3 ). However, only products at the lowest end of such volatility distributions (K p = 10 −1 m 3 µg −1 or C* = 10 µg m −3 ) would be expected to condense at an atmospherically relevant M o of ∼ 5 µg m −3 , and for those products, only ∼ 33 % would be expected in the condensed phase.
When the 2p fitting approach is applied to chamber data from experiments carried out at high HC levels (and thus high M o ), the relatively volatile products with higher stoichiometric yields (α) form in significant levels, "masking" the presence of lower volatility products with much lower α values. Thus, while lower volatility products do not influence K p values derived from high M o chamber experiments, such products may explain most of the SOA formation in the atmosphere. Evidence for this has been provided by low M o chamber experiments (Presto and Donahue, 2006;Pathak et al., 2007a;Shilling et al., 2008). As described in Presto and Donahue (2006), the VBS fitting approach has some advantages over the 2p fitting approach that are achieved by fixing the volatility bins (C* values) based on experimental and/or ambient M o ranges and fitting only the α values. For a typical 4-species basis set (e.g., C* = {1, 10, 100, 1000} µg m −3 ) the number of free parameters, four, is the same as with the 2p approach; however, the VBS parameters are much less covariant because the volatility space is fixed. Furthermore, because of the fixed logarithmically-spaced volatility bins, VBS parameters may be better able to represent SOA formation at low M o , specifically when limited data exist. In this work, parameters based on VBS fits are developed and evaluated in an effort to take advantage of the robustness of the VBS fitting approach within the computationally economical, precursor specific, and widely used 2p modeling framework. These new parameters are herein called "2p-VBS".
Principles of G/P partitioning theory are used here to guide a detailed analysis of the often overlooked, but non-trivial linkages between experimental conditions, parameter optimization, and predictions of SOA using CTMs. A detailed comparison of predicted SOA yields and mass concentrations using the 2p, VBS, and the new 2p-VBS parameters with published smog chamber data is conducted and used to recommend the "best" parameters based on currently available data. The "best available" parameters then are used in CMAQ to simulate SOA and PM 2.5 over the continental US during a two-week summer period. Results of the analysis and model predictions are used to highlight current knowledge gaps and may be used to guide future chamber experiments and SOA modeling efforts.

Development of 2p-VBS parameters
In this section, the motivation and approach for developing the new 2p-VBS parameters are described. Figure 1a and b il-lustrate the relationship between chamber M o and HC levels and predicted SOA yields and mass concentrations using 2p and VBS fitting approaches for dark α-pinene ozonolysis experiments (shown only for M o ≤ 10 µg m −3 , see Supplement Table S1 for a descriptive list of all of the experimental data considered, including full M o and HC ranges). As introduced above, the SOA fitting parameters are influ-  (2008) suggest that when sufficient data points were available at low M o both the 2p and VBS parameterizations represented the observed yields ( Fig. 1a) and captured the observed SOA formation at the lowest HC levels (Fig. 1b). For the Presto et al. (2005) dataset, while the observed yields at M o > 50 µg m −3 were represented by the published 2p parameterization (not shown here, see Presto et al., 2005), observed SOA formation at the lowest HC levels (15-25 ppb) was not captured (Fig. 1b). In this work, VBS parameters were fit to the Presto et al. (2005) dataset; the VBS parameters were better able to represent observed SOA formation at HC levels < 25 ppb in the experiments from which the parameters were derived, as well as in other chamber experiments for the same VOC+oxidant system Cocker et al., 2001a;Pathak et al., 2007b;Song et al., 2007). These results suggest that the VBS approach may be better able to represent SOA formation at low HC levels and M o , specifically when data are available but sparse, due to the fixed logarithmically-spaced volatility bins across the experimentally relevant M o range. The ability of any individual parameterization to represent SOA formation will further depend on the quality of data used in the fitting and the chemical similarity between the observed and modeled systems.
In the context of chemical transport modeling, the inability of some chamber-based parameterizations to accurately capture SOA formation at low, atmospherically relevant HC levels has important consequences for spatial and temporal predictions of atmospheric PM 2.5 , as well as implications for analyses of the relative contributions of specific SOA precursors, including source-attribution analyses. Therefore, in an effort to exploit the fitting advantages of the VBS approach and potentially provide improved parameters for use within the 2p modeling framework, 2p-VBS parameters were developed for evaluation as follows. For the traditional SOA precursors, the published VBS parameters of Tsimpidi et al. (2010) at T = 298 K were used to generate 263 pseudodata points (yield vs. M o ) for M o = 0 to 200 µg m −3 at each of three temperatures (272, 298, and 324 K) using an effective H vap = 30 kJ mol −1 (see Pathak et al. 2007b); those 789 pseudo-data points were then fit to generate a set of 2p-VBS parameters for each set of VBS parameters. The 2p-VBS parameters are presented in Table 1 for T = 298 K and ρ = 1.5 g cm −3 (the same temperature and density reported in Tsimpidi et al. (2010); see Supplement for derivation of the density correction). In addition to the volatile SOA precursors, 2p-VBS parameters were derived for semi-volatile alkanes and POA (Table 2) based on the VBS parameters of Presto et al. (2010), Shrivastava et al. (2008) and Grieshop et al. (2009). Following Shrivastava et al. (2008) in which the effective H vap varied with C* for POA, here H vap was treated as an additional fitting parameter (values are included in Table 2). Published VBS parameters were chosen as the starting point for this work because of the ability of VBS parameterizations to represent SOA formation over a wide HC and M o range and the limited availability of validated data within the range of atmospherically relevant HC and M o .
For each of the traditional SOA precursors, the 2p-VBS parameters reproduced the yield curves from the VBS parameters over the range of M o data, at each of the three temperatures, and were able to represent SOA formation with the same degree of uncertainty as the VBS parameters (i.e., no additional error is introduced by the 2p-VBS fit, see Supplement Figure S1). Therefore, the SOA yield and mass predictions using the Tsimpidi et al. (2010) VBS parameters and the 2p-VBS parameters derived here produce equivalent results for "first generation" SOA formation, including the temperature dependence of SOA yields. Consequently, only predictions using the 2p-VBS parameters are shown in subsequent figures (i.e., predictions using Tsimpidi et al. (2010) VBS parameters are not shown). Differences between the 2-VBS parameters in this work and the reduced species VBS parameters in Shrivastava et al. (2011), also developed to reduce computational burden, are described in the Supplement (see Fig. S2).

Chemical transport modeling
CMAQ (Byun and Schere, 2006) version 4.7.1 was used to simulate SOA mass concentrations over the continental US (12 × 12 km resolution) up to 50 mb with 34 vertical layers (4 666 194 grid cells) for 12-31 July 2006. This date range is representative of typical US summertime conditions when biogenic SOA is a measurable component of total PM 2.5 (Kleindienst et al., 2010). The simulation results for the first three days were excluded from subsequent analysis to allow for model initialization and spin-up. The gas-phase chemistry mechanism SAPRC07 (Carter, 2010) was used for the simulations, with updated isoprene photo-oxidation chemistry to improve isoprene nitrate yields, isoprene nitrate lifetimes, and NO x recycling rates (Xie et al., 2013). Anthropogenic emissions were based on the 2005 National Emissions Inventory (NEI) projected to 2006; biogenic emissions were generated with the Biogenic Emissions Inventory System (BEIS) model version 3.14. Meteorological inputs for BEIS and pollutant transport were from version 3.1 of the Weather Research Forecasting (WRF) model. Three cases were considered: a base case using the revised CMAQv4.7 parameters (i.e., CMAQv4.7.1 parameters) described in Carlton et al. (2010) and two additional cases exploring best available SOA parameters and sensitivity to NO x -dependent biogenic SOA formation (BA-highNO x and BA-lowNO x ). Selection of the best available parameters was based on the comparison of 2p, VBS and 2p-VBS predictions with chamber data, as described in detail in the results and discussion section. The default aging mechanism of CMAQv4.7.1 was retained, wherein traditional SOA is converted to nonvolatile SOA with a rate constant k olig = 9.6 × 10 −6 s −1 (Carlton et al., 2010).
CMAQv4.7.1 allows NO x -dependent SOA formation for anthropogenic precursors only (see Carlton et al., 2010); thus two case studies (BA-highNO x and BA-lowNO x ) were constructed to illustrate the limits of SOA formation from monoterpenes under "high" and "low" NO x conditions. For the aromatic precursors within CMAQ, the branching between the high-and low-NO x SOA formation pathways is treated dynamically as a function of the ratio of nitric oxide (NO) to hydroperoxy radical (HO 2 ) and the reaction rates of the peroxyradical (RO 2 ) with NO and HO 2 . Therefore, the anthropogenic high-NO x parameters were the same in the prescribed BA-highNO x and BA-lowNO x case studies, and were selected as described below. For the anthropogenic low-NO x parameters, the default CMAQv4.7.1 values were used. While legitimate questions exist as to the relationship between NO x conditions in chambers and NO x conditions in the real atmosphere (and how each are defined), a detailed investigation is beyond the scope of this manuscript. For biogenic precursors, the division between high-and low-NO x experimental data and SOA parameterizations was thus based on a number of factors: (1) the designations given in Table 1. 2p-VBS parameters, based on VBS parameters of Tsimpidi et al. (2010), for SOA precursors under high-and low-NO x conditions at T = 298 K and ρ = 1.5 g cm −3 .    (Presto et al., 2010), naphthalene (Pye et al., 2010), undifferentiated POA (Shrivastava et al., 2008), wood smoke POA and diesel POA (Grieshop et al., 2009) under high-NO x conditions for T = 298 K and ρ = 1.0 g cm −3 .
Precursor the associated publications, (2) reported HC initial / NO xinitial and/or HC / NO xinitial ratios, and (3) comparisons among reportedly similar data/parameterizations (see Supplement  Table S1 for chamber experiment details). The selection of biogenic SOA parameters, specifically for monoterpenes, under high-NO x conditions (BA-highNO x ) and low-NO x conditions (BA-lowNO x ) is described below. The parameters selected for each case are summarized in Table 3.

Biogenic precursor parameters
In Figs

Isoprene parameters
In Fig. 2, the 2p-VBS theoretical yield (Fig. 2a) and SOA formation ( Fig. 2b) curves for isoprene are compared with those from two additional parameterizations widely used in chemical transport modeling: (1) the Henze and Seinfeld (2006) low-NO x 2p parameterization based on the chamber experiments of Kroll et al. (2006), and (2) the high-NO x "3p" parameterization of Pandis et al. (1991). Also shown are upperbound (low-NO x ) and lower-bound (high-NO x ) parameterizations from Carlton et al. (2009) (note: the lower-bound parameterization is outside the axis range in Fig. 2b). For the low-NO x conditions, the 2p-VBS underpredicted SOA yields compared to chamber observations (Fig. 2a) and was not able to reproduce the observed SOA formation at the lowest HC levels (Fig. 2b) (chamber data: Kroll et al., 2005Kroll et al., , 2006Chan et al., 2010;. The low-NO x VBS parameterization, on which the 2p-VBS parameterization was based, relied on extrapolation of chamber data as described in Lane et al. (2008b). Briefly, the high-NO x VBS parameters Table 3. Default parameters (base case) and best available parameters for biogenic high NO x (BA-highNO x ) and biogenic low NO x (BA-lowNO x ) used in CMAQv4.7.1 simulations a ; T = 298 K and densities b matched to reported densities for base case (Carlton et al., 2010). Data references not provided in this work can be found in Carlton et al. (2010) for 2p parameters and in Tsimpidi et al. (2010) for VBS parameters.
Base Case Best Available (BA) Precursor   (Lane et al., 2008a;Tsimpidi et al., 2010), based on the "3p" parameterization of Pandis et al. (1991), were adjusted using an M o -dependent yield correction from the α-pinene experiments and parameterizations of Pathak et al. (2007a). It is thus not unexpected that the low-NO x 2p-VBS parameterization was not able to represent observed SOA formation, particularly at the lowest HC levels. In contrast, the low-NO x 2p parameterizations of Henze and Seinfeld (2006) and of Carlton et al. (2009) were derived directly from chamber data and were in better agreement with the chamber observations . The default low-NO x parameters based on Henze and Seinfeld (2006), which notably produce the highest predicted SOA yields, were retained as the best available parameters for the CMAQ simulations.
There have been limited studies investigating the effects of NO x on isoprene SOA yields (Carlton et al., 2009 and references therein). The parameterizations shown here suggest that increasing NO x potentially results in lower SOA yields (Fig. 2a); however, as described by Surratt et al. (2010) and Chan et al. (2010), SOA yields depend on relative concentrations of HO 2 , NO and NO 2 , complicating the interpretation of NO x dependence. For the high-NO x isoprene conditions, none of the parameterizations were able to represent the SOA yields (Fig. 2a) or SOA formation observed at the lowest, atmospherically relevant, HC levels (Fig. 2b). NO x dependence of SOA formation by isoprene was not considered here, given that: (1) under some conditions, highest yields have been observed under high-NO x conditions when NO 2 / NO ratios are high and RO 2 +NO 2 reactions are favored over RO 2 +NO reactions (e.g., Chan et al., 2010); and (2) the effects of NO x on the volatility of the initially formed products (e.g., the point at which SOA formation is observed) are not clear (Fig. 2b).

Monoterpene parameters
In Fig. 3, the 2p-VBS theoretical yield (Fig. 3a) and SOA formation (Fig. 3b) curves for lumped monoterpenes are compared with those obtained from parameterizations used in CMAQv.4.7.1 (Carlton et al., 2010) and GEOS-Chem (Pye et al., 2010). Given the limited data available from photooxidation studies of monoterpenes, data also are shown for dark α-pinene ozonolysis chamber experiments (low NO x referenced in Fig. 1, high NO x : Presto et al., 2005;Presto and Donahue, 2006;Ng et al., 2007a). As argued by Pye et al. (2010), dark α-pinene ozonolysis parameters may serve as a good proxy for lumped monoterpene photo-oxidation parameters because the parameters derived from dark αpinene ozonolysis experiments likely overestimate yields from photo-oxidation of α-pinene, but likely underestimate yields from photo-oxidation of other monoterpenes known to have higher yields than α-pinene.
The CMAQ (Carlton et al., 2010) high-NO x 2p parameters were based on the chamber experiments of Hoffmann et al. (1997) and Griffin et al. (1999); there is no low- The lower yields and mass concentrations predicted in this work with the 2p-VBS parameters, relative to those predicted with the Pye et al. (2010) VBS parameters, are a consequence of both the lower observed SOA yields for UV conditions (data used in low-NO x VBS parameterization) and the greater yield correction in calculating the high-NO x parameters. Note that while the use of the high-NO x isoprene VBS parameters (Lane et al., 2008a) to obtain the low-NO x isoprene parameters leads to a likely underestimation of SOA formation (Fig. 2a), the use of the low-NO x monoterpene VBS parameters (Lane et al., 2008a;Pye et al., 2010) to obtain the high-NO x parameters leads to reasonable and perhaps an overestimation of SOA formation (Fig. 3). The high-NO x monoterpene parameterization of Pye et al. (2010), derived from the low-NO x Shilling et al. (2008) experiments, appears to overestimate SOA formation at low HC and M o levels (Fig. 3b). However, the data are insufficient to make robust conclusions regarding the best available parameters, highlighting the need for monoterpene photo-oxidation studies under varying atmospherically relevant NO x conditions. Based on the available data, the 2p-VBS parameters for both low-and high-NO x conditions were chosen for the CMAQ simulations.

Sesquiterpene parameters
In Fig. 4, the 2p-VBS theoretical yield (Fig. 4a) and SOA formation (Fig. 4b) curves for lumped sesquiterpenes are compared with curves from the 2p parameterization used in CMAQv.4.7.1 (Carlton et al., 2010) and the VBS parameterization in GEOS-Chem (Pye et al., 2010). Relative to the 2p and VBS parameterizations, the 2p-VBS parameterization underestimated SOA yields (Fig. 4a) and M o (Fig. 4b) (chamber data: Griffin et al., 1999;Ng et al., 2007a). The VBS parameters (Lane et al., 2008b;Tsimpidi et al., 2010), on which the 2p-VBS parameters were based, and the CMAQ (Carlton et al., 2010) and Pye et al. (2010) parameters all were derived from chamber experiments involving αhumulene or β-caryophyllene as the sesquiterpene precursor; however, the Lane et al. (2008b)/Tsimpidi et al. (2010 VBS parameters were derived using data from photo-oxidation as well as dark ozonolysis experiments . For α-humulene and β-caryophyllene, the dark ozonolysis yields were significantly lower than the photo-oxidation yields, which likely resulted in the low bias of the Lane et al. (2008b) parameterization, and thus the low bias of the 2p-VBS parameterization as compared with CMAQ (Carlton et al., 2010) and GEOS-Chem (Pye et al., 2010).
Both the CMAQ (Carlton et al., 2010) and Pye et al. (2010) parameterizations were based on the chamber photo-oxidation data of Griffin et al. (1999), which had HC [ppbC] / NO xinitial [ppb] ratios of 0.5 to 8.0. The 2p parameterization of Carlton et al. (2010) was based on all seven data points and was categorized as relevant for high-NO x conditions; whereas the VBS parameterization of Pye et al. (2010) was based on four of the seven data points, with HC [ppbC] / NO xinitial [ppb] > 3, and was categorized as relevant for low-NO x conditions. As shown in Fig. 4a, b the two parameterizations produced quantitatively similar results. These results are consistent with the Griffin et al. (1999) data from which no clear trend as a function of VOC / NO x ratio was observed. The VOC / NO x ratios span a much smaller range than that of Ng et al. (2007a)   conditions would be classified as high-NO x based on Presto et al. (2005). Somewhat surprisingly, the clear NO x -dependency observed by Ng et al. (2007a) over all mass loadings (M o = 20-214 µg m −3 ) is no longer observable at the lowest M o (Fig. 4a, b). Instead there appears to be a greater dependence of SOA yields on the specific sesquiterpene precursor than on VOC / NO x ratios (see Supplement  Fig. S3).
Without the availability of additional data on the NO xdependency of SOA formation from different sesquiterpene precursors, the default CMAQv.4.7.1 parameters for sesquiterpenes were retained as the best available for high-NO x conditions and it was concluded that there were insufficient data to support the derivation and/or use of low-NO x sesquiterpene parameters. The CMAQ parameters however are not physically realistic, as they indicate a relatively high increase in the mass of the condensing compounds relative to the precursor (α ≈ 1.5) without a substantial decrease in volatility (unless it is assumed that the sesquiterpene SOA is dominated by highly oxidized sesquiterpene  Fig. 4. A test set of parameters, more in accord with the monoterpene parameters, reproduced the observed chamber data reasonably well and resulted in a calculated SOA yield of ∼ 45 % at M o = 5 µg m −3 . This finding supports the need for additional constraints, chamber data, on sesquiterpene+oxidant systems.

Anthropogenic precursor parameters
In Figs. 5 and 6, theoretical yield curves (SOA yield vs. M o ) are shown for each of the anthropogenic precursors: lumped high-yield (refers to yield in the gas phase) aromatics (ARO1 in SAPRC, includes toluene), lumped low-yield aromatics (ARO2 in SAPRC, includes xylene), and lumped alkanes (ALK5 in SAPRC). The anthropogenic 2p, VBS, and 2p-VBS parameters were evaluated for high-NO x conditions only.

Toluene/ARO1 parameters
For toluene/ARO1, the calculated SOA yields were consistent with the data on which each of the parameterizations were based (Fig. 5a). Hildebrandt et al. (2009) reported a range of SOA yields that were highly sensitive to experi-mental conditions such as UV intensity, temperature, and NO x levels. For comparable temperatures, the reported SOA yields of Hildebrandt et al. (2009) are higher than those of Ng et al. (2007b); the latter of which were used to derive the 2p parameters in CMAQ (Carlton et al., 2010). Hildebrandt et al. (2009) described the likely reasons for these discrepancies: temperature differences during the experiments (slightly higher in Ng et al., 2007b;less variable in Hildebrandt et al., 2009), differences in NO 2 / NO ratios (NO 2 dominated Hildebrandt et al., 2009; a more atmospherically relevant NO 2 / NO mix in Ng et al., 2007b), and corrections made for vapor loses to walls in Hildebrandt et al. (2009). The Tsimpidi et al. (2010 parameters used to derive the 2p-VBS parameters were based on the data of Ng et al. (2007b) and Hildebrandt et al. (2009), and best represented the middle point of these two datasets (see Fig. 5a). The 2p-VBS parameters for toluene/ARO1 under high-NO x conditions were thus chosen for the CMAQ simulations.

Xylene/ARO2 parameters
The lumped aromatics category ARO2 in SAPRC07 (Carter, 2010) contains xylenes, as well as the PAH naphthalene. In Fig. 5b, chamber data using naphthalene precursors (Chan et al., 2009;Kautzman et al., 2010;Shakya and Griffin, 2010) were differentiated from chamber data using xylene (Cocker et al., 2001b;Song et al., 2005;Ng et al., 2007b;Zhou et al., 2011) and "other" ARO2 precursors, e.g., methyl-and ethylbenzenes . There were significant differences in yields among these ARO2 precursors, particularly between naphthalene and xylene/"other". These differences were reflected in the predicted SOA yields using the naphthalene VBS parameters of Pye et al. (2010), based on the chamber data of Chan et al. (2009), and the xylene 2p parameters of Carlton et al. (2010), based on the chamber data of Ng et al. (2007b). Each of these parameterizations represents the available data well, with the caveat that neither parameterization is appropriate for naphthalene and xylenes/other lumped ARO2 compounds. The high-NO x naphthalene VBS parameters of Pye et al. (2010) were used to obtain 2p-VBS parameters, which are provided in Table 2. The naphthalene 2p-VBS parameters were not used in the CMAQ simulations because naphthalene is not treated explicitly in the SAPRC gas-phase chemical mechanism but is lumped with xylene.
The high NO x ARO2 VBS parameters of Lane et al. (2008a)/Tsimpidi et al. (2010, from which the 2p-VBS parameters were derived, were calculated from the low NO x ARO2 VBS parameters (Lane et al., 2008b) based on the chamber data of Ng et al. (2007b), by applying a M odependent yield correction based on the α-pinene parameterizations of Pathak et al. (2007a). This approach led to a significant overestimation of SOA formation from xylene and other ARO2 aromatics (excluding naphthalene). Thus, the default CMAQ parameters for ARO2 under high-NO x conditions were retained as the best available.

Alkane/ALK5 parameters
The lumped alkane species ALK5 includes C6 and higher cycloalkanes, C7 and higher n-alkanes, and C8 and higher branched alkanes. From an emissions perspective, the lumped ALK5 species is largely representative of a ∼ C8 alkane (e.g., Carlton et al., 2010;Pye and Pouliot, 2012). The CMAQ ALK5 parameters are from Pandis et al. (1992)/Strader et al. (1999, based on the chamber experiments of Grosjean and Seinfeld (1989). They roughly represent SOA formation from C8-C10 n-alkanes as measured by Grosjean and Seinfeld (1989). The VBS parameters (Lane et al., 2008b;Tsimpidi et al., 2010) used to obtain the 2p-VBS parameters were based on chamber data of Wang et al. (1992), Takekawa et al. (2003), and Lim and Ziemann (2005) for C8-C15 n-alkanes and methylcylcohexane (Wang et al., 1992). Due to limited data availability, both Pandis et al. (1992) and Lane et al. (2008b) derived only one-product fits for this class of lumped alkanes. Calculated SOA yields with the CMAQ 2p parameters (Carlton et al., 2010) and 2p-VBS parameters were compared with chamber data from Lim and Ziemann (2009) for linear and cyclic C8 alkanes (Fig. 6). The default CMAQ parameters were in good agreement with that data for linear C8 alkanes, though may overestimate SOA at lower M o (Fig. 6b). The 2p-VBS parameters resulted in higher SOA yields at higher HC levels and M o . This likely was due to the inclusion of cyclic alkane data in the fitting. Lim and Ziemann (2009) demonstrated that alkane SOA yields followed the trend: cyclic alkanes > linear alkanes > branched alkanes; furthermore within each class, SOA yields increased with carbon number.
In addition to 2p and 2p-VBS parameters, VBS parameters from Presto et al. (2010) were compared with the data of Lim and Ziemann (2009) (Fig. 6). Presto et al. (2010) derived VBS parameters for C12-C17 n-alkanes, based on n-heptadecane data (2p-VBS parameters based on Presto et al. (2010) are provided in Table 2). The theoretical yield curves showed an increase in SOA yield as a function of carbon number, as observed by Lim and Ziemann (2009). At high M o , the calculated SOA yields were higher than the reported yields of Lim and Ziemann (2009), particularly for the C12 alkanes; however, the experiments were conducted over very different M o ranges with no overlapping data points and thus, the yields may not be directly comparable. At low M o (Fig. 6b), there are no data points for evaluation other than those from which the parameterization of Presto et al. (2010) was derived (not shown). Based on current emissions inventories and the results of Presto et al. (2010), the 2p-VBS parameters were chosen the best available.
The SOA yields from cyclic and C12 and higher n-alkanes (Fig. 6) and naphthalene (Fig. 5) were significantly underestimated by the default 2p parameters for the volatile SOA precursors with which they are lumped (cyclic and > C12 alkanes with ALK5 and naphthalene with ARO2) in the gas-phase chemical mechanism SAPRC07 (Carter, 2010). If emissions of such compounds are indeed sufficient to contribute measurably to SOA, as indicated by ambient observations (alkanes: Liu et al., 2011;Russell et al., 2011;de Gouw et al., 2011;naphthalene: Chan et al., 2009;Shakya and Griffin, 2010;Zhang and Ying, 2012), separation of the VOCs with intermediate to low volatility from VOCs in the gasphase and aerosol models likely will result in more accurate SOA predictions. Pye and Pouliot (2012) recently reported on the explicit treatment of C6-C19 alkanes and PAHs, represented by naphthalene, in CMAQv.5.0. They concluded that C6-C19 alkanes and PAHs could represent 20-30 % of SOA formation (up to 50 ng m −3 ) with highest contributions in winter, using current emissions inventories. Though similar modification of SAPRC07 and CMAQv4.7.1 was outside the scope of this study, it is recommended that SOA formation by cyclic alkanes, ≥ C12 n-alkanes and naphthalene be treated independently in future model applications.

CMAQ model simulations
The base case CMAQ predictions for total SOA, averaged over 15-31 July 2006 are shown in Fig. 7. In regions with the highest predicted concentrations of anthropogenic SOA (up to 1 µg m −3 ), a net decrease in anthropogenic SOA (up to 20 %) was predicted (figure not shown); the use of best available parameters for ARO1/toluene (2p-VBS) resulted in a slight increase in predicted SOA mass while the use of best available parameters for ALK5 (2p-VBS) resulted in a slight decrease. In regions with the highest predicted concentrations of biogenic SOA (1-2 µg m −3 in northern California, southern Oregon and Southeastern US), the predicted increase in total SOA mass was significant, ∼ 10-15 % for high-NO x conditions and up to ∼ 200 % (∼ 3 µg m −3 ) for low-NO x conditions (see Fig. 8). The increase in total SOA was largely a consequence of an increase in biogenic SOA (see Supplement Fig. S4) attributed to the use of the 2p-VBS parameters for lumped monoterpenes. The predicted increases in total SOA correspond to increases in PM 2.5 of up to 7 % and 55 % for the high-and low-NO x conditions, respectively, in Western US where PM 2.5 concentrations in the base case were ∼ 2 µg m −3 . The 2p-VBS fitting resulted in a 2-fold decrease in the C* 1 value for lumped monoterpenes (high NO x ), from C* 1 = 14.8 µg m −3 (default) to C* 1 = 6.3 µg m −3 , which increased the predicted contribution of traditional monoterpene SOA (excluding oligomerization) to total SOA by ∼ 10 % in the Southeastern US (from 15-30 % in base case, figure not shown). Under low-NO x conditions, that contribution was increased by ∼ 20-30 % in the Southeastern US (figure not shown). Figure 9 shows the fraction of RO 2 reacting with NO as compared to that reacting with HO 2 , and thus the fractional weighting of high-vs. low-NO x parameters, illustrating the relative importance of high-vs. low-NO x pathways in the CMAQ simulations. As noted previously, this fractional weighting is considered in CMAQv.4.7.1 for anthropogenic precursors only, therefore the sensitivity simulations performed here using the high-and low-NO x 2p-VBS monoterpene parameters indicate the range of SOA that can be formed for the limiting assumptions. It can be seen in Fig. 9 that based on current treatment, low-NO x pathways and therefore low-NO x parameters are relevant for SOA formation in many regions of the US.
In Fig. 10, model-based secondary organic carbon (SOC) mass concentrations are compared with observationallybased SOC concentrations. Observationally-based SOC concentrations were calculated according to the method of Yu et al. (2007) using measured organic carbon (OC) and elemental carbon (EC) data from 155 IMPROVE sites. The sites were grouped into six regions: West Pacific, West, Central, Midwest, Northeast, and Southeast; 115 of the 155 sites are in locations where ≥ 50 % of RO 2 was predicted to react with HO 2 (i.e., low-NO x pathway; see Fig. 9). For all three cases, the model-and measurement-based trends in predicted SOC mass concentration follow a similar pattern from region to region, except for the Midwest. For all regions, model-based SOC mass concentrations were in better agreement with measurement-based SOC using the best available parameters, particularly for the low-NO x case. Averaged over all sites, the percent bias improved from −63 % to −15 % from the base case to the best available low-NO x case. This is consistent with the higher predicted SOA yields at low M o and better agreement with chamber data achieved by the best available parameters in the parameter comparisons. SOC mass still was significantly underpredicted in the Fig. 8. Difference in total SOA averaged over 15-31 July 2006 between the best available parameter simulation and the base case CMAQ simulation: using the high NO x 2p-VBS parameters for lumped monoterpenes (a), and using the low NO x 2p-VBS parameters for lumped monoterpenes (b). Fig. 9. The fraction of RO 2 reacting with NO (vs. HO 2 ), indicating the relative importance of high-vs. low-NO x pathways, respectively, predicted in the CMAQ simulations averaged over the simulation period, 15-31 July 2006.
Midwest, Central and Northeast regions, where the percent bias were −43 %, −23 % and −21 % respectively, for the best available low-NO x case, suggesting "missing" anthropogenic source(s) and/or other pathway(s).

Conclusions
The linkages between experimental conditions, parameter optimization, and predictions of SOA were explored here by: (1) comparing calculated SOA yields and mass concentrations using 2p, VBS, and newly-developed 2p-VBS parameters with a comprehensive list of published smog chamber data for common volatile SOA precursor species; (2) selecting a set of "best available" (BA) parameters defined by best agreement with published chamber data; and (3) analyzing CMAQv4.7.1 model output for the default (base case) and selected sensitivity (BA-highNO x and BA-lowNO x ) simulations. With regard to parameter fitting, VBS parameterizations may be more robust and less likely to underestimate SOA formation at atmospherically relevant M o ranges when data are sparse. However, their use is not justified when the underlying data are limited or event absent, especially at low, atmospherically relevant HC and M o . Extrapolating from high-to low-NO x conditions, and vice versa, does not pro- Fig. 10. Regional comparison of model-based (base case and best available high-and low-NO x cases) and observationallybased secondary organic carbon (SOC) mass concentrations. Observationally-based SOC concentrations were calculated from data averaged over the simulation period from 155 IMPROVE sites. duce reliable parameters, particularly when further extrapolating across precursors: data are required for each precursor under a range of NO x levels (NO 2 / NO ratios). For the common SOA precursors treated in the 2p framework, data gaps are most significant for photo-oxidation of monoterpenes and sesquiterpenes under a range of HO 2 : NO : NO 2 levels and for alkanes at low M o .
While only SOA formation in the traditional view was considered, VOC oxidation followed by condensation of semi-volatile oxidation products, some insight was gained on intermediate to low volatility SOA precursors. The SOA yields from naphthalene and C12 and higher n-alkanes, which are currently lumped with VOCs in the gas-phase chemical mechanism SAPRC07 (Carter, 2010), were significantly underestimated by the default 2p parameters. 2p-VBS parameters are provided for these precursors, as well as POA, though the current SAPRC07/CMAQv4.7.1 configuration did not allow for their evaluation in the context of chemical transport modeling.
Recognizing that many important processes currently are not treated in the CMAQ SOA model (e.g., oxidation of intermediate to low volatility organic compounds, partitioning of POA, and kinetically controlled partitioning), the use of the selected best available parameters in CMAQ nonetheless significantly improved the agreement between modeland measurement-based SOC mass concentrations. More importantly, as demonstrated, the choice of model parameters will impact source-attribution analyses, as well as spatial and temporal distributions of modeled SOA (through the physicochemical properties of SOA they represent), which may adversely affect the accuracy of air quality and climate predictions from CTMs that rely on parameterizations of chamber experiments. In addition to the implementation of more advanced representations of important gas-and particle-phase processes in CMAQ, better representation of "first generation" SOA formation is also needed. Development and application of the 2p-VBS parameters for ALK5, toluene, and particularly monoterpenes, advances that goal within the 2p modeling framework; however, critical data gaps exist for many of the SOA precursors under atmospherically relevant conditions, currently limiting the progress that can be made with chamber data fitting approaches.