Rates of secondary organic aerosol (SOA) formation, due to the reactions of aromatics and monoterpenes, were estimated for southeast Texas by incorporating a modified version of the Statewide Air Pollution Research Center's chemical mechanism (SAPRC99) into the Comprehensive Air Quality Model with extensions (CAMx version 3.10). The model included explicit representation of the reactions of five SOA precursors (α-pinene, β-pinene, sabinene, d-limonene, and Δ3-carene). Reactions of each SOA precursor with O3, OH radical, and NO3 radical were included. The model also included separate reactions for low- and high-SOA-yield aromatic groups with the OH radical. SOA yields in the mechanisms were estimated using compound-specific yield information (ΔSOA/ΔHC) derived from smog chamber experiments conducted by J. R. Odum and colleagues and R. J. Griffin and colleagues. The form of the SOA yield model was based on the work of J. R. Odum and colleagues and is a function of existing organic aerosol concentrations. Existing organic aerosol concentrations were estimated on the basis of ambient measurements of total organic carbon in southeast Texas. The reactions of monoterpenes (predominantly α-pinene and β-pinene) with ozone led to the most regional SOA formation, followed by monoterpenes with the nitrate radical. Aromatic-OH reactions led to less regional SOA formation compared to monoterpenes; however, this formation occurs close to the urban and industrial areas of Houston. In contrast, SOA formation due to the reactions of monoterpenes occurred in the forested areas north of the urban area. The results of this study are in qualitative agreement with estimates of SOA formation based on ambient data from the same time period.
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 In the United States, the mass of atmospheric particles, with aerodynamic diameters less than 2.5 microns (PM2.5, fine particulate matter), is dominated by the mass of inorganic salts and carbonaceous material [NARSTO, 2003]. The chemistry associated with the formation of the inorganic salts (primarily ammonium sulfate and ammonium nitrate) is reasonably well understood, however, the detailed chemical composition and the formation mechanisms for carbonaceous material in PM2.5 remain largely uncharacterized.
 The carbonaceous material in PM2.5 is generally characterized as either elemental carbon or organic carbon. Elemental carbon (EC) consists of graphitic structures and other chemical components, produced in high-temperature combustion processes, which are emitted directly to the atmosphere. The organic carbon (OC) in PM2.5 exists as thousands of different compounds. Some of these compounds are emitted directly (primary organic carbon); others are low-volatility compounds produced by reactions in the atmosphere, that condense onto existing PM (secondary organic carbon) or that nucleate to form new particles. Secondary organic carbon mass in PM2.5 along with the noncarbon mass associated with these compounds is often referred to as secondary organic aerosol (SOA). The sources, spatial distribution, and temporal distribution of SOA concentrations have been characterized for a relatively small number of areas.
 This work will examine the formation mechanisms for SOA in southeast Texas. Previous analyses have shown that organic compounds comprise 30–40% on average of PM2.5 mass throughout the region and in all seasons [Tropp et al., 1998; Russell et al., 2004]. In southeast Texas, primary organic carbon is the largest fraction of organic compounds during winter months; however, secondary organic carbon was predicted to be at a maximum and roughly equivalent to primary organic carbon during the ozone season [Russell and Allen, 2004]. The work presented here is the first attempt to predict SOA formation rates in southeast Texas using a three-dimensional photochemical grid model.
2. SOA Formation Mechanisms
 Atmospheric reactions of volatile organic carbon (VOC) gases can, for some compounds, lead to the formation of lower-volatility oxidized hydrocarbons. Secondary organic aerosol (SOA) is generally presumed to form as these low-volatility oxidized hydrocarbons condense onto existing particles or nucleate to form new particles. Alternative mechanisms for the formation of SOA have been proposed, including the polymerization of low-molecular-weight aldehydes on acidic aerosol surfaces [Jang et al., 2002; Kalberer et al., 2004]; however, little quantitative information exists concerning these alternative mechanisms.
 Condensation of low-volatility reaction products to particulate matter is widely considered to occur via physical absorption, and the equilibrium partitioning of low-volatility reaction products between gas and particle phases is frequently modeled using equation (1) [Pankow, 1994].
gas-particle partitioning coefficient, m3/μg;
aerosol organic phase species concentration, ng/m3;
gas-phase species concentration, μg/m3;
total suspended particle matter concentration, μg/m3;
fraction of organic matter in the aerosol;
mean molar mass of the organic matter, g/mol;
activity coefficient of the species in the absorbing organic matter;
gas constant, equal to 8.314 J/mol K;
liquid vapor pressure of pure organic compound, Pa.
 In all cases, m3 refers to volume of atmosphere. The reactions of a single VOC may form multiple condensable products. Characterization of all condensable reaction products from a single precursor is challenging because many products are hard to identify. As a result, detailed reaction mechanisms have been proposed only for a small number of VOCs [Kamens et al., 1999; Yu et al., 1999; Kalberer et al., 2000; Jaoui and Kamens, 2001]. Since reaction pathways and condensable product structures have remained largely unknown, most SOA formation has been characterized by measuring total SOA mass formed per VOC mass reacted, or yield Y:
where ΔHC is the amount of hydrocarbon reacted (μg/m3) and ΔMo is the organic aerosol mass produced (μg/m3).
Odum et al.  proposed the following model for SOA yield, which is the sum of the individual yields over i condensable reaction products, and which accounts for gas/particle partitioning:
where Mo is total absorbing organic aerosol mass (μg/m3), αi is the stoichiometric coefficient of the reaction product i (mass/mass), Kom,i is the partitioning coefficient of i to the organic phase, defined as Kom = (FOM/Mo)/A.
Equation (3) has been used as a model for SOA formation, using empirical estimates of α and K from smog chamber oxidation experiments [Odum et al., 1997a, 1997b; Griffin et al., 1999]. Using this approach, SOA formation is only a function of reacted hydrocarbon, ΔHC, and existing absorption mass Mo. More recent models [Barthelmie and Pryor, 1999; Kamens and Jaoui, 2001; Pankow et al., 2001; Seinfeld et al., 2001] for SOA have been more explicit, including the limited reaction mechanism data available and partitioning the reaction products on the basis of first principles (i.e., calculating α and K explicitly). Such an approach requires detailed information on gas- and particle-phase compositions, which is often not available, or which is assumed in order to predict SOA. The lack of information on identities and physical properties of semivolatile products is a major source of uncertainty in predicting SOA formation.
 A small but growing number of studies have incorporated SOA formation into airshed models and some important insights have been gained. Notably, Pandis et al.  modeled SOA formation in the Los Angeles basin and found that both anthropogenic and biogenic precursors were important in forming SOA. Strader et al.  improved upon these methods by accounting for gas/particle partitioning and found that SOA formation was a strong function of temperature in the San Joaquin valley in California. Recently, R. J. Griffin and coworkers have reported on the development of a highly detailed model for SOA formation, including chemical mechanism formulation [Griffin et al., 2002b], partitioning of semivolatile organic compounds [Pun et al., 2002a], and application of the model to the Southern California area [Griffin et al., 2002a]. The authors found that SOA from anthropogenic sources dominated aerosol in the urban area and that biogenic precursors contributed more in the rural areas than urban areas. The SOA was dominated by hydrophobic compounds from both biogenic and anthropogenic precursors. There are a number of other examples of SOA models: in grid models [e.g., Meng et al., 1998; Pun et al., 2002b], in box models [e.g., Barthelmie and Pryor, 1999; Kamens and Jaoui, 2001] and in Lagrangian trajectory models [Andersson-Skold and Simpson, 2001].
 Although three-dimensional photochemical grid models are becoming more sophisticated in simulating SOA formation, most succeed only in distinguishing the relative importance of major classes of SOA precursors, notably between biogenic and anthropogenic precursors, but stop short of a comprehensive quantitative characterization of SOA formation. Quantitative characterizations of the SOA formation potential of individual compounds are limited because secondary condensable reaction products have only been characterized for a few precursors; ambient data with which to evaluate any model for SOA formation are also limited. This work will expand upon the previous models of SOA formation by modeling, within a three-dimensional photochemical grid model, the reactions of individual hydrocarbon precursors, and by comparing these predictions to observations made during a large air quality field program conducted in southeast Texas.
 The grid model chosen for this research was Comprehensive Air Quality Model with Extensions (CAMx) version 3.10 (referred to as CAMx31). CAMx31 is a public domain model available at http://www.camx.com. The modeling episode used in this research was developed by the Texas Commission on Environmental Quality (TCEQ) and covered the 10-day 23 August 2000 through 1 September 2000 period. The tri-nested modeling domain is shown in Figure 1 and consists of a large “regional” domain at 36-km resolution, an “east Texas” domain at 12-km resolution, and a Houston-Galveston, Beaumont–Port Arthur (“HGBPA”) domain at 4-km resolution. This episode coincided with two major field studies in the area: Texas Air Quality Study 2000 (TXAQS2000) and the intensive sampling period of the Gulf Coast Aerosol Research and Characterization Program (GC-ARCH or Houston Supersite for PM). The episode is referred to as the TXAQS episode. The reader is referred to the following two URLs where numerous documents and technical reports can be accessed that describe the TXAQS episode development in detail (these links were accessed on 12 September 2003): http://www.tnrcc.state.tx.us/air/aqp/airquality_photomod.html#section4 and http://www.tnrcc.state.tx.us/air/aqp/airquality_contracts.html#section3.
 The representation of gas-phase compounds and chemistry is a key component of any model for SOA formation. A widely used chemical mechanism for ozone modeling is the Carbon Bond IV (CBIV) mechanism [Gery et al., 1989], which uses a lumped structure approach for gas-phase compounds. Since formation of SOA can vary considerably between compounds it is desirable to use a chemical mechanism with a more detailed representation of gas-phase compounds. The most recent Statewide Air Pollution Research Center chemical mechanism (SAPRC99) uses a lumped molecule approach to group compounds, allows individual chemical species to be explicitly represented, and comes with software that allows the user to control lumping and customize the mechanism [Carter, 1990, 1995]. The SAPRC99 software was downloaded from http://pah.cert.ucr.edu/∼carter/SAPRC99.htm. CAMx31 contains a standard, fixed parameter version of SAPRC99 [see Carter, 2000] as one of its built-in chemical mechanisms. For this research, however, SAPRC99 software was used to create a custom, fixed-parameter chemical mechanism treating important SOA precursors explicitly. More specifically, five monoterpenes were represented explicitly in the reaction mechanism (α-pinene, β-pinene, sabinene, d-limonene, Δ3-carene), and aromatics were lumped on the basis of their SOA-forming potential (high-yield aromatics, low-yield aromatics and no-yield aromatics).
 The reaction mechanisms for the five individual monoterpenes were drawn from the SAPRC99 software. Each individual monoterpene reacts with the hydroxyl radical (HO· in SAPRC99 notation), ozone (O3), nitrate radical (NO3) and excited oxygen atom (O3P). Information in the SAPRC99 user's guide [Carter, 2000] describes how these reaction mechanisms were generated on the basis of reactions of similar alkenes and limited experimental data [e.g., Atkinson, 1997a, 1997b]. Table 1 lists the reactions of the monoterpenes considered as explicit chemical species in this work, their kinetic rate parameters, and their SAPRC99 model representations.
Table 1. SAPRC99 Reaction Mechanisms/Notation for the Reactions of α-Pinene, β-Pinene, Limonene, Δ3-Carene, and Sabinenea
SAPRC99 Reaction Mechanism
Data in Table 1 are taken from Carter . Reaction rate constants are of the form k = A*exp (−Ea/RT)*(T/300)B, where B = 0 for all reactions. The units of Ea are kcal/mol, and the units of A are cm3 molec−1 s−1. The reader is referred to SAPRC99 documentation for more detail on reaction product identity and SAPRC99 species and operators. Read 1.21E-11 as 1.21 × 10−11.
 The lumping of aromatic compounds into groups based on SOA formation potential was based on the work of Odum et al. [1997b]. Compounds were grouped into either a high-SOA-yield or low-SOA-yield category. A number of aromatics were classified as no-SOA-yield aromatics simply because of lack of SOA formation data; however, as shown in Table 2, these compounds accounted for only 7% of all aromatic emissions in the southeast Texas domain used in this work. The standard SAPRC99 mechanism splits aromatics into one of two lumped groups on the basis of whether the aromatic-OH rate constant is less than or greater than 2 × 10−4 ppm−1min−1 (for low-reactivity and high-reactivity aromatics, respectively). A further split of aromatic compounds into the three SOA yield categories used in this work resulted in six lumped aromatic categories (three SOA yield categories, high, low and none, for each of two reaction rate categories, high and low); however, no aromatic compound fell into the low-SOA-yield, low-reactivity category, resulting in five lumped groups (as listed in Table 2). Table 3 lists the SAPRC99 reactions used for the five lumped aromatic model species in SAPRC99 notation. The reader is referred to SAPRC99 documentation [Carter, 2000] for details on aromatic reaction mechanisms and lumped aromatic reaction mechanisms.
Table 2. Texas Statewide Aromatic Emissions From Different SOA Yield Categoriesa
Texas Anthropogenic Emissions, Typical Day, 103 kg (%)
Compound-specific emissions were grouped into yield categories on the basis of data given by Odum et al. [1997b].
High SOA yield, low reactivity
Low SOA yield, high reactivity
High SOA yield, high reactivity
No SOA yield, high reactivity
No SOA yield, low reactivity
Table 3. SAPRC99 Reaction Mechanisms/Notation for the Reactions of the Five Defined Lumped Aromatic Groupsa
SAPRC99 Reaction Mechanism
Reaction rate constants are of the form k = A*exp (−Ea/RT)*(T/300)B, where B = 0 for all reactions. The units of Ea are kcal/mol, and the units of A are cm3 molec−1 s−1. The reader is referred to SAPRC99 documentation for more detail on reaction product identity and SAPRC99 species and operators.
 All compounds other than aromatics and monoterpenes were represented/lumped in the same way as in the standard SAPRC99 mechanism. Rate constants and stoichiometry for lumped groups (including those in Table 3) were derived using the relative mix of compounds in a Texas-wide anthropogenic emissions inventory rather than the “typical urban” mix of VOC used in the standard SAPRC99 fixed-parameter chemical mechanism. The lumped parameters are described, in detail, by Russell . The new mechanism is referred to as S99SOA.
 Two major tasks were performed to implement S99SOA into the grid model: development of a modeling emissions inventory in S99SOA model species, and modification of SAPRC99 software and CAMx31 software to accommodate the chemical mechanism source code. Finally, an independent module was added to CAMx31 to predict yields of SOA from the concentration of oxidation products of precursors.
3.1. Emissions Inventory Development
 The S99SOA emissions were developed by (1) speciating raw (total VOC) emissions to individual VOC compound emissions and (2) lumping VOC compounds to S99SOA model species. Raw emissions data were obtained from the Texas Commission on Environmental Quality (TCEQ) for all anthropogenic sources in the modeling domain and these emissions were speciated by applying speciation profiles (relative amounts of each compound in the total emissions) specific to each emissions source. Speciation profiles for Texas point sources were derived directly from a detailed speciated inventory compiled by the TCEQ (documentation and files downloaded from http://www.tnrcc.state.tx.us/air/aqp/airquality_photomod.html#ei3a). Speciation profiles for Texas mobile sources were obtained from an emissions measurement study in a vehicular tunnel during the TXAQS period (ftp://narsto.esd.ornl.gov/pub/EPA_Supersites/houston/WASHBURN_TUNNEL) Speciation profiles for all other anthropogenic sources were obtained from EPA's SPECIATE3.2 model (http://www.epa.gov/ttn). The bottom-up speciation of point sources and the region-specific mobile emissions composition resulted in the most detailed modeling inventory to date for Texas.
 A Microsoft Excel tool called emitdb.xls (downloaded from ftp://ftp.cert.ucr.edu/pub/carter/emitdb/emitdb.xls) was used to create a set of split factors (moles of S99SOA model species per mass total VOC) from each speciation profile. Emitdb.xls automates the assignment of individual compounds to CB-IV and standard SAPRC99 model species (i.e., lumping). The tool was modified to process S99SOA species. Once all split factors had been created, TXAQS emissions were processed to model-ready format using the Emissions Preprocessor System version 2.0. EPS2.0 can be obtained from EPA (http://www.epa.gov/ttn); however, the version used here resides on the UNIX systems at the Center for Energy and Environmental Resources at the University of Texas and has been modified and upgraded considerably from the original release.
 Biogenic emissions were processed directly into model ready format using the Global Biosphere Emissions and Interaction System (GLOBEIS) version 2.2 (available at http://www.globeis.com). This version was modified to output emissions in S99SOA model species by adding speciation profiles for nonterpene, nonisoprene reactive emissions after Guenther et al. . GLOBEIS2.2 was also modified to speciate total monoterpene emissions to fourteen individual monoterpene compounds using data summarized by Geron et al. . Although monoterpene speciation was not available for all tree species in the domain, ∼90% of monoterpene emissions in southeast Texas were from trees with speciation profiles in the reference. Tree species with no known speciation profile were assigned an average monoterpene emissions speciation profile. This biogenic monoterpene inventory is the most detailed to date for the area. Table 4 summarizes the emissions of the SOA precursors in southeast Texas (within the 4-km “HGBPA” modeling domain shown in Figure 1). Biogenic emissions of monoterpenes, especially α- and β-pinene, dominate the emissions of SOA precursors considered here. Figure 2 shows the spatial distribution of ground-level (low-level) aromatic and monoterpene emissions in the 4-km “HGBPA” modeling domain. Elevated emissions of these compounds are insignificant compared to low-level emissions. Areas of high aromatic emissions occur in the urban/industrial centers of Houston. Areas of high monoterpene emissions are located just north of the urban/industrial areas of Houston.
Table 4. Daily Emissions of SOA Precursors in the 4-km Houston-Beaumont Southeast Texas Modeling Domain (HGBPA Domain in Figure 1)a
Units are103 kg/d.
3.2. SOA Formation Module
 The model for SOA formation used in this research is based on the gas/particle partitioning yield coefficient first proposed by Odum et al. :
This is a summation over i condensable reaction products from a single precursor. Kom refers to a partitioning coefficient to organic matter (om) and will be referred to simply as K hereinafter. Partitioning of condensable organic compounds is assumed to occur predominantly to organic matter in the particle phase.
 The work of Odum et al. [1997a] and Griffin et al.  assumed two hypothetical, condensable reaction products per SOA precursor (i = 2), and derived α1, α2, K1, K2 by fitting equation (3′) to smog chamber results of Y versus Mo for each individual precursor. Aromatics are assumed to be oxidized exclusively by the OH radical; however, as shown in Table 1, the chemical mechanism represents the oxidation of each monoterpene species separately with O3, the OH and NO3 radicals, and O3P. SOA formation has been investigated for O3, OH radical and NO3 radical, and the SOA formation depends on the oxidant [Hoffmann et al., 1997; Griffin et al., 1999]. Griffin et al.  conducted monoterpene oxidation experiments under three conditions: in sunlight with NOx (photo-oxidation experiments), in the dark with NO3, and in the dark with O3; the latter two conditions were used to derive yield parameters that describe aerosol formation from NO3 and O3 oxidation, respectively. Aerosol yields from OH oxidation were calculated in this work from data provided by Griffin et al. and assuming that aerosol yields from individual reactants were additive in photo-oxidation experiments. Specifically, the expected SOA yield from ozone and nitrate radical reactions were subtracted from total SOA formation in the photo-oxidation experiments, to estimate the yield from hydroxyl radical. The most significant assumption made in this analysis was that aerosol formation in a single oxidant system is the same as in a multiple oxidant system, which may be a gross simplification. This method gave a best estimate of aerosol yields from the monoterpene-OH reactions, based on available data. The OH yields were then used to derive yield parameters for OH oxidation of each monoterpene. All yield parameter data are summarized in Table 5, where monoterpene-OH oxidation parameters were calculated on the basis of data presented by Griffin et al. .
Table 5. Empirical Parameter Data for Yield Expressions of SOA Precursors
 The yields of SOA can be adjusted via the partitioning coefficients K to account for the temperature difference between model simulations and smog chamber experiments [Sheehan and Bowman, 2001]:
where the asterisk indicates smog chamber conditions, R is the universal gas constant, and ΔHvap is the latent heat of vaporization.
 A constant value for ΔHvap of 17.0 kcal/mol was chosen for all condensable products, following an example in the literature [Sheehan and Bowman, 2001]. The value of ΔHvap itself can vary with temperature; however, this is not considered in this work.
 The gas/particle yields described above were coupled with the S99SOA mechanism developed in this work and were incorporated into the 3-D grid model. In principle, the aerosol concentration of a single condensable product can be written as:
Where SOAi is particle-phase concentration of species i,Ctot,i is total (gas- plus particle-phase) concentration of species i, and xi is mass fraction of component i in the aerosol phase.
 The time rate of change of SOAi (SOA formation), which is calculated by the photochemical model, can be written as
In principle, equation (6) forms the basis for calculating SOA formation in this research, however, the equation was reduced by a set of significant assumptions.
 1. The dxi/dt was assumed to be zero. The mass fraction of condensable product is a function of the processes that govern the partitioning of a compound between the gas and aerosol phase. The partitioning is assumed to be absorptive, and is thus a function of temperature and composition. Although yields are adjusted at the beginning of each model time step for temperature and Mo concentration, the yields are held constant for each time step, even though parameters such as temperature and Mo can change over the length of a time step.
 2. The dCtot,i/dt is contributed to only by chemical reaction. The lack of data on individual condensable reaction products does not permit explicitly accounting for all other processes contributing to gain and loss of these compounds such as deposition and dilution/entrainment, and chemical reaction is assumed to be the dominant process. Condensable product formed from chemical reaction, assuming first-generation products, is assumed to be equal to
where d HC is the amount of precursor reacted.
 3. The dSOA/dt for each hydrocarbon precursor (e.g., α-pinene) is calculated directly as the sum of all condensable products from the precursor. This was a necessary result of using the experimental data from the references given above, where only the total SOA formation from individual hydrocarbon precursors was measured and characterized.
 Using the assumptions listed above, equation (6) is reduced to the form as applied in the grid model, where SOA* refers to all SOA formed from a single precursor:
SOA* is calculated for each time step used by the 3-D model's chemistry solver, Δtchem, for each grid cell, and for each precursor-oxidant reaction.
 Although Δtchem is typically 15 min, the mass of SOA formed is summed for each hour. Furthermore, the mass of SOA formed is summed vertically for all cells under the planetary boundary layer (which remains constant for each hour time period). Since the model here calculates only SOA formation, formation in the mixed layer was thought to be more useful than SOA formation in the lowest vertical layer of the model, since, presuming the mixed layer is indeed well mixed, SOA formation aloft may be contributing to ground-level SOA concentrations significantly. SOA formation is predicted separately for each of the five monoterpenes via OH-radical, NO3-radical and O3 oxidation, and for high- and low-yield aromatics via OH-radical oxidation. There are a number of important assumptions to the SOA model that are worth discussing:
 1. SOA yield is an empirical estimation of SOA formation and is used in lieu of a first principles approach to calculating the amount of secondary organic mass that partitions to the aerosol phase. A comprehensive first principles approach is limited by lack of physical and chemical data on semivolatile reaction products from the precursors in question.
 2. The parameters used to calculate Y were derived from smog chamber experiments under chemical conditions very different from ambient air and during time periods different than Δtchem. The time rate of change of SOA formation is expected to be different in ambient air versus controlled smog chamber experiments, since semivolatile product formation is known to occur via complex reaction pathways and is dependent on many intermediate reactant concentrations. The assumption of first-generation reaction products may not always be valid [Dechapanya et al., 2003a, 2003b].
 Despite the simplified nature of the model used here, the lack of experimental data on SOA formation prevents detailed first principles calculations of SOA formation from the set of SOA precursors considered in this research. The yield model does capture the gas-particle partitioning characteristic observed in smog chambers and provides a consistent way to evaluate both anthropogenic and biogenic precursors in a grid model.
3.3. Estimation of Preexisting Organic Aerosol Mo
 Previous data analysis showed that ambient organic carbon (OC) in southeast Texas is mostly primary [Russell and Allen, 2004], and it is this primary OC that will likely act as absorbing medium for condensable reaction products. A major limitation to modeling SOA formation is the lack of primary OC emissions inventories. There is currently no primary OC inventory compiled for the modeling domain used in this work. The common approach to modeling SOA is to make “rough” approximations of primary OC emissions or to assume that secondary OC partitions only to a solution of secondary reaction products, thus ignoring primary OC as partitioning medium. Both of these approaches can introduce significant uncertainty in predicting SOA.
 The Mo concentrations in this research were estimated from ambient data that were specific to the modeling episode. It was assumed that the total amount of organic carbon in PM2.5 was a good estimate of total Mo. The PM2.5 monitoring network in southeast Texas is extensive, and estimates of total OC (i.e., Mo) were obtained by interpolating Federal Reference Method, ambient measurements of OC, to model grid cells within a domain bounded by the southeast Texas area PM monitoring sites. The kriging interpolation method was chosen for the interpolation (point kriging, linear variogram, slope = 1, no drift). The FRM data are 24-hour average concentrations. Rather than assuming that these concentrations were constant over the day, hourly measurements of total PM2.5 mass (as measured using TEOM instruments) were used to allocate the daily average OC mass to specific hours. Representative interpolations of Mo are shown in Figure 3.
 Although there is uncertainty associated with interpolation in general, the uncertainty associated with estimating emissions from thousands of sources is avoided. The area in which Mo fields were interpolated, and also in which SOA formation is calculated, is referred to as the SOA formation subdomain, and is shown in Figures 2 and 3. Ambient Mo fields were confined to a small domain near Houston-Galveston. Mo concentration beyond these boundaries were not estimated and this prohibited the model from solving for SOA concentrations since transport in and out of the subdomain could not be determined without assuming arbitrary boundary conditions for SOA concentrations.
 Prior to presenting results, it is important to point out that the modified grid model predicts only the hourly SOA formation rate in each grid cell, not ambient concentrations. Formation rates cannot be directly compared to SOA concentrations because other transport and loss processes have not been considered; however, there are two advantages to predicting formation rates. The first is that formation rates are predicted here without the need for emissions inventories of primary organic carbon, which might introduce considerable uncertainty to the results. The second advantage is that the model gives a direct indication of how local emissions contribute to SOA concentrations; in this model formulation, chemical reaction is the only process that produces SOA, and so formation rates show the temporal and spatial distribution of total SOA formation in the airshed.
 SOA formation rates were calculated in units of total mass in the planetary boundary layer (PBL) per hour, since this is the mass that would contribute to concentrations of SOA in the mixed layer. Base case formation rates are also normalized by the volume of each grid column under the PBL giving SOA formation rate per unit volume. Formation rates in these units give another perspective on the contribution of local SOA formation to SOA concentrations.
 The initial base case simulation predicted SOA formation rates for 25 August 2000 through 1 September 2000, but for purpose of this research the results are presented for the 3-day period of 29 August 2000 to 31 August 2000. This period was chosen because SOA formation increased throughout the 3 days, and the results were representative of results on other modeling days. In addition, 31 August 2000 experienced the highest ozone concentrations during the TXAQS episode.
 The totals in Table 6 demonstrate the relative importance of each reaction pathway to SOA formation in southeast Texas. Time series of SOA total formation in grams/hour in the subdomain are shown in Figure 4; only the aromatic pathways and the most significant α-pinene, β-pinene and limonene pathways are shown in Figure 4 (Δ3-carene and sabinene pathways are omitted because they are relatively insignificant compared to the three other monoterpenes).
Table 6. Daily Total Formation of SOA From Each Reaction Pathway for 29, 30, and 31 August 2000a
 The data in Table 6 and Figure 4 suggest that SOA formation via the oxidation of α-pinene by ozone is a major contributor to ambient SOA levels in the area. This formation is linked to the diurnal cycle of ozone which tends to peak in late afternoon. To a lesser extent, α-pinene reactions with the OH and NO3 radicals are also significant. There were no yield parameters available for the reactions of α-pinene with the nitrate radical, and so this pathway was not considered in the model. The reaction of α-pinene with nitrate showed insignificant aerosol formation in at least one study [Griffin et al., 1999]; however, considering the importance of α-pinene chemistry, this pathway should be considered in future modeling. There were also no partitioning parameters available for reactions of limonene with either the nitrate radical or ozone. Limonene-OH reactions form the fourth largest amount of SOA mass on all three episode days (see Table 6). Reactions of limonene with other oxidants may be significant pathways and should be considered in future model applications.
 SOA formation rates in micrograms under the PBL were divided by the volume of each grid column, for each time step, to give formation rates normalized vertically by volume, i.e., in μg/m3 per hour in each grid column. The grid column volume was the grid cell length squared (4000 m × 4000 m), multiplied by the height of the PBL for that time step (note that this was done as a postprocessing step with a FORTRAN script written especially for this purpose; PBL heights were extracted from CAMx input files). Formation rates in μg/m3-h give a closer estimate of how much SOA is contributing to concentration increases in each cell; however caution should be taken to infer any information about absolute SOA concentrations since other gain and loss processes are not taken into account.
Figure 5 shows time series of hourly SOA formation rates in μg/m3-h, averaged over all grid cells in the SOA formation subdomain (also referred to as the mean grid cell SOA formation rate). The figure shows that the relative importance of nitrate reactions is much greater when normalized by volume, and this is a result of nitrate reactions occurring under lower mixing heights. Strong SOA formation (in units of μg/m3-h) by ozone reactions occurs at similar times as formation by nitrate reactions, in the 1900–2200 local time (LT) period. The relative importance of ozone to nitrate reactions increased during this period when SOA formation was normalized by volume, indicating that SOA formation by ozone is generally occurring in locations with even lower mixing heights than SOA formation by nitrate. This is not unexpected since the mixing height changes both spatially and temporally. Note also that the relative importance of OH reactions is much less when SOA formation is normalized by volume. SOA formation by OH reactions occurs at midday, when mixing heights are highest. The relative importance of SOA formation from aromatic precursors is less for this same reason.
Figures 6a through 6d show the spatial distributions of daily SOA formation (μg/m3-d) from aromatics with OH, from all five monoterpenes (summed) with OH, from all five monoterpenes with NO3 and from all five monoterpenes with O3, respectively. It should be noted that SOA formation rates from α-pinene and β-pinene comprised the vast majority of the monoterpene-SOA formation. The spatial distribution of SOA formation from these two compounds individually is virtually identical to the spatial distributions of SOA formation from all monoterpene compounds shown in Figures 6b through 6d. These are shown for 30 August 2000 for the SOA formation subdomain. Figures 6a through 6d show that the reactions of monoterpenes with ozone contribute the most to SOA mass formation, and Figures 4 and 5 show this is almost entirely α-pinene. The SOA formation from monoterpene reactions is spatially very similar to the distribution of biogenic emissions. It is expected that monoterpene-SOA formation is spatially similar to biogenic monoterpene emissions, since these dominate the anthropogenic monoterpene emissions in the inventory (see Table 5). The notable exception to SOA formation occurring near emission sources is for the SOA formation via nitrate reactions, which occurs much closer to urban and industrial Harris County, at the edge of areas where biogenic emissions increase. This indicates that nitrate, formed in plumes near the urban and industrial centers, is reacting quickly with any monoterpenes in the atmosphere.
Figure 6a shows that SOA formation rates from aromatic precursors are lower than formation rates from monoterpene pathways; however, aromatic precursors lead to SOA formation over the urban center of Houston, which is where total PM2.5 mass tends to be highest. From a regulatory standpoint, aromatic precursors may be important if they contribute to total PM2.5 mass concentrations in the urban/industrial areas of Houston.
 The mean grid cell SOA formation rate, summed over all pathways for 31 August 2000 is ∼1 μg/m3 per day. In other words, a hypothetical air parcel traveling through the subdomain for 24 hours on 31 August would gain ∼1 μg/m3 of SOA from local formation if it gained SOA mass each hour at the mean hourly formation rate over all grid cells. Since chemical reaction is the only SOA formation mechanism (SOA is not emitted), and large-scale winds in August are from the south/southeast and presumably have little to no background SOA, it is reasonable to expect SOA concentrations in the local area to be on the same order of magnitude as integrated formation rates of SOA in the subdomain. Data presented by Russell and Allen  suggested SOA concentrations at local sites were on average between 1 and 3 μg/m3. These concentrations as well as total PM concentrations on these episode days were typical for this area and season. It is very encouraging that this first attempt at predicting SOA formation shows such consistent results with concentrations derived from ambient data.
 The mean local SOA formation of 1 μg/m3 is based on the assumption of an air parcel remaining in the subdomain for a 24-hour period. Analysis of animated ozone concentrations shows that local urban plumes are generally advected out of the subdomain in under 24 hours, even under light winds. Under stagnant conditions, however, an air parcel could reside in the subdomain for a period longer than 24 hours (e.g., at wind speeds of 1.5 m/s a parcel would not traverse the south-to-north distance of the subdomain in 24 hours). There may also be background concentrations of SOA that are not insignificant. A value of 1 μg/m3 is taken to be reasonable order-of-magnitude estimate of the contribution of local source emissions to SOA concentrations in the SOA subdomain on a day with intense photochemical activity (as is 31 August). Higher wind speeds, less photochemical activity and loss processes of SOA would lower the contribution of local emissions to SOA concentrations.
 There are a number of additional issues worth considering in the interpretation of the results from this study.
 The first issue is whether there are other significant SOA precursors that have not been considered in this model. Aromatics and monoterpenes were found to be the most significant SOA precursors in Los Angeles, California [Grosjean and Seinfeld, 1989; Pandis et al., 1992]; however, there are other anthropogenic organic compounds that have been shown to have high aerosol yields (see reviews given by Seinfeld and Pandis  and Jacobson et al. ). The industrial emissions in southeast Texas have unusually strong contributions from petrochemical facilities, and there may be important SOA precursors were not included in SOA calculations, for example n-dodecane or naphthalene [Dechapanya et al., 2003c]. On the other hand, there are biogenic precursors that have also not been considered, namely sesquiterpenes, which are known to have high aerosol yields, but whose emissions rates are uncertain [Vizuete et al., 2004]. In addition, recent evidence suggests that isoprene oxidation may contribute significantly to SOA formation simply because of high emission rates [Claeys et al., 2004]. On the basis of the body of available literature on SOA formation, however, aromatics and monoterpenes are assumed to be the dominant SOA precursors.
 The second point is whether SOA formation is occurring via alternate physicochemical mechanisms other than absorptive partitioning of low-volatility reaction products as described by the model used in this research. Recent findings have shed light on the importance of heterogeneous reactions of high-volatility organic compounds on acidic aerosol surfaces resulting in formation of low-volatile particle-phase organics [Jang et al., 2002; Kalberer et al., 2004]. In other words, organic precursors that do not form low-volatility gas-phase reaction products may form significant aerosol in the presence of an acid catalyst. Heterogeneous reactions may increase aerosol yields from biogenic as well as anthropogenic compounds. The chemistry behind these processes is only beginning to be understood, and this will need to be incorporated in a grid model as more data becomes available.
 Finally, it is also important to note that the model used here is a simplified representation of condensable product formation and gas/particle partitioning. The mass yields of condensable products are represented by two fixed values, i.e., α1 and α2, and gas/particle partitioning parameters are for hypothetical species, and do not take into account the interaction of condensable species with existing aerosol components. The smog chamber conditions under which the yield parameters were derived are likely different from actual ambient conditions in southeast Texas. The limitations of using simplified SOA models are not clear; however, the four parameter yield model has represented smog chamber SOA formation remarkably well. In addition, it is not practical from a computational standpoint to include multistep reaction mechanisms for thousands of SOA precursors into a grid model and to track individual aerosol components throughout the simulation. Simplified mechanisms for SOA are a necessity for including this pollutant in grid model applications.
 Since SOA cannot be directly measured, model performance is at best qualitatively assessed. A number of researchers have measured various aerosol properties in southeast Texas from which spatial and temporal patterns of SOA can be inferred. Brock et al.  measured particle volume and number concentrations aboard an aircraft in industrial, urban and power plant plumes from the Houston area during the TXAQS period. Data were presented for 27 and 28 August 2000, when winds were southerly and distinct plumes could be detected advecting north from urban and industrial Houston. There was a significant increase in particle number close to the plumes' origins and there was also a significant increase in particle volume further downwind of some plumes origins. Modeled SO2 chemistry in the plumes showed that formation of ammonium sulfate accounted for particle volume increases, except in the ship channel (industrial) plume. The authors suggested that the additional particle volume in the ship channel plume was from heterogeneous reactions of organic gases on the acidic aerosol surface, in other words SOA from nontraditional precursors. Results from this research suggest that monoterpene-ozone reactions may also be contributing to the observed SOA formation.
Lemire et al.  present measurements of geologically modern carbon during TXAQS by measuring the ratio of 14C/13C in filter samples of total PM2.5 mass. The fraction of modern carbon is defined as the ratio of 14C/13C of the sample to 14C/13C of a reference material of purely non-fossil-fuel carbon. Modern carbon is expected to come from a limited number of sources including vegetative debris, secondary organic aerosol from biogenic precursors, primary organic carbon from biomass burning and primary organic carbon from meat cooking. The fraction of modern carbon (pMC) was calculated at two sites: Conroe (a rural site north of Houston surrounded by biogenic sources) and Aldine (an urban site influenced heavily by motor vehicle emissions and less heavily by biogenic sources). Results showed that the fraction of modern carbon correlated positively with the fraction of organic carbon in the samples. In other words, as the relative amounts of OC to EC increased, the additional OC was not of fossil fuel origin (which excludes SOA from aromatics and other anthropogenic sources). Furthermore, the authors provide arguments that biomass burning, meat cooking and vegetative debris are not contributing significantly to the OC in the samples. The authors conclude that SOA in the samples at both sites is biogenic in origin and that there is a greater biogenic SOA contribution to the OC in samples measured at the Conroe site compared to the Aldine. Model results in this study confirm these findings and suggest that the SOA is from monoterpene oxidation.
 Finally, airborne measurements of aerosol backscatter as a function of height were made during the TXAQS period and data are available online from National Oceanic Atmospheric Administration Environmental Technology Laboratory at http://www.etl.noaa.gov/et2/data/data_pages/texaqs/air_aerosol.html. A spatial analysis of these data showed that for the 28 August through 31 August period, the largest vertical cross sections of high aerosol backscatter occurred on 28 August in plumes that were situated north of Houston (flight paths on the other 3 days did not go very far north of urban Houston). The profiles probably show the same urban/industrial plumes detected by measurements made by Brock et al. The vertical profile showed that the areas of intense backscatter were high in the mixed layer, such that ground based monitors may not have measured high PM concentrations. SOA formation was calculated in this work as an average rate throughout the mixed layer, so vertical gradients of SOA formation were not available. An examination of model results showed little vertical variation of ozone concentrations in the mixed layer in the area of interest, which is an indication that the model is overmixing pollutants vertically. Regardless of the vertical variation in aerosol backscatter, the enhanced backscatter detected north of Houston is consistent with formation of SOA due to monoterpene oxidation.
 SOA formation rates due to multiple chemical pathways were estimated for the areas in and around Houston, Texas. A state-of-the-science photochemical grid model was modified to (1) explicitly represent reactions of monoterpenes and classes of aromatic compounds using a current chemical mechanism, (2) include a detailed emissions inventory for SOA precursors, and (3) calculate the mass rate of SOA formation separately through individual reaction pathways for these precursors. SOA formation was modeled using empirical yields (ΔSOA/ΔHC) derived from smog chamber experiments documented in the literature. The form of the yield model considers gas/particle partitioning as an absorptive process, and ambient measurements of total particulate phase organic carbon concentrations were used as a basis to estimate the partitioning of semivolatile compounds to the particle phase.
 Results indicate that formation of SOA is predominantly via the reactions of biogenic monoterpenes, notably α-pinene, reacting with ozone and to a lesser extent the nitrate radical. Substantial emissions of biogenic monoterpenes occur north of the urban and industrial areas of Houston. Model output shows that ozone and radicals that form as a result of photochemical activity in urban/industrial Houston, advect north and oxidize the biogenic precursors to form SOA. The highest rates of SOA formation in μg/m3-h occur in the early evening.
 The results found here are in qualitative agreement with a number of indicators of SOA concentrations measured during the same time period. The results of this study are most useful in identifying the spatial and temporal distributions, and predominant pathways of SOA formation.