Sub-daily (i.e., 1-hour, 3-hour, or 4-hour duration) styrene, benzene, toluene, ethylbenzene, m/p-xylenes, and o-xylene measurements from 183 monitoring stations were downloaded from the Environmental Protection Agency (EPA) Air Quality System (AQS) database for the Gulf States and Georgia (GA) in 2006 to 2017. These observation data were assigned a measurement error based on their measurement federal method detection limit (MDL). Sub-daily data were averaged to produce daily estimates. To reflect the ubiquitous nature of environmental VOCs,⁴⁴ measured-zero daily values were assigned the mean and variance of log-normal distribution truncated above the federal MDL. Data from collocated monitors were averaged to account for the incompleteness of sub-daily observations and measurement error, yielding unique, daily SBTEX concentrations at each monitoring site (see Supporting Information [SI] for details).

An exploratory analysis revealed that using the natural logarithm of measurements, as opposed to untransformed data, enhanced the visualization of the distribution of the data and the spatial and temporal trends (see SI Figures S1 and S2 for details). This indicated that performing a natural logarithm transformation of the data before BME data fusion would improve estimation performance.

To evaluate the usefulness of emissions data trends for predicting SBTEX, a LUR model was created to predict annual concentrations of each SBTEX component from 2008 to 2017 in the Gulf States. SBTEX emissions data was downloaded from the EPA’s National Emissions Inventory (NEI) and traffic data was downloaded from the Federal Highway Administrations (FHWA) Highway Performance Monitoring System.

Three LUR predictor variables were created for point source and nonpoint source emissions and on-road traffic using the Sum of Exponentially Decaying Contributions (SEDC) method, which assumes pollution from a source will experience a 95% (exponential) decay over a distance, α.^42,45,46 The Find, Inform, and Test (FIT) method^45,46 was used to determine the optimal α for each SEDC predictor based on a positive and maximum Pearson and Spearman R, and p-value < 0.05. No multicollinearity (i.e., Variance Inflation Factor<10) was identified between the three SBTEX LUR predictor variables. Forward stepwise regression, with a priori positive relationship between the SEDC predictor and annual SBTEX concentration, was performed, using the Akaike Information Criterion and p-value<0.05.

LUR results differed across SBTEX components and were primarily predictive at a coarser scale than CAMx. Predictor data, processing, and results are described in the SI, and the final SBTEX LUR equations and model performance from 2011-2012 are shown in Table S1.

This work continues prior research that developed an air quality model to improve high-resolution SBTEX estimation for health risk assessment in the Gulf States.¹ Hazardous air pollutant (HAP) reporting (except benzene) to the NEI is voluntary, so air quality models constructed using NEI emissions typically have incomplete input data.¹ In earlier work by the authors, SBTEX was modeled using CAMx; meteorological data from the Weather Research and Forecasting Model (WRF); and styrene, toluene, ethylbenzene, and xylenes (STEX) emissions not reported to the NEI were estimated using the novel HAPs Imputation (HAPI).^1,12 Hourly SBTEX concentrations were estimated on a horizontal 4km-by-4km grid resolution in the Gulf States, capturing spatiotemporal variability, seasonality, chemical reactions, transport, deposition, and more complete emissions.¹ Results suggested that STEX emissions were underestimated by 2-22% in the 2012 NEI, with missing emissions primarily from oil and gas non-point and non-electric power plant point sources.¹ CAMx (+HAPI) estimates were limited by emissions data accuracy, model simulation mechanisms, and the exclusion of observed data, which we seek to address through BME data fusion.¹

Daily SBTEX CAMx estimates for 2011-2012 were calculated as the arithmetic average of hourly CAMx (+HAPI) estimates. The CAMx output was lognormally distributed based on exploratory analyses, so a natural logarithm transformation was applied (see Figure S3 for details). CAMx zero-values were omitted because they appeared to be a boundary artifact based on exploratory analyses.

Daily CAMx outputs were calibrated for BME data fusion using the Constant Air Model Performance (CAMP) correction method for 2011 and 2012 separately. The CAMP method is a stationary, nonlinear, non-homoscedastic correction for model bias performed by pairing observations and model outputs.^{32–34,36,37,40}

Daily observed SBTEX log-concentrations inside and within 0.05 degrees of the CAMx modeled region were paired with the closest CAMx model output. Observed-modeled pairs were sorted in ascending modeled values and divided into model value deciles. The mean (λ₁) and variance (λ₂) of observed log-concentrations within each model decile were calculated to create a piecewise-linear λ₁ curve used for model correction, and a λ₂ curve providing the associated uncertainty. The endpoints of the curves were extrapolated using the average slope of the piecewise linear segments, and segments of the λ₁ curve with negative slopes were replaced with zero slope segments to ensure the λ₁ curve remained monotonic and positive between observed and CAMx-modeled SBTEX.³⁷ Lastly, modeled values were interpolated along the λ₁ and λ₂ curves to create CAMP-corrected CAMX mean, ym_s, and variance, yv_s, values, respectively. Detailed CAMP curves are shown in Figures S4–S8 of the SI.

BME is an advanced non-linear method of modern geostatistics^38,47 that has been used with global offsets to successfully map many pollutants^{32,35,38,47,48}, however, SBTEX has not previously been evaluated. Hence, a critical goal of this work is to implement BME with global offsets for each VOC species.

Let p=(s,t) be a space/time location, where s=[s1,s2] is a 2D spatial location and t is time. To implement BME with various global offsets, we generalize the space/time BME data fusion framework as follows:

Define a spatiotemporal link function g(.;p) to transform the VOC z-data observed at p into the transformed data x=g(z;p)

In step 1, we consider a link function that log-transforms the z-data, and removes a global offset capturing global spatial and temporal trends in log concentrations at some resolution δ, i.e., (1)x=g(z;p)=log(z)−oδ(p) (2)oδ(p)=oδ,s(s)+oδ,t(t)−oδ,t(t)¯ where log(.) is the natural log, oδp is the global offset of log-concentrations at resolution δ,oδ,ss is its spatial component with an average oδ,ss¯ equal to that of log concentrations, and oδ,tt-oδ,t(t)¯ is its temporal component on average equal to zero.³³ In this work, we aim to evaluate the performance of three global offsets at the following resolutions: flat (or constant-value), medium, and fine.

The flat global offsets were calculated as the mean of observed log-concentrations across the study domain. The temporal component, oδ,tt, was calculated via exponential kernel smoothing (described in Akita et al. 2007) of spatially-averaged, observed log-concentrations using a kernel smoothing range of 365 to 730 days for the medium resolution, and 90 to 180 days for the fine resolution. The spatial component of the global offset, oδ,ss, was obtained using LUR (described earlier) for benzene, and, for the other VOCs, via exponential kernel smoothing of time-averaged, observed log-concentrations using a kernel smoothing range of 2.5 to 7.5 degrees for the medium resolution, and 0.2 to 0.6 degrees for the fine resolution. Details are described in the SI (Tables S2–S6, Figures S9–S14). Critically, as the global offset resolution progresses from flat to fine it becomes informed and the link function removes z-data variability at progressively finer scales, reducing residual variability of the transformed x-data.

In step 2, we perform a BME data fusion^38,47 of hard and soft data transformed using the spatiotemporal link function (Equations 1–2). For a given VOC and resolution δ, we obtain the transformed hard data, xh, using the equation xh=log(zh)-oδ(ph), where zh is the vector of observed values at hard data points ph.³³ The soft data consists of the means, yms, and variances, yvs, of the CAMP-corrected CAMx log-concentrations at each CAMx computational points, ps. The corresponding transformed soft x-data consists of Gaussian distributions, fS(xs), at points, ps, with means xms=yms-oδ(ps) and variances xvs=yvs.³³

We model the residual variability and associated autocorrelation of xh using a homogenous/stationary Space/Time Random Field (S/TRF), X(p), with a constant mean mX=EXp and a covariance between any two points p and p’ expressed as (3)cX(r,τ)=E[X(p)X(p')]−mX2 where E. is the expectation operator and r=s-s' and τ=t-t' are the spatial and temporal lags, respectively, separating p and p’.³³ The covariance was manually modeled as a three-structure exponential model described in detail in the SI (Tables S7–S11, Figure S14). The covariance models contained long and short structures, which were driven by steady emissions over time and the short half-life (or quick decay) of SBTEX.^1,18–22 Generally, xh derived from global offsets with finer resolution produced lower residual variability.

The BME data fusion of the hard data and soft distributions is performed in two stages. In the first, Maximum Entropy (ME), stage, we construct a maximum entropy probability density function (PDF) fGxk,xh,xs, where xmap=(xk,xh,xs) are the values of X(p) at pmap=(pk,ph,ps), based on general knowledge G={mX,cX(.)}.³² In the second, Bayesian (B) knowledge blending, stage, we integrate site-specific knowledge S={xh,fs(xs)} and obtain the B-ME PDF under knowledge K={G,S}, (4)fK(xk)=A−1∫dxsfG(xk,xh,xs)fS(xs) where A is the normalization constant.³² Lastly, we calculate the expected value and variance of fKxk to obtain the mean xmk and variance xvk of X_k.

In step 3, we evaluate Zk=g-1Xk;pk=exp⁡(Xk+oδ(pk)). Since Zk represents VOC concentration, it is convenient to define Yk=Xk+oδ(pk) so that Zk=exp⁡(Yk). Taking the log, we get Yk=log⁡(Zk), indicating that Yk represents log-concentrations. Since Yk=Xk+oδ(pk), then its mean and variance are ymk=xmk+oδ(pk) and yvk=xvk. The BME PDF (Equation 4) is Gaussian since the soft data is Gaussian, as a result Yk~Gaussian(ymk,yvk), and it follows that Zk=exp⁡(Yk) has a median, mean, and variance given by (5)zmedian,k=exp(ymk) (6)zmean,k=exp(ymk+yvk2) (7)zvariance,k=[exp(yvk)−1][exp(2ymk+yvk)]

In this work, MATLAB and the BMElib package,⁴⁷ which provides a computational implementation of the theoretical BME framework, were used to perform SBTEX estimation. A flowchart for the BME data fusion with global offsets methodology (Figure S15) and a detailed description of how each BME step contributes to SBTEX estimates is in the SI (Figures S16–S23).

SBTEX estimation methods were evaluated away from monitoring stations using radius cross-validation (RCV), which consists, for a given radius, of removing observations at each station one at a time and estimating these observations using only data from stations that are at least one radius distance away from the station in consideration.^37,41 Performance for a radius is evaluated using the Pearson or Spearman correlation R between observed values and estimated values. For each method, we obtained the full RCV curve and displayed the Pearson R if its curve decreases monotonically and is on average at least half the Spearman R, otherwise, we displayed the more robust Spearman R ‘Best (SBTEX) estimation methods’ were selected based on the highest R-value at a cross-validation radius of 3 degrees. For estimation methods that use only observations, the R-values are expected to drop substantially over small cross-validation radii and then slowly decay over larger distances.^37,41 More detail on RCV is available in the SI (Figure S24).

We used RCV to compare the performance of only observational data (i.e., observational interpolation) using 1) flat (i.e., simple kriging; least intense), 2) medium-resolution (moderately intense), and 3) fine-resolution (moderately intense) global offset, and observational data and CAMx predictions (i.e., BME data fusion) with a global offset (most intense). . We evaluated BME data fusion (i.e., we use both observations and CAMx output) using the best of three global offset subtypes. Method intensities were based on data, computational, and temporal demands. Details on global offsets and their subtypes (Tables S2–S6, S13; Figures S9–S13) and method intensities (Table S12) are described in the SI.

When calculating the R-values and determining best estimation methods, we divided these data into two geographical domains: within the CAMx 4 km modeled domain,¹ and the outside CAMx domain. For the inside CAMx domain, we calculated the R-value between observed and CAMx-predicted values and displayed it as a flat line. For the outside domain, we could not calculate an R-value for CAMx since CAMx did not predict outside of the CAMx domain and selected data fusion as the best estimation method if it did not diminish observation interpolation performance.

Composite methods to estimate SBTEX concentration in the Gulf States were created from the best estimation methods 1) within and 2) outside the CAMx-modeled domain. Best estimation and composite methods were also evaluated using the Pearson and Spearman R values from averaged RCV curves and leave-one-out cross-validation (LOOCV), which measured estimation performance at a monitoring station location when historical measurement data at that location was available. Full validation and evaluation results are available in the SI (Tables S14–S16; Figures S25–S39).

All residences for GuLF Study cohort members within the CAMx-modeling domain were gathered (n=33894). On average, there were 1.62 residence locations per participant enrolled because some participants moved during the study period. Using the composite SBTEX estimation methods, daily SBTEX from 2011-2012 (731 days) was estimated at selected points within the CAMx-modeled domain (30x15 regular grid points, monitoring station locations, and Voronoi points). Daily SBTEX estimates at residence locations were approximated by interpolating grid estimates to residence locations.

A 2003 survey from the US Department of Transportation found that over 50% of commuters traveled 10 miles or less to work.⁴⁹ Based on this assumed commuting radius, at each residence, the number of NEI-reported point sources (preparation described in section 3.2 and SI) active between 2011 and 2012 and within 0.15 degrees of each residence location was calculated. Residence locations that had a greater number of point sources than the 75^th percentile number of point sources were said to have “high source density,” corresponding to a larger emitting industry presence. Residence locations with an equal or fewer number of point sources were said to have “low source density,” or low industry presence.

The 2.5^th, 50^th, and 97.5^th percentile daily exposures were calculated for SBTEX for all residence locations, high source density residence locations, and low source density residence locations within the GuLF Study cohort.

Interpolation of SBTEX observations using global offsets performed in the expected order within the CAMx-modeled domain. The flat global offset had the worst performance, the medium-resolution offset performed slightly better, and the fine-resolution offset performed best (Figure 1). Cross-validation R-values for interpolation of SBTEX observations using a flat global offset decreased quickly as the radius limit increased to 0.5 degrees (Figure 1), demonstrating that observational interpolation using a flat global offset (i.e., simple kriging) can only reliably be used to estimate SBTEX well when close to monitoring stations Improvements from flat to fine resolution were surprisingly noticeable, however, with SBTEX global offsets created using a fine-resolution global offset maintained consistent performances over larger radius limits (Figure 1), suggesting that historical SBTEX measurements and emissions were representative of 2011 and 2012 observations. Compared to observational interpolation with a flat global offset, medium- and fine-resolution global offsets performed better, demonstrating that moderately intense methods are a useful tool for SBTEX estimation in monitoring station-scarce when most resource-intensive methods are not possible.

CAMx generally estimated SBTEX better than low and moderately-intensity estimation methods within the CAMx-modeled domain (Figure 1). CAMP correction of CAMx improved SBTEX estimation performance within the CAMx-modeled domain (Figure 1). Based on Figure 1, a fine-resolution global offset+CAMx data fusion was selected as the best estimation method within the CAMx-modeled domain for all SBTEX. Surprisingly, the data fusion approach improved upon both observational interpolation and CAMx, indicating that it is more than just the best of the two. The data fusion curve for styrene demonstrated improving performance as the radius limit increased from 0 degrees to a radius limit of 0.5 degrees, which may be attributed to the high variability in styrene measurements (Figure 1).

Compared to CAMx performance alone, the selected estimation method within the CAMx-modeled domain yielded 6.1 to 15.5% increases in average RCV Pearson R values of BTEX, but a 10.6% decrease for styrene, and 3.8 to 10.1% increases in Spearman R for SBTEX (Table 1, Table S14). SBTEX Spearman R values increased by 0.48 on average from least to most intense methods (Table 1). The LOOCV performance using selected estimation methods was 32.2 to 51.8% higher for Pearson R and 21.9 to 31.5% higher for Spearman R than the respective CAMx Pearson or Spearman R values for all SBTEX (Table 1, Table S14). Validation results suggest that the most resource-intensive estimation methods always improved rank estimation of SBTEX exposures within the CAMx modeled domain.

Compared to previous BME estimation, this work 1) outperformed previous BME rank performance improvements compared to kriging (e.g., average Spearman R increase of 0.04 (over RCV radii of 0-108 km) for daily O₃ versus 0.39-0.54 for SBTEX),³³ 2) mostly outperformed previous BME linear performance improvements compared to an air quality model (e.g., Pearson R increase of 0.11 for NO₂ versus 0.10-0.14 for SBTEX)³⁹, and 3) similarly improved estimation away from monitoring stations.^32,33,37,40 This work’s improved success can be attributed to the CAMP correction of CAMx data and the incorporation of observational and emissions trends in global offsets.

Outside of the CAMx-modeled domain, interpolation of STEX observations using global offsets performed as expected, where performance from worst to best was a flat global offset, medium-resolution global offset, and fine-resolution global offset (Figure 1). Again, observation interpolation was best at small radius limits and quickly decreased as the radius limit increased (Figure 1). The interpolation of benzene observations did not behave as expected when the flat global offset performed the best (Figure 1). The flat global offset may have performed better for benzene estimation than the more spatially resolved global offsets because the flat offset had the largest spatial long-range covariance structure among the tested methods, meaning that it could pull information from monitoring stations further away. These results demonstrated that, outside of the CAMx-modeled domain, moderately intense STEX estimation methods improved estimation performance compared to the least resource-intense methods. In the case of benzene, the least resource-intense methods performed better than moderately intense methods, which demonstrated the trade-off between higher resolution global offsets revealing less autocorrelation in datasets.

The best estimation methods outside the CAMx-modeled domain were a fine-resolution global offset+CAMx data fusion to predict STEX and a flat global offset+CAMx data fusion to predict benzene (Figure 1). Data fusion with CAMx improved SBTEX estimation performance for locations outside the CAMx-modeled domain (Figure 1). This was likely due to low validation R values from only observational data and long-range spatial covariance structures that allowed CAMx information to be pulled when estimation locations were far away. For each of the best-selected SBTEX methods outside the CAMx-modeled domain, data fusion performance appeared to plateau (or slightly increase) at large RCV radii (Figure 1). It was not possible to confirm whether this plateau was real or was a slow decrease in performance because of the limited size of the study domain. RCV results of SBTEX outside the CAMx-modeled domain suggest that the most intense methods, utilizing information from nearby CAMx, performed the best for ambient SBTEX estimation (Figure 1).

Figure 2 shows SBTEX median and mean estimations and error standard deviation (SD) on the randomly selected date, August 4^th, 2012. Toluene, ethylbenzene, and xylene estimates showed similar spatial distribution, which is consistent with previous findings of high Pearson correlation and comparable industry patterns between these pollutants^50,51 (Figure 2). Benzene estimates demonstrated similar areas of elevated concentrations to toluene, ethylbenzene, and xylenes, but showed more widespread distribution, potentially from high wildfire and on-road vehicle emissions contributions in 2012¹ (Figure 2). Conversely, styrene estimates exhibited more localized high concentrations likely from point source emissions and its short ambient lifetime^1,18 (Figure 2). Additional log-, mean, and median concentration spatial estimates (Figures S40–S45) and a detailed comparison of CAMx and BME estimates (Figure S46) are available in the SI

Importantly, all SBTEX estimates demonstrated high concentrations along the Interstate 10 corridor (between Houston, TX, and Baton Rouge, LA) and near the Mississippi River corridor (between Baton Rouge and New Orleans, LA). These corridors are known for high vehicular traffic and petrochemical industry activity^1,52,53 and the Mississippi corridor, colloquially referred to as “Cancer Alley,” has long been the subject of environmental justice concerns within lower-income and Black communities.^52–54 The ability of BME to estimate SBTEX at user-specified space/time locations provides epidemiologists with a novel framework to determine, at a high resolution and accounting for seasonality (from observational and air quality model information), the most at-risk populations and exposure inequities.

SBTEX estimation SD within the CAMx-modeled domain was mostly lower than outside the CAMx-modeled domain because estimates within the CAMx-modeled domain had more information sources to pull from, leading to less uncertainty and more detail in median and mean SBTEX estimates (Figure 2). For median SBTEX estimates, the transition from within to outside the CAMx-modeled domains was gradual over a short distance and minimal, which would not greatly affect the rank order of participants’ exposure for an epidemiological study that included participants residing outside (and nearby) the CAMx-modeled domain (Figure 2). As expected, mean SBTEX estimates were higher and the CAMx-availability transition was more distinct than median SBTEX estimates due to the inclusion of variance in mean calculations, but not in median calculations (Figure 2). Based on these findings, median estimates alone or mean estimates accounting for estimation SD (e.g., using estimation inverse SD-weighted linear regression) are recommended for use in epidemiological analyses and to limit differential exposure misclassification.

Using composite methods, we estimated daily SBTEX exposures at participant residence locations to evaluate potential exposure inequities in the Gulf States. Table 2 shows each pollutant’s 2.5^th, 50^th, and 97.5^th percentile of daily exposure. For styrene in the low source density group, the 2.5^th and 97.5^th percentile of exposure were 0.0022 and 0.01 parts per billion (ppb), indicating a noticeable contrast between the least and most exposed study participants. There was a similar ratio of least to most exposed for the other subgroup and components of BTEX (Table 2). This contrast is a potential asset for future epidemiological analyses of ambient SBTEX-related health effects.

The possibility that participants may work at facilities that emit SBTEX was also investigated based on the presence of polluting industries within typical commuting distance of residences. The 75^th percentile number of point sources within commuting distance of residence locations was 15, 19, 23, 20, and 8 for SBTEX compounds, respectively. As seen in Table 2, those who lived within typical commuting distance of high styrene source density had a 97.5^th percentile daily exposure of 0.024 ppb, compared to those who lived within typical commuting distance of low source density who had a 97.5^th percentile exposure of 0.010 ppb. This means there was a 2.4-fold increase in 97.5^th percentile exposures between residence locations within commuting distance of low versus high source density. Likewise, the ratio of 97.5^th percentile daily exposures between low versus high source density areas were 1.4, 1.7, 1.8, and 1.0 for benzene, toluene, ethylbenzene, and xylenes, respectively (Table 2). It is possible this relationship was smaller for xylenes because the 75th percentile of xylenes point sources within commuting distance (n=8) was half, or less, than the number of point sources for other SBTEX compounds (n=15-23).

Since individuals who live near a given polluting industry are more likely than those who live further away to work in that industry,^55–58 it is ideal for epidemiological studies to account, when possible, for both workplace and environmental exposures.⁵⁹ Furthermore, previous investigations have found that nonwhite and Hispanic households more frequently lived near emitters^{57,58,60–62} and were exposed to higher air pollution levels.^63–66 If the situation for SBTEX-emitting industries is like that for other polluting industries, then total SBTEX exposure inequities in the Gulf States may be magnified as a function of race, ethnicity, and occupation. Additional details on cancer and noncancer health effects and the benefits of BME estimation are included in SI.