Observational data from 189 CSN monitors were used for model development and evaluation (Fig. 1). Data were obtained on 1 in every 3 or 6 days in January 2004 for a total of 9 days (e.g., 4, 7, 10, ... 28 January), which led to varying sample sizes for each observation day. The number of available monitors with speciated PM2.5 data on observation days ranged from approximately 40 to 150 and each site had 5 to 9 observations over the period examined. CSN monitor measurements include total PM2.5, organic and elemental carbon, ions, and 35 metals. CSN monitors tend to be located in more densely populated areas such as urban and suburban areas, and data are more associated with high-population emissions sources such as mobile and cooking sources. Speciated PM2.5 data are also available from the SEARCH (Hansen et al., 2003, 2006) and IMPROVE (Chow et al., 1993) networks, and those data were used for further model evaluation. The SEARCH network includes eight monitors in the southeastern USA, configured as urban/rural pairs. IMPROVE monitors are mainly located in pristine locations such as national parks and wilderness areas. Thirty-eight IMPROVE monitors in the eastern USA were used for model evaluation. IMPROVE monitors in the eastern USA were used due to their closer proximity with urban monitoring sites (e.g., less than 50 km), as opposed to western IMPROVE sites which are much more spatially sparse. Additionally, modeled processes have higher uncertainty for the western USA due to complex terrain and meteorology, leading to added bias in the observation and model comparison (Baker et al., 2011).

This study utilizes a hybrid SA method that combines techniques of both CTMs and RMs to generate adjustment factors (symbolized by R) that improve source impact estimates. Hu et al. (2014) described the hybrid approach in detail, but it is briefly summarized here. First, gridded concentrations and emissions sensitivities of PM2.5 species are generated using CMAQ–DDM (v. 4.5). CMAQ–DDM model sensitivities to emissions are designated as the original (base case) source impacts (SAi,jbase) for species i and source j. CMAQ–DDM was run with strict mass conservation (Hu et al., 2006), the SAPRC-99 chemical mechanism (Carter, 2000) and the aerosol module described in Binkowski and Roselle (2003). The modeling domain contains the continental USA, southern Canada, and northern Mexico, with 36 km grid resolution, Lambert Conformal Conic geographic projection, and 13 vertical layers of variable thickness extending from the surface to 70 hPa. Meteorological inputs were generated using the fifth-generation PSU/NCAR (Pennsylvania State University-National Center for Atmospheric Research) mesoscale model (MM5) with 35 vertical layers, implemented with the Pleim–Xiu land surface model (Grell et al., 1994, Pleim and Xiu, 1995; Xiu and Pleim, 2001). Emissions inputs were processed using the Sparse Matrix Operator Kernel Emissions (SMOKE) module (CEP, 2003). Emissions data originated from a 2004 inventory that was projected from the 2002 National Emissions Inventory (NEI2002). Please refer to the preceding publication by Hu et al. (2014) for additional details about the emissions inventory.

Next, the original source impacts, receptor observations, and uncertainties are used as inputs to the objective function (Eq. 1) of the hybrid SA model: X2=∑i=1Nciobs-cisim-∑j=1JSAi,jbase(Rj-1)2σi,obs2+σi,CTM2+Γ∑j=1Jln⁡(Rj)2σln⁡(Rj)2,

where the adjustment factors Rj are optimized by minimizing the objective function, χ2. The initial Rj values are specific to 1 site and 1 day, as the method is applied at monitors when speciated PM2.5 data are available on observation days, and are then kriged and interpolated. The terms ciobsand cisim represent the observed and CMAQ-simulated concentrations, respectively; Γ weights the amount of change in source impact. Uncertainties in observation measurement (σi,obs), modeled concentrations (σi,CTM), and source strength (σln⁡(Rj)) are also included in the model. Specifically, σi,obs is reported with measurements for each day from the CSN network; σi,CTM is error in modeled concentrations, which is proportional to observed concentrations and remains constant for all sites and days; and σln⁡(Rj) is uncertainty in source contribution expressed as the log of the factor of uncertainty, which also remains constant for each site and day.The uncertainties weight the adjustment of modeled source impacts, in that components with larger uncertainties are weighted less.

The objective function is minimized by using a nonlinear optimization approach known as sequential quadratic programming (Fletcher, 1987; Gill et al., 1981). The function is modeled using a ridge regression structure, as demonstrated by the second term, and uses an effective variance approach to balance model outputs. The effective variance approach is also utilized by versions of CMB, and the optimization method used here is, in essence, an extended CMB approach (Watson et al., 1984). Uncertainties in the first term of the objective function serve as effective variances of the numerator and are specified for each species i. Finally, Rj are applied to SAi,jbase to adjust original source impact estimates (Eq. 2) and reconstruct simulated concentrations (ciadj) at receptors to more closely reflect observations (Eq. 3). SAi,jadj=RjSAi,jbaseciadj=cisim+∑j=1JSAi,jbase(Rj-1) Given that many of the source impact profiles are similar between categories such that colinearities are present, the variation of the Rj values are constrained to 0.1≤Rj≤10.

Source impact profiles are derived from the information provided by Reff et al. (2009). In this manuscript, “source impact profiles” are different than “source profiles” in that they describe the source fingerprint at the receptor. In other words, the source profile can be altered, for example by the formation of secondary species. However, for many of the species, there is no secondary formation. It is assumed that within the accumulation mode, which contains most of the fine PM mass in CMAQ, the composition of the primary portion of the PM2.5 from any source is the same, but secondary species can be formed, altering the source profile at the receptor. The specific steps taken in applying source profiles to CMAQ-generated data are described as follows. Source profiles for 84 source categories were presented in Reff et al. (2009), which were aggregated from roughly 300 PM2.5 SPECIATE v4.0 profiles and contain estimates of trace metal contributions. The 84 PM2.5 profiles were further aggregated into 33 categories, consistent with the sources of interest in this study. Then the contributions in the 33 profiles were used to speciate the “other” (sometimes called unidentified) portion of PM2.5 (species name: A25) as output by CMAQ. The contributions of the 35 trace species were then used to split the “other” PM2.5 into individual species, and results for these species, along with the other primary and secondary species are used. At the receptor, both the primary and secondary PM2.5 contribution at the receptor are used to determine the new, receptor-oriented, source impact profiles. This same approach was used to generate receptor-oriented profiles in the preceding publication by Hu et al. (2014).

The hybrid method produces results that more closely reflect observations than the original CTM results, which are often biased (Hu et al., 2014). It accounts for more known source categories than traditional RM approaches (e.g., 33 vs. 6), and it links sources and observations both temporally and spatially. Additionally, the hybrid method generates estimates of the uncertainty in source impact predictions and identifies potential errors in source strength and composition. One limitation of the hybrid method is that results are only available at receptor locations when observations are available, limiting its spatial and temporal scope. In this paper, a spatial hybrid method is presented and evaluated, and it extends the benefits of the hybrid CTM–RM method through spatial interpolation.

Spatial and temporal source impact fields can be developed by combining the hybrid CTM–RM method and geostatistical techniques. Hybrid-generated Rj values were spatially interpolated for each observation day using kriging to generate spatial fields of source impact adjustment factors. Matlab^© (v. 7.14.0.739) was used to perform all geostatistical and optimization calculations. Daily-averaged spatial fields of CMAQ–DDM source impacts are adjusted by grid-by-grid multiplication of the original fields by the corresponding adjustment factor field, resulting in spatial fields of hybrid-adjusted source impacts that are available every third day, as are observations. Source impact fields for intervening periods are developed by interpolation of the Rj spatial fields. Temporally interpolating Rj values and then applying those adjustments to simulated source impact fields is preferred over simply interpolating the 1-in-3 day hybrid-adjusted source impact fields because temporally interpolating adjusted source impacts would smooth the fields, and the day-specific spatial and temporal variability in the emissions and meteorology captured by the CTM would be lost.

Performance of the spatial extension was evaluated using a data withholding approach, as well as by comparison with data from the SEARCH and IMPROVE networks. For data withholding, we removed 10 % of the available observations (75 sets of observations at the monitors with speciated PM2.5 data) and re-ran the spatial hybrid model. This led to a total of 75 observation sets being used in the model evaluation. All references to “withheld CSN data” refer to these 75 sets of withheld data. The remaining 90 % of the available observations were used to fit the variogram models, which were used in kriging to produce spatial fields of Rj values. Concentrations are reconstructed using Eq. (3) with the spatially interpolated adjustment factors. Additionally, hybrid CTM–RM optimization is directly applied to withheld observation sites to assess the performance of the kriging model. Then the original CMAQ–DDM, directly applied hybrid (CTM–RM), and spatial hybrid (SH) concentrations are compared to measurements at withheld observation locations to evaluate the performance of each method in simulating concentrations. Linear regression was used to assess correlations between observations and modeled concentrations for each method.

In order to evaluate prediction performance in remote locations and in locations independent of CSN, CMAQ–DDM and SH concentrations were compared to observations at SEARCH and IMPROVE locations. Note that the application of the CTM–RM hybrid method, as conducted here, did not include SEARCH and IMPROVE data, and CTM–RM/SH results are independent of those observation data. The SEARCH and IMPROVE comparisons also address the issue of spatial representativeness of using only CSN data to produce spatial fields. This study uses available speciated CSN data over the entire USA, thereby providing a very spatially heterogeneous data set that is representative of key emissions and meteorology in each USA region. The lack of rural data available may present uncertainties in the spatial representativeness of Rj values outside of urban regions.

Also note that 41 species, including total PM, were used for spatial field construction, but only results for 20 species are presented for comparison of CSN results and 15 species for SEARCH and IMPROVE results, as measurements for some trace metals are seldom above measurement detection limit. The possibility of added uncertainty in the optimization step due to detection limit issues was considered. Optimization was tested with the absence of species with limited availability, and no significant differences in model performance were found. The use of the measurement uncertainty in the objective function minimizes the role of those measurements on days when they are below the detection limit, but still accounts for the concentration levels being low. Using all available measurements in the optimization model is the preferred approach.

CTM–RM and SH adjustment factors at withheld observation locations were compared using regression to evaluate the spatial interpolation that was performed using kriging. For each observation day (9 days), 10 % of available observations were randomly withheld, resulting in a total of 2,475 Rj data points (75 observations locations × 33 source categories). Five outlying data pairs (< 0.5 %) were removed from this regression. Outlying data pairs are determined by examining the distribution of the directly calculated Rj values (mean = 0.84, SD = 0.48) and the kriged Rj values (mean = 0.83, SD = 0.30) at the withheld observation locations. Data pairs were removed if either value was more than 6 standard deviations from the mean Rj value. The removed data points (5 points out of 2475) were well outside of this range. The remaining CTM–RM and SH factors had a Pearson correlation coefficient of 0.89, a linear regression slope of 0.83 ± 0.02, and an intercept of 0.14 ± 0.02 (Fig. 2).

Root mean square errors (RMSEs) were calculated for the adjustment factors by source (Eq. 4) RMSEj=∑i=1NRjCTM–RM-RjSH2N,j=1,…Jsources,N=75sites. RMSEs for all sources were less than 0.4, with the exception of RMSEs for lawn waste burning, prescribed burning, and wood stoves (Table S1 in the Supplement). This is expected given the uncertainty in the burn emissions (Table S2). Sources such as diesel, liquid petroleum gas, non-road natural gas, and Mexican combustion all had very low RMSEs, mean Rj values near 1, and median Rj values near 1. This indicates that there is little to no adjustment to these source impacts and that kriging captures the Rj values calculated by the CTM–RM application. Mean and median Rj values are within 20 % for most sources (Table S1). The overall mean Rj value at withheld observation locations for all sources for CTM–RM and SH adjustment factors was 0.84 and 0.83, respectively, indicating a high bias in CMAQ–DDM overall, as expected from the base model performance evaluation (PM2.5 was biased approximately 40 % high).

Cumulative distributions were examined for CTM–RM and SH adjustment factors for each source, and adjustment factors were highly correlated for each source (Fig. S1). Spatial interpolation captured CTM–RM trends for sources dominated by adjustment factors near 0.1, such as dust, lawn waste burning, prescribed burning, and wood stoves, though did not capture all of the extremely low adjustments (e.g., meat cooking in some locations). Sources that found little adjustment (Rj=1) include aircraft, diesel combustion (stationary sources), fuel oil burning, Mexican combustion, non-road liquid petroleum gasoline combustion, and sea salt, and were well captured by the spatial extension, as demonstrated by nearly identical cumulative distributions. The cumulative distribution plots exceed 1.0 (x axis) for dust, lawn waste burning, prescribed burning, and wood stoves. These sources are highly variable day-to-day, and CMAQ–DDM underestimations are possible in cases where the original emissions missed an actual burn or dust event.

Spatial fields of hybrid adjustment factors are presented for dust, on-road diesel and gasoline combustion, and wood stove sources (Fig. 3). Average Rj values over all observation days are also presented for reference (Fig. S2). Typically, Rj values were less than 1 for dust and wood stove impacts, indicating a high bias in those source impacts in the base CMAQ–DDM simulations. Spatial field values for on-road diesel and gasoline combustion Rj are generally near one over most of the USA; however, Rj values for those sources tend be below one in the southeastern region of the USA.

In general, for an Rj value less than 1, the initial CMAQ–DDM estimate is reduced to be more consistent with observations. In turn, for an Rj value greater than 1, the initial CMAQ–DDM estimate is increased to be more consistent with observations. An Rj value of 1 indicates that no adjustment to the CMAQ–DDM is necessary to improve consistency with observations. As such, after application of the SH method, it was found that while many of the source impacts were adjusted relatively little (i.e., Rj≈1.0), dust-related and biomass burning-related impacts were often biased high in the original CMAQ–DDM simulation and therefore considerably reduced.

The distribution of all Rj values was approximately lognormal, and an analysis was performed to determine whether log-transformation of Rj values prior to the kriging step was necessary to reduce bias in source impact and concentration estimates (Fig. S3). In one approach, we log-transform the Rj values at the monitors before kriging, and then the kriged values are unlogged before use in reconstruction. In the second approach, we do not log-transform before kriging. From the analysis it was determined that lognormal transformation of Rj values was not necessary, as no significant difference was observed in reconstructed concentrations and source impact fields as a result of the transformation.

Additionally for method evaluation, withheld CSN observations were compared with SH concentrations, which were calculated using kriged Rj values and Eq. (3) (Table S3). The mean concentrations of total PM2.5 for withheld observation locations were 11.7 (± 8.3), 16.3 (± 11), 8.59 (± 4.7), and 9.2 (± 5.7) µg m-3 for the observations CMAQ–DDM, CTM–RM, and SH estimations, respectively. Levels of crustal metals (Al, Si, Ca, and Fe), K, and Cl were biased very high in the base CMAQ–DDM simulation, oftentimes an order of magnitude greater than observations. SH concentrations of metals were closer to the CSN observations. Error in simulated (sim) concentrations is calculated using Eq. (5): Error=1N∑i=1Nobsi-simiobsi. In Eq. (5), i represents observations and N represents the total number of observations withheld for evaluation. The error was 295 and 139 % for CMAQ–DDM vs. observations and SH vs. observations, respectively, for vanadium; and 1340 and 326 % for CMAQ–DDM vs. observations and SH vs. observations, respectively, for manganese. The large remaining errors stem from the source profiles leading some elements to being biased consistently high and others low. Further work to optimize source profiles can reduce residual errors.

Performance indicators for some species indicate poorer correlation, such as the β values for calcium for CMAQ–DDM (β = 1.22) and SH (β = 0.16) regression comparison (Table S4). However, all metrics presented must be taken into account and evaluated holistically. The α values for calcium indicate an improvement in performance, as the spatial hybrid value (α = 0.044) is closer to 0.0 than the CMAQ–DDM value (α = 0.13). Further, mean concentrations at withheld observation locations also indicate better performance of the SH model, where mean calcium concentrations were 0.041 (observed), 0.18 (CMAQ–DDM), and 0.050 (SH) (Table S3). According to the mean concentrations, the SH method performs best. Throughout the analysis, CMAQ–DDM estimates of trace metal concentrations were orders of magnitude too high, while SH results were closer to observations. While some individual metrics indicate better performance of CMAQ–DDM, overall performance of the SH method is most favorable. An important point is that the species where performance is less good are typically those species that have a smaller role in determining source impacts. For example, those species are very trace and/or have high uncertainties in the measurements or source profiles relative to their observed concentrations.

The SH method was further evaluated by comparing simulated concentrations to independent data from the SEARCH and IMPROVE networks (Tables S5 and S6). The mean concentrations over observation days were compared, as well as regression statistics for observations vs. modeled results. For the SEARCH network (N=8 monitors), average concentrations of 15 species were compared to observations. Error in mean concentrations for crustal elements was significantly decreased (CMAQ–DDM and SH): Al, 2203 to 540 %; Si, 1228 to 271 %; K, 365 to 61 %; Ca, 402 to 61 %; Fe, 260 to 3 %; Cu, 231 to 38 %; and Se, 63 to 25 %. For the IMPROVE network (N=38 monitors), errors in mean concentrations for crustal elements were also significantly decreased: Al, 704 to 24 %; Si, 371 to 24 %; K, 599 to 48 %; Ca, 361 to 36 %; Fe, 334 to 18 %; Cu, 186 to 57 %; and Se, 22 to 11 %. Linear regression metrics are also presented for SEARCH and IMPROVE monitors (Tables S7 and S8). Correlations for all SEARCH and IMPROVE species did not improve; however, estimation performance for most trace metals and ions improved.

Refined dust and biomass burning source impacts led to better agreement between simulated and observed concentrations of crustal (Al, Ca, Fe, Si) and biomass burning-derived elements (Cl, K). Original CMAQ–DDM estimates were biased very high for these species compared to observations. This is due to the apparently high bias in source impact profile estimates for biomass burning sources, which do not take into account long-range transport and deposition of biomass burning-related PM. Results suggest that due to atmospheric transformation processes, the source impact profiles are in error for some species, similar to the findings in Balachandran et al. (2013). Observations for some elemental species (Mg, P, V, Se) were highly influenced by measurement limitations (i.e., at or below detection limit) and showed the poorest correlation with modeled concentrations. Additionally, conversion of observed carbon species between analytical methods, from total optical transmittance to total optical reflectance equivalents, introduced potential bias into concentration comparisons. Other studies have shown that conversions may overcorrect observations of carbon species (Balachandran et al., 2013).

Average source contributions to PM2.5 at withheld CSN observation locations were ranked from largest to smallest for base CMAQ–DDM, CTM–RM, and SH (Table 1). The top three sources were wood stoves, dust, and livestock emissions for base CMAQ–DDM simulations, the latter source capturing the influence of ammonia emissions on the formation of nitrate. The livestock category includes impacts from agricultural and farming activities. For CTM–RM and SH results, wood stoves (10th for both) and dust (13th for CTM–RM, 14th for SH) were ranked much lower than for CMAQ–DDM. Livestock emissions were ranked 1st for both the CTM–RM and SH hybrid applications. Source ranking for open fires was reduced from 10th (CMAQ–DDM) to 20th for both the CTM–RM and SH applications. The fuel oil source impact ranking increased from 12th for the base CMAQ–DDM simulation to 6th and 5th for CTM–RM and SH results, respectively. The order of source contributions at withheld observation locations for the CTM–RM and SH applications compared well, though often differed greatly from the base CMAQ–DDM rankings. The difference in rankings between CTM–RM and SH contributions was, at most, two positions.

The top three sources of primary PM2.5 for January 2004, based on source emissions, were dust, wood stoves, and coal combustion, estimated at 1275, 5301, and 3407 metric tons per day, respectively (Table S2). However, uncertainties associated with dust and wood stove emissions are much higher than most of the other sources, a factor of 10 and 5, respectively (Hanna et al., 1998, 2001; Hu et al., 2014). This uncertainty is driven in part by source variability. The large uncertainty and potential bias is reflected in the large shift in rankings for dust and wood stove source contributions to PM2.5. Other biomass burning sources such as lawn waste burning and wildfires have similarly large emissions uncertainties and likely large temporal variabilities, and their rankings were also significantly decreased.

Coal combustion includes the secondary formation of sulfate and remains in the top three sources for average SH PM2.5 contributions, as its emissions uncertainties are low due to the availability of continuous emission monitoring data. SO2 emissions are large (January 2004 domain totals: 72924.7 metric tons per day), as are NOX emissions (74619.7 metric tons per day) (Table S9). During the study period, coal combustion had the highest contribution to SO2 emissions (35080.3 metric tons per day) and the second highest contribution to NOX emissions (14250.1 metric tons per day) behind mobile sources. The source impacts found here account for the transformation of these gaseous emissions from coal combustion.

Secondary formation processes increase the impact of coal combustion, biogenic and livestock emissions relative to their initial primary PM contribution. January 2004 primary PM emissions estimates for biogenic and livestock were ranked 33rd and 31st, respectively. However, CMAQ–DDM, CTM–RM, and SH hybrid contributions ranked both sources significantly higher (biogenic rankings: 14th, 11th, and 9th, respectively; livestock rankings: 3rd, 1st, and 1st, respectively). Although primary PM2.5 emissions from these sources are not large, secondary processes and emissions from gaseous precursors led to high source contributions (Table S9). Biogenic sources emit large quantities of volatile organic compounds which go on to form secondary organic aerosols. Livestock emissions of gaseous ammonia react with sulfate, nitrate, and other acids to form ammonium salts. Therefore, the SH method captures and refines impacts from sources that contribute precursors of PM2.5.

Base CMAQ–DDM spatial fields were refined by applying Rj fields for each source and on each observation day. An example of the adjustment can be found in Fig. 4, where the CMAQ–DDM spatial field of dust impacts is adjusted on 4 January 2004. Sources with high occurrences (∼ > 50 %) of adjustment factors less than 1 include biomass burning, metals processing, and natural gas combustion, and refined spatial fields for these sources are presented in the Supplement (Figs. S5–S7). Biomass burning includes impacts from agricultural burning, lawn waste burning, open fires, prescribed burning, wildfires, wood fuel burning, and wood stoves. The SH method significantly decreases impacts from biomass burning on 4 and 22 January in the eastern USA and for portions of the west coast (Fig. S5), largely driven by the observed potassium and organic compound (OC) levels being lower than simulated levels. On average, CMAQ–DDM simulated levels were a factor of 3.1 (± 1.1) times higher than SH values on 4 January, and a factor of 5.2 (± 1.0) times higher on 22 January. Metal processing impacts were reduced for areas highly impacted by smelting and metal works industries including the Ohio River valley and mid-Atlantic regions (Fig. S6). On average, the CMAQ–DDM values were 21 (± 21) % higher than SH values on 4 January, and 25 (± 21) % higher on 22 January for metal processing impacts. Natural gas combustion impacts (area and point sources only) were reduced for the southeastern USA, the Ohio River valley region, the Gulf of Mexico states, and parts of California and Texas (Fig. S7). On average, CMAQ–DDM levels were 35 (± 14) % higher than SH values on 4 January, and 72 (± 28) % higher on 22 January for natural gas combustion impacts.

Refined spatial fields of January 2004 averaged source impacts are presented for eight sources: (c, d) dust, (e, f) on-road mobile sources, (g, h) coal combustion, (i, j) sea salt, (k, l) metal-related sources, (m, n) fuel oil combustion, (o, p) biomass burning, and (q, r) agricultural activities (Fig. 5). Total PM2.5 concentration fields are also included with overlapped observed concentrations from 28 January (a, b). The CMAQ–DDM spatial field overestimates concentrations in the Eastern USA, while overlapped concentrations agree more with spatial hybrid results. Modeled concentrations at monitors in mountainous areas, such as Salt Lake City, Utah, are underestimated due to local meteorological conditions (Gillies et al., 2010; Kelly et al., 2013). Wintertime temperature inversions, which cause stagnation in air circulation and consequently high air pollution episodes in industrial valleys, are challenging to capture in models.

Improved spatial field correlation is reflected in monthly averaged spatial fields (Fig. 5). SH dust impacts are greatly reduced domain-wide as compared to CMAQ–DDM. Monthly averaged refinement of biomass burning, where impacts were also greatly reduced, and metal-related source impact fields are consistent with results previously mentioned for 4 and 22 January. Sea salt impacts are localized to coastal areas as expected, and agricultural activity most greatly impacts the mid-western USA, an area dominated by farm lands. Coal and fuel oil combustion impacts are highest in the eastern USA and western Mexico (fuel oil only) and were adjusted very little as compared to the original CMAQ–DDM field.