Spatial distribution of source locations for particulate nitrate and sulfate in the upper-midwestern United States

Spatial distribution of source locations for particulate nitrate and sulfate in the upper-midwestern United States

ARTICLE IN PRESS Atmospheric Environment 41 (2007) 1831–1847 www.elsevier.com/locate/atmosenv Spatial distribution of source locations for particula...

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ARTICLE IN PRESS

Atmospheric Environment 41 (2007) 1831–1847 www.elsevier.com/locate/atmosenv

Spatial distribution of source locations for particulate nitrate and sulfate in the upper-midwestern United States Weixiang Zhaoa, Philip K. Hopkeb,, Liming Zhouc a

Department of Chemical and Biomolecular Engineering, Center for Air Resources Engineering and Science, Clarkson University, P.O. Box 5708, Potsdam, NY 13699-5708, USA b Department of Mechanical and Aeronautical Engineering, University of California, Davis, CA 95616, USA c Providence Engineering and Environmental Group LLC, Baton Rouge, LA 70808, USA Received 16 April 2006; received in revised form 12 October 2006; accepted 30 October 2006

Abstract Two back-trajectory analysis methods designed to be used with multiple site data, simplified quantitative transport bias analysis (SQTBA) and residence time weighted concentration (RTWC), were applied to nitrate and sulfate concentration data from two rural sites (the Mammoth Cave National Park and the Great Smoky Mountain National Park) and five urban sites (Chicago, Cleveland, Detroit, Indianapolis, and St. Louis) for an intensive investigation on the spatial patterns of origins for these two species in the upper-midwestern area. The study was made by dividing the data into five categories: all sites and all seasons, rural sites in summer, rural sites in winter, urban sites in summer, and urban sites in winter. A general conclusion was that the origins of the nitrate in these seven sites were mainly in the upper-midwestern areas, while the sulfate in these seven sites were mainly from the Ohio and Tennessee River Valley areas. The upper-midwestern areas are regions of high ammonia emissions rather than high NOx emissions. In the winter, metropolitan areas showed the highest nitrate emission potential suggesting the importance of local NOx emissions. In the summer, ammonia emissions from fertilizer application in the lower midwestern area made a significant contribution to nitrate in the rural sites of this study. The impact of the wind direction prevalence on the source spatial patterns was observed by comparing the urban and rural patterns of the summer. The differences between the results of two methods are discussed and suggestions for applying these methods are also provided. r 2006 Elsevier Ltd. All rights reserved. Keywords: SQTBA; RTWC; Back trajectory; Nitrate; Sulfate; Trajectory ensemble methods

1. Introduction Ambient particles have been shown to have adverse effects on human health and environmental quality (Dockery et al., 1993), so how to locate possible Corresponding author. Tel.: +1 315 268 3861; fax: +1 315 268 4410. E-mail address: [email protected] (P.K. Hopke).

1352-2310/$ - see front matter r 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.atmosenv.2006.10.060

origins of these air pollutants has become more and more urgent. Potential source contribution function (PSCF) is a simple back-trajectory-based approach for locating sources, estimating the conditional probability of a high concentration upon the arrival at the monitoring site that passed through each cell (Ashbaugh et al., 1985). This method has been widely applied (Zeng and Hopke, 1989; Cheng et al., 1993; Begum et al., 2005; Zhao and Hopke, 2006a, b).

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Seibert et al. (1994) developed a concentration weighted trajectory (CWT) method in which a mean concentration is calculated for each grid cell of a spatial domain by using time spent by air parcels over each cell as a weighting factor. This method is a modification of PSCF (Lupu and Maenhaut, 2002). Indicating a drawback of the Seibert procedure that the gradients of the ‘‘true’’ concentration fields are underestimated, Stohl (1996) developed a concentration redistribution method called residence time weighted concentration (RTWC). Keeler and Samson (1989) proposed the quantitative transport bias analysis (QTBA) method that used probability functions to estimate the potential fields of emission sources. Zhou et al. (2004) simplified QTBA, neglecting the effects of chemical reactions and deposition and applied the simplified QTBA (SQTBA) to locate particle sources for two rural New York sites. Brook et al. (2004a) also used SQTBA to examine sources areas of PM2.5 measured at 12 rural or suburban locations in eastern North America. In this study, RTWC and SQTBA were used to investigate the spatial patterns of sources for nitrate and sulfate in upper-midwestern areas. Different from the previous studies (Zhao and Hopke, 2006a, b; Lee and Hopke, 2006; Kim and Hopke, 2006) that used PSCF for an individual site, this study employed the concentrations of nitrate and sulfate from five urban sites (Indianapolis, St. Louis, Chicago, Cleveland, and Detroit) and two rural sites (the Great Smoky Mountain National Park and the Mammoth Cave National Park) in the upper-midwestern area. The urban sites are part of the Speciation Trends Network (Kim et al., 2005) while Mammoth Cave and Great Smokey National Parks are sites in the IMPROVE network (Malm et al., 1994). This set of sites makes it possible to make a broader study of the origins for nitrate and sulfate in this area. The formation rates and concentrations of these two secondary aerosol species depend on gas-phase precursor concentrations and meteorological conditions. Generally PM2.5 (particulate matter with diameter p2.5 mm) has long residence time in the atmosphere and can be transported over a large geographic region (Wilson and Suh, 1995; Eldred and Cahill, 1994). Therefore, this study explores the apparent locations of nitrate and sulfate sources in upper-midwestern areas that affect these seven sites, and examines the differences among the patterns derived from various subsets of

data (summer/winter and rural/urban). These results permit the discussion of possible factors that determine the results for each season and region, test the utility of these two multi-site back-trajectory methods, and provide suggestions for their general application. The results of this study may be helpful for designing specific strategies to control the concentrations of these two species in different seasons and regions. 2. Model description 2.1. RTWC Stohl (1996) in RTWC analysis redistributes the concentration fields obtained by CWT based on the following approach. Suppose some different trajectories pass through a specified grid cell and assume that all but one be ‘‘clean’’ trajectories and be associated with low concentrations at the receptor site. Thus, no major pollutant sources are located in the grid cell shared with the one ‘‘polluted’’ trajectory. Therefore, the ‘‘polluted’’ trajectory must have transported its pollutants somewhere else along its path (Stohl, 1996). For trajectory l, cl is the concentration measured upon the arrival of this trajectory. Let Cil be the mean concentration of the grid cell that is crossed by segment i (i ¼ 1yNl) of trajectory l. The redistribution for trajectory l is C il N l cil ¼ cl PN l . j¼1 C jl

(1)

After the redistribution of all trajectories, the redistributed concentrations cil are used to calculate the new concentration field C mn : C mn ¼

Nl M X X 1 logðcil Þtmnil , Nl SM l¼1 Si¼1 tmnil l¼1 i¼1

(2)

where tmnil is the residence time of segment i of trajectory l in grid cell (m, n). The difference between the concentration fields of RTWC and CWT is that redistributed concentrations cil are used in RTWC instead of the measured concentration cl. The connecter between these two equations is C il ¼ 10C mnði;lÞ , with (m, n) being the grid cell hit by segment i of trajectory l. The above iteration procedure is repeated until the average difference between the concentration fields of two successive iterations is below a pre-determined threshold value. In this study, the threshold value was set to be 3%.

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It was reported that RTWC was better at estimating the gradients of the concentration field (Stohl, 1996). 2.2. SQTBA Compared with QTBA, SQTBA neglects the effects of chemical reactions and depositions from the calculation of the potential field. The key concept of both methods is to estimate a concentration weighted potential field using Gaussian probability function. The basic principle of SQTBA (Brook et al., 2004a; Zhou et al., 2004; Keeler and Samson, 1989) is given below. Assume the transition probability of a tracer from a point along the trajectory to a grid cell can be expressed by a normal distribution function: "   0 0 0 1 1 x  x0 ðt0 Þ2  Qðx; y; t x ; y ; t Þ ¼ exp  2psx sy 2 sx !#   y  y0 ðt0 Þ 2 þ , ð3Þ sy where x and y are the coordinates of the grid cell, x0 (t0 ) and y0 (t0 ) are coordinates of the trajectory point, i.e. t0 in time upwind from the receptor site. sx and sy are the standard deviations (Gaussian widths) and are assumed to increase linearly in time upwind: sx ðt0 Þ ¼ sy ðt0 Þ ¼ at0 ,

(4)

where a is the dispersion speed and suggested to set to be 5.4 km h1. The potential mass-transfer field for a given trajectory l is a two-dimensional probability field of natural transport and can be written as  Rt  0 0 tx0 ; y0 ; t0 Þ dt0 0 Qðx; y;  Rt T l ðx; y x ; y Þ ¼ . (5) 0 0 dt The natural transport probability field weighted by the corresponding concentration yields the concentration-weighted mass transfer potential field. Finally the SQTBA field is represented as  0 0  ¯  0 0 SK l¼1 T l ðx; y x ; y Þcl   SQTBAðx; y x ; y Þ ¼ K wðw; yÞ, Sl¼1 T¯ l ðx; yx0 ; y0 Þ (6) where K is the number of trajectories and cl the concentration of the sample corresponding to trajectory l. The numerator of right part of Eq. (6) is the concentration weighted natural transport field

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spanned by all the trajectories, while the denominator is the natural transport field spanned by all the trajectories. The last term, w(x,y), is a weighting function to resist possible noise disturbance. An empirical and complex weighting function was used in Zhou et al. (2004) to reduce the noise in the SQTBA field, but in this study a simple weighting function similar to the one widely used in PSCF model was applied and it is expected that the feasibility of this simple method could provide a simple but effective weighting approach to general SQTBA applications. The weighting function in this study was defined as 8 1 pðx; yÞX2ave_p > > > > < 0:75 2ave_p4pðx; yÞXave_p , (7) wðx; yÞ ¼ 0:5 ave_p4pðx; yÞX0:5ave_p > > > > : 0:2 pðx; yÞo0:5ave_p where p(x,y) is the value of the grid cell (x,y) in the whole natural transport probability field (i.e., the denominator part in Eq. (6)), and ave_p is the average value of all the p(x,y) values. 3. Data analysis The concentrations of nitrate and sulfate for this study were collected at two rural sites (the Mammoth Cave National Park and the Great Smoky Mountain National Park) and five urban sites (Chicago, Cleveland, Detroit, Indianapolis, and St. Louis). The nylon filters were analyzed for anions by ion chromatography (IC). Data characterizing the samples from all of these sites collected in 2000–2003 were used in this study. The seven sites contain 324 (the Mammoth Cave), 379 (the Great Smoky Mountain), 210 (Chicago), 294 (Cleveland), 294 (Detroit), 246 (Indianapolis), and 369 (St. Louis) samples, respectively. The average nitrate and sulfate concentrations (mg m3) for the full year, summer and winter periods at each site are shown in Table 1. It can be seen that the average nitrate concentration in the urban sites is more than three times that for the rural sites. This significant difference reflects the impact of local sources, so it could be expected to see a difference between estimated patterns derived from the data characterizing urban and rural sites. The NOAA HYSPLIT model was used to calculated the back trajectories of each sampling site (Draxler and Rolph, 2003). The major parameters for the HYSPLIT model in this study was

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Table 1 Average nitrate and sulfate concentrations (mg m3) of all seasons, summer and winter for each site Nitrate

Chicago Cleveland Detroit Indianapolis St. Louis Great Smokey Mt Mammoth Cave

Sulfate

Mean (all)

Mean (summer)

Mean (winter)

Mean (all)

Mean (summer)

Mean (winter)

2.5 2.9 3.2 2.9 2.6 0.5 1.3

1.5 1.8 1.9 1.4 1.1 0.2 0.4

4.1 4.4 5.1 5.0 4.5 0.8 2.3

3.9 4.9 4.2 5.0 4.3 4.3 4.6

4.9 6.3 5.3 6.6 5.7 6.7 6.4

2.7 3.8 3.2 3.5 3.1 2.4 3.2

vertically mixed model and starting at 500 m above the ground level, which have been used in a number of prior studies (Fan et al., 1995; Gao et al., 1993: Hafner and Hites, 2003; Hsu et al., 2003; Begum et al., 2005). 4. Results and discussion An intensive investigation of the spatial patterns of nitrate and sulfate sources in upper-midwestern area was made by examining the results from five data sets: all sites and all seasons, rural sites in summer, rural sites in winter, urban sites in summer, and urban sites in winter. In this study, summer was defined as May–September and winter as November–March. RTWC (Stohl, 1996) requests a fixed length for all the trajectories, so the back trajectories for this model were computed with 97 ending points (four days duration with 1 h steps plus the starting point). SQTBA is more flexible in terms of trajectory length, so a very small number of trajectories with less than 97 points were also included. The units for all the SQTBA and RTWC figures in this paper are mg m3. 4.1. All sites and all seasons 4.1.1. Nitrate Fig. 1 shows the results from the two analyses of the nitrate source locations based on the data from all seasons and all sites. The SQTBA plot shows the upper-midwestern areas are the high potential areas of nitrate origins that agrees with the result of the study based on the data from CASTNET and CAPMON networks (Brook et al., 2004b). These high nitrate emission potential areas correspond to the areas, where there are major ammonia sources such as large-scale animal husbandry facilities and

significant use of anhydrous ammonia as a fertilizer (Goebes et al., 2003). Prior studies of St. Louis, MO (Lee and Hopke, 2006), Bondville, IL (Kim et al., 2005), Indianapolis, IN (Zhao and Hopke, 2006a), the Great Smokey National Park (Kim and Hopke, 2006), and the Mammoth Cave National Park (Zhao and Hopke, 2006b) have suggested that the nitrate concentrations generally appear to be more strongly related to source areas for ammonia than being related to areas rich in combustion sources of NOx. Thus, part of this study is to further examine the relative roles of nitrate and ammonia source areas in relationship to observed high concentrations of ammonium nitrate. The SQTBA plot also shows the high nitrate potentials in the Chicago and Detroit areas. NOx emitted from vehicles in those metropolitan areas could be one reason for the higher nitrate concentration in this area (Seinfeld and Pandis, 1998). The RTWC plot also indicates high nitrate potentials in the upper-midwestern area and the Detroit metropolitan area, but the locations are somewhat different from those of SQTBA. A difference between nitrate spatial patterns of these two methods was also observed in Zhou et al. (2004). Aerosol nitrate formation from reaction of gasphase HNO3 with available NH3 is largely influenced by the neutralization of H2SO4 (Olszyna et al., 2005; Seinfeld and Pandis, 1998) and possible rapid dry deposition of gaseous nitric acid. These factors may cause less stability of the formation of nitrate and the difference between two methods. A detailed discussion (including that for the other four site/ season categories) of these two methods will be provided in subsequent sections of this paper. There are significant differences in the emissions areas for ammonia from fertilizer use depending on the season (Goebes et al., 2003). The results in Fig. 1

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Fig. 1. Locations of nitrate source areas based on the data from all sites and all seasons (upper: SQTBA, lower: RTWC).

appear to reflect averaging over the various seasons. Thus, it will be useful to determine if these differences can be observed when the data are separated by season. 4.1.2. Sulfate Fig. 2 shows the spatial patterns of sulfate origins for all seasons and all sites. The SQTBA indicates that southern Ohio, southern Pennsylvania, West Virginia, eastern Kentucky, and western North Carolina have high sulfate emissions. This result agrees with the locations of large coal-fired power plants in the upper Ohio and Tennessee River Valleys. The RTWC plot also indicates the high sulfate emission potential across Ohio and Pennsylvania areas. However, the highest potential is in

southern Pennsylvania, a little different from the locations of highest SQTBA potential. In addition, the RTWC also located a high sulfate potential spot at the border of North Carolina and South Carolina, which is in agreement with the study (Chu, 2004) showing the North Carolina and South Carolina border area had high sulfate concentration in July. 4.2. Rural sites in summer 4.2.1. Nitrate Fig. 3 shows the spatial patterns of nitrate origins for the rural sites in summer. The SQTBA plot indicates a high nitrate emission potential in the lower-midwestern area. This pattern is different

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Fig. 2. Locations of sulfate source areas based on the data from all sites and all seasons (upper: SQTBA, lower: RTWC).

from the winter one shown in the following sections and that for all the seasons (Brook et al., 2004b), but it is close to those of Goebes et al. (2003) showing that regions with high ammonia emissions from fertilizer applications in the summer are mainly located in the lower-midwestern US (Kansas, Oklahoma, and Texas). The RTWC plot does not show a clear pattern except for the medium concentration areas at the border of upper Kansas and upper Missouri and a hot spot in the upper Oklahoma. During the summer, the winds are predominantly from the southwest and south (Schwartz and Elliott, 2002) reducing the influence of the upper-midwestern region as an ammonia source area. The high temperatures in summer inhibit the formation of

ammonium nitrate from HNO3 and NH3, resulting in the relatively low nitrate concentrations observed nationwide. Therefore, it is difficult to find stable areas that had predominantly influenced the observed high nitrate concentrations. The strong influence of atmospheric conditions could produce the difference in patterns between two methods. 4.2.2. Sulfate The locations of the sulfate emissions affecting the rural sites in summer are shown in Fig. 4. The SQTBA located a high sulfate emission source in the eastern US including Pennsylvania, Virginia, Ohio, and North Carolina. There are a number of coalfired plants in the upper Ohio River Valley and in the coastal states from North Carolina to Pennsylvania.

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Fig. 3. Locations of nitrate source areas based on the data from the rural sites in the summer (upper: SQTBA, lower: RTWC).

There will also be some additional emissions from oil-fired power plants in the coastal area. The SQTBA also shows a weak influence of the southeastern US including areas, with a number of coalfired power plants in Georgia and Alabama. The RTWC plot shows a hot spot at the border of Pennsylvania, Maryland, Virginia and some relatively high potential areas in Ohio, North Carolina, and Georgia that are in agreement with the general pattern of the SQTBA. The RTWC also indicates high sulfate emission potentials in upper Michigan and Texas. The high sulfate potential in upper Michigan was also observed in the PSCF analysis of the summer secondary sulfate resolved from the PM2.5 samples in the Great Smoky Mountain IMPROVE site (Kim and Hopke, 2006).

4.3. Rural sites in winter 4.3.1. Nitrate Fig. 5 presents the nitrate pattern based on the winter data from the rural sites. The SQTBA shows high nitrate influence in a wide area of the upper midwest. The high concentration of the ammonia from fertilizer applications in this area in the winter (Goebes et al., 2003) and low ambient temperatures are major factors in this high nitrate potential. It is an area where high emissions from cows are also expected (Pinder et al., 2004). This pattern also reflects the higher prevalence of northwesterly winds during the winter. The RTWC results also indicate high nitrate potential in upper-midwestern areas, but some high

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Fig. 4. Locations of sulfate source areas based on the data from the rural sites in the summer (upper: SQTBA, lower: RTWC).

potentials (hot spots) are absent from the area with the highest SQTBA value. A possible explanation will be provided later. Fig. 6 shows the ammonia emission estimates for the winter of 2002 (Kenski et al., 2004). The unit for this figure is ton day1. Clearly, the emission of ammonia (primarily from confined animal feeding operations and fertilizer application to agricultural crops) in the ‘‘Corn Belt’’ is substantial and dominates the concentrations in mass and spatial extent further supporting the results of this study. 4.3.2. Sulfate Fig. 7 shows the sulfate emissions areas for the rural sites in the winter. Neither SQTBA nor RTWC shows a high sulfate emission potential area

in the eastern coastal regions. The SQTBA shows high sulfate potential in Michigan, upper Ohio, Mississippi, and Alabama, while the RTWC shows a hot spot in Michigan and a high potential area in Kansas. Both methods indicate a high potential area in Michigan, although not in good spatial agreement. The Michigan area was found to have high sulfate concentrations in November 2001 (Chu, 2004) that could produce the observed influence of this area. The high SQTBA area in the south could be due to the higher temperatures that would enhance the photochemical conversion of SO2 to sulfate. The sulfate concentrations across the entire country were low and similar in January (Chu, 2004), so it could be hard to find stable and significant hot spots.

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Fig. 5. Locations of nitrate source areas based on the data from the rural sites in the winter (upper: SQTBA, lower: RTWC).

Fig. 6. Estimated ammonia emission rates for the winter of 2002 (Kenski et al., 2004).

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Fig. 7. Locations of sulfate source areas based on the data from the rural sites in the winter (upper: SQTBA, lower: RTWC).

4.4. Urban sites in summer 4.4.1. Nitrate The nitrate source locations for data from the urban sites in summer are presented in Fig. 8. The SQTBA shows a very different pattern from that in Figs. 1, 3, or 5, with high nitrate emission potential in the area of the upper Ohio River Valley and across Ohio up to metropolitan Detroit. Sufficient NOx emissions (mobile emission and combustion sources) in this area had sufficiently rapid conversion to HNO3, such that high gaseous HNO3 along with sufficient local ammonia would allow the production of some particulate nitrate even at the higher summer temperatures. However, it would be anticipated that only in the urban source areas

would such particulate nitrate be observed. The rural/urban differences in concentrations supports this scenario. In addition, the SQTBA pattern for the rural summer data (Fig. 3) does not show any high potential areas in Ohio and Tennessee in contrast to the urban summer pattern. One possible reason is the prevalent southwesterly–southerly wind in summer could prevent NOx emitted by coal-fired power plants in the Ohio and Tennessee River Valleys reaching the two upwind rural sites. The RTWC plot shows a hot spot in upper Texas and a relatively high potential in the Detroit area. The relatively high potential in Detroit may suggest NOx from vehicles in this area, in agreement with the SQTBA result. The hot spot in upper Texas

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Fig. 8. Locations of nitrate source areas based on the data from the urban sites in the summer (upper: SQTBA, lower: RTWC).

could correspond to high NH3 concentration in this area, as Goebes et al. (2003) reported that upper Texas and Oklahoma had the highest NH3 concentration in summer. 4.4.2. Sulfate The SQTBA plot in Fig. 9 shows the pattern of sulfate origins for the urban sites in the summer with a high emission potential in southern Ohio, West Virginia, eastern Kentucky, and eastern Tennessee, where there are many large coal-fired power plants. The RTWC indicates three hot spots in eastern coastal area. The hot spot at the border of eastern Kentucy and eastern Tennessee is in the highest potential area of SQTBA. The other two spots in southern Pennsylvania and North Carolina,

respectively, agree with the observed high summer sulfate concentrations in these two areas (Chu, 2004). The hot spot in southern Pennsylvania was also found in the study of annual North American SO2 emissions for 1990 (Brook et al., 2004b). Compared with the highest rural summer sulfate SQTBA area (Fig. 4), the highest SQTBA potential area for the urban summer data is located to the south of the urban sites, indicating a more direct influence of the coal-fired power plants in Ohio, West Virginia, eastern Kentucky, and eastern Tennessee. The more common southerly and southwesterly winds in summer could help drive this pattern, bringing sulfate or SOx from the Ohio River Valley area to the downwind urban sites.

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Fig. 9. Locations of sulfate source areas based on the data from the urban sites in the summer (upper: SQTBA, lower: RTWC).

4.5. Urban sites in winter 4.5.1. Nitrate Fig. 10 presents the nitrate source areas for the urban sites in the winter. The SQTBA shows the highest nitrate emission potential in the area surrounded by the urban sites and its neighboring area including Ohio, Indiana, Kentucky, and Tennessee. The RTWC also shows the highest potential area in the metropolitan areas. Again, the inclusion of only the urban sites suggests a much greater role of the area enclosed by the sites as a source region than when the rural sites are added or examined by themselves. These results suggest that much of the nitric acid may have been produced from NOx emitted by metropolitan vehicles, building heating, and the coal-fired power plants in the

Ohio River Valley area. Large areas to the west of these urban sites produce substantial ammonia emissions (Goebes et al., 2003). Thus, it would appear that with the colder temperatures in winter and lower rates of oxidation of NOx to HNO3, local and transported ammonia is still a major cause for ammonium nitrate. The second highest level of SQTBA emission potential is shown in the wide upper-midwestern area rich in high ammonia emissions from fertilizer application in winter (Goebes et al., 2003). The RTWC also shows a number of hot spots in this area. The comparison with the pattern (Fig. 5) for the rural winter category tells the shift of the highest potential area from the wide upper-midwestern area to the urban sites, which indicates local urban NOx emissions are likely to have a determining impact on

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Fig. 10. Locations of nitrate source areas based on the data from the urban sites in the winter (upper: SQTBA, lower: RTWC).

nitrate concentrations at the urban sites although transported ammonia still appears to be important. 4.5.2. Sulfate Fig. 11 shows the spatial patterns of sulfate origins for the urban sites in the winter. The high potential in Ohio by SQTBA and the high potential at the border of Pennsylvania and West Virginia by RTWC could be caused by the coal-fired plants there, supported by the observed sulfate concentrations in a winter episode (Chu, 2004). The reason for the hot spot in the North Carolina coastal area by RTWC is not clear yet. Compared with SQTBA pattern (Fig. 7) for the rural winter category, the SQTBA pattern for the urban winter category seems to be more directly influenced by the coal-fired

plants in the Ohio River Valley area. The reason for this result is not clear, but it agrees with the somewhat higher average sulfate concentrations over the five urban sites (3.3 mg m3) compared to that for the two rural sites (2.8 mg m3). Lower temperatures and photochemical activity in the winter reduces the rate of formation of sulfate. Thus, similar sulfate concentrations across the area may reduce the ability of these methods to locate stable areas with high emission potential. 4.6. Discussion As shown in Table 1, the rural and urban sites have relatively comparable sulfate concentrations, while they have quite different nitrate concentrations.

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Fig. 11. Locations of sulfate source areas based on the data from the urban sites in the winter (upper: SQTBA, lower: RTWC).

The comparable sulfate concentrations suggest sulfate is distributed relatively uniformly given the time for conversion and the insensitivity to the ammonia concentrations. However, the significant difference between the nitrate concentrations of two types of sites indicates that there must be significant local sources in the urban areas and an interaction between local and regional sources. It can be seen from the results that in the winter both the local and transported (regional) sources are responsible for the high nitrate concentrations, while in the summer local urban sources seems a major cause for the high urban values. In the figures for nitrate in all seasons, sulfate in all seasons, nitrate in winter, and sulfate in summer, the STQBA and RTWC are in reasonable agree-

ment, showing high nitrate potential in uppermidwestern area or high sulfate potential in eastern coastal area, but there are deviations between the locations of the highest potential areas (hot spots) provided by the two methods. In the results for nitrate in summer and sulfate in winter, these two methods either represent quite different patterns or show a distribution pattern without any high potential areas. Low nitrate concentrations in summer or low sulfate concentrations in winter across the area could result in difficulties in finding stable emission areas. The disagreement between nitrate origin patterns by RTWC and SQTBA and the possible overestimated RTWC value for sulfate were also reported in Zhou et al. (2004). The calculation of

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RTWC is a high dimensional optimization problem with an iteration process, so it is very likely to fall into local optima, which is common in optimization processes. In general, an optimization problem with multiple minima in its solution plane may be more easily trapped into local optima compared to a problem with a single global minimum. Thus, it can be difficult to find the global solution in some situations. This study has a similar problem. The wide upper-midwestern area is rich in nitrate or its gas-phase precursor (NH3), so this area is composed of multiple small areas with high nitrate concentration, which means this is a multiple-peak (or multiple local minima) optimization problem. Therefore, possible local minima (solutions) of RTWC could result in such a result that some relatively higher concentration peaks could be pulled down while some relatively lower concentration peaks could be over-promoted and finally lead to the deviations of the highest potential locations of these two methods. In addition, with the improved estimation of the gradients of the concentration fields (Stohl, 1996), RTWC is apt to reduce a relatively wide high potential area to a hot spot, so the high potential area by SQTBA could be reflected by a number of hot spots in RTWC. The metropolitan areas with high NOx concentration seem to produce stable high potential areas in both SQTBA and RTWC. The higher urban nitrate concentrations caused by local NOx and transported NH3 in these areas generate sharp concentration peaks that could be found by RTWC. The differences in the sulfate patterns between these two methods may arise in a similar manner, as the wide east coastal area is also composed of multiple small areas with high concentration of sulfate or its gas-phase precursor (SO2). Moreover, the difficulty in locating the stable high potential areas for winter sulfate and summer nitrate could also be attributed to the possible local optimal solution in some extent, since there are not significantly high concentration peaks in the observed areas. 4.7. Parameter determination In order to help general applications of these two trajectory analysis methods, it is necessary to summarize the parameters and some specific strategies used in this study.

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The concept of SQTBA is to use Gaussian kernel functions to estimate a tracer transfer probability field. Thus, a key choice in the use of this method is the selection of the proper Gaussian width. An overly large or overly small width would result in too similar probability responses across the whole field or too sharp responses (hot spots) along the trajectories, respectively. This study set the Gaussian width for each ending point along a back trajectory to be the product of the dispersion speed (5.4 km h1) and the backward time of the ending point, assuming the trajectory standard deviation is increasing linearly upwind in time (Keeler and Samson, 1989). The successful applications of this width estimation (Keeler and Samson, 1989; Brook et al., 2004a; Zhou et al., 2004) and the reasonable results in this study support the feasibility of this method. The weighting function applied to the different cases in this study has been found to be a simple but effective weighting method for SQTBA. The criteria values used in this study to set the intervals for different weights in the SQTBA seem feasible comparable to the previous successes in PSCF analyses. The threshold value to determine a grid cell as valid (i.e., source area) or not in terms of the number of ending points in this cell is a critical parameter for RTWC. In this study, the threshold values for more than half of the RTWC figures (cases) were half of the average ending points over all the cells in the whole domain area. Therefore, it was suggested that ‘‘half of mean’’ could be a feasible choice for this threshold value. 5. Conclusions Two back-trajectory analysis methods, SQTBA and RTWC, were applied to the nitrate and sulfate concentration samples of seven midwestern sites for locating potential emission origins for these two species in the midwestern area. The results for the case of all sites and all seasons provided a comprehensive view of the potential high emission areas. The high probability areas for nitrate at these seven sites were mainly in the upper-midwestern area, where ammonia was evolved from fertilizer applications and animal husbandry operations. The sulfate at these sites was mainly from the upper Ohio River and Tennessee River Valley areas where a number of coal-fired plants are located. There was good agreement with previously published PSCF analyses for these sites and the results of a study of

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spatial patterns of concentrations based on CASTNET and CAPMON network data. In addition to this general conclusion, other inferences could be drawn from the results of the other four cases. The overall source location patterns observed for all of the data were dominated by the patterns of the winter nitrate and the summer sulfate. For the urban sites, it is likely that NOx emitted from vehicles and local combustion including building heating was likely to be a major nitrate source. Particularly in the winter, sufficient local NOx along with both local and transported ammonia assigned the highest nitrate potential to the metropolitan areas. The comparison between the nitrate potential patterns of urban and rural sites indicates local NOx could be a determining factor in the formation of ammonium nitrate at the urban sites. The impact of the wind direction prevalence on the source spatial patterns was observed by comparing the urban and rural patterns in the summer. The discussion of these two methods and the suggestions for their general applications were also provided in detail. Acknowledgments This work was supported by the US EPA through Science to Achieve Results (STAR) grant RD83107801 and the New York State Energy Research and Development Authority through contract 7919. The authors also gratefully acknowledge the NOAA Air Resources Laboratory (ARL) for the provision of the HYSPLIT transport and dispersion model and/or READY website (http:// www.arl.noaa.gov/ready.html) used in this publication.

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