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Quantitative back-trajectory apportionment of sources of particulate sulfate at Big Bend National Park, TX
ARTICLE IN PRESS
Atmospheric Environment 40 (2006) 2823–2834 www.elsevier.com/locate/atmosenv
Quantitative back-trajectory apportionment of sources of particulate sulfate at Big Bend National Park, TX Kristi A. Gebhart, Bret A. Schichtel, Michael G. Barna, William C. Malm National Park Service, Air Resources Division, CIRA Building, Colorado State University, Fort Collins, CO 80523, USA Received 2 June 2005; received in revised form 6 January 2006; accepted 6 January 2006
Abstract As part of the Big Bend Regional Aerosol and Visibility Observational (BRAVO) study, a quantitative back-trajectorybased receptor model, Trajectory Mass Balance (TrMB) was used to estimate source apportionment of particulate sulfur measured at Big Bend National Park, Texas, during July–October 1999. The model was exercised using a number of sets of trajectories generated by three different trajectory models, with three different sets of input gridded meteorology, and tracked for 5, 7, and 10 days back in time. The performance of the TrMB model with the different trajectory inputs was first evaluated against perfluorocarbon tracers and synthetically generated sulfate concentrations from a regional air quality model, both of which had known attributions. These tests were used to determine which trajectories were adequate for the TrMB modeling of measured sulfate concentrations, illustrated the magnitude of the daily uncertainties as compared to the uncertainties in the mean attributions, and demonstrated the value of a robust evaluation process. Depending on trajectories, mean sulfate source apportionment results were 39–50% from Mexico, 7–26% from the eastern US, 12–45% from Texas, and 3–25% from the western US. These ranges were inclusive of the best BRAVO attribution estimates for Mexico, Texas, and the western US, but TrMB underestimated the eastern US contribution as compared to the BRAVO best estimates. Published by Elsevier Ltd. Keywords: Receptor modeling; Back-trajectory modeling; Big Bend National Park; Source apportionment; Tracer studies
1. Introduction The Big Bend Regional Aerosol and Visibility Observational (BRAVO) study (Pitchford et al., 2004, 2005; Schichtel et al., 2005a), designed to determine the causes of visibility impairment at Big Bend National Park, Texas (BBNP), was conducted during July–October 1999. A feature of BRAVO Corresponding author. Tel.: +1 970 491 3684; fax: +1 970 491 8598. E-mail address: [email protected] (K.A. Gebhart).
1352-2310/$ - see front matter Published by Elsevier Ltd. doi:10.1016/j.atmosenv.2006.01.018
was the use of several techniques to estimate the attribution of particulate sulfate concentrations measured at the park to sulfur emission sources in the US and Mexico. These techniques included receptor models, chemical dispersion models, qualitative data analyses, and finally, a model reconciliation and assessment, which led to the development of a hybrid source apportionment model to form the final BRAVO estimates. A key feature of the BRAVO study was the release of perfluorocarbon tracers from four sites in Texas, which aided model assessment.
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As part of BRAVO, a quantitative back-trajectory-based receptor model, Trajectory Mass Balance (TrMB), was first tested and then used to estimate the four-month average contributions to fine particulate sulfate measured at BBNP from several source regions. This paper describes that modeling effort, the evaluation of the TrMB model using tracer data and synthetic sulfate concentrations, and finally its application to source attribution at BBNP during BRAVO. 2. Methodology 2.1. Model equations The TrMB model (e.g., Pitchford and Pitchford, 1985; Iyer et al., 1987; Gebhart et al., 1988; Gebhart and Malm, 1989, 1994; Malm, 1992) is a receptor model in which measured concentrations at a receptor are assumed to be linearly related to the frequency of airmass transport from and duration in emission source areas before arriving at the receptor by the following formulation of the conservation of mass: C it ¼
J X
units of concentration per endpoint. These are estimates of the study-long (July–October 1999) mean relationship between airmass residence time in the source area and measured concentration at the receptor. The intercept was fixed at zero, forcing all identified source areas to account for the measured concentrations. When the intercept is allowed to float it often becomes larger than is physically reasonable because it will include the error term as shown in Eq. (2). Although emissions data were available for BRAVO, they were not included explicitly in this modeling, given that sulfur emissions in Mexico are very uncertain (Kuhns et al., 2005). The error in Eq. (2) is due to measurement error and deviations of the daily unknown transfer coefficients from their means, ðajt a¯ j ÞN jt . Additional assumptions inherent in the model include that uncertainties in measured values are random, uncorrelated, and normally distributed and the contributions of the source regions are linearly independent. Also, the number of source regions modeled cannot exceed the number of time periods. 2.2. Source areas
Qijt T ijt N jt .
(1)
j¼1
The subscripts i,j, and t refer to chemical species, source areas, and times, respectively. C are the measured concentrations, Q the emission rates, T the transformation and deposition factors to account for deposition, diffusion, and chemical conversion, and N the number of back-trajectory endpoints. An endpoint is defined as the position of an air parcel that eventually will arrive at the receptor, in this case, BBNP. Endpoints are calculated hourly for up to 10 days back in time. In this application the only variables inputted explicitly were C, the daily measured sulfate concentrations at BBNP; and N, the number of back-trajectory endpoints in each source area for each day. The remaining terms, QT, called the ‘‘transfer coefficients’’ were estimated by ordinary least-squares regression such that Eq. (1) simplifies to C t ¼ a¯ 0 þ
J X
a¯ j N jt þ errort .
(2)
j¼1
The subscript i has been dropped for simplicity since only particulate sulfate was modeled. The values of a ¼ QT are the regression coefficients with
Source areas were chosen based on several criteria including: (1) Location: Understanding the relative influence of sources in Mexico vs. sources in Texas and other areas of the US was a primary goal of BRAVO. (2) Size: Source areas should generally get larger as the distance from the receptor increases to accommodate the increased uncertainty in endpoint locations and increased dispersion around the trajectory center line as distance and travel time increase. However, they should be small enough so that a single regression coefficient is sufficient to explain the mean relationship between source area and receptor. Most trajectories passing through a region should ideally have similar exposure to emissions, dispersion, and transformation en route to the receptor. (3) Emissions: Model performance relies on the contribution from the area being larger than the errors in the model, so source areas should have significant emissions of the pollutant of interest, in this case SO2. (4) Independence: To avoid collinearity between source regions, the timing and number of trajectories passing through each region should be reasonably independent from other regions. Multi-collinearity between source areas was examined by two methods, the correlation matrix of the endpoints and the Variance Inflation
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3
4
2
1
concentrations from two types of samplers. When the higher time resolution data were averaged to 24 h, there were from 1 to 7 daily measurements of fine particulate sulfur or sulfate for each day. The daily range and medians are shown in Fig. 2. Days of particular interest were 1, 14–15 September and 12 October, which, because they had high measured concentrations, were influential points in the TrMB regressions. Details of the particulate measurements are discussed in Malm et al. (2003) and Pitchford et al. (2004). Synthetic sulfate concentrations were also used for testing purposes only. These are discussed in Section 4.1.
5
9 6
12
10
8
7
15 16 17 19 13 14 18
20
11 21
22 23 24 25
26 27
Fig. 1. Source areas used for source attribution of sulfate at Big Bend National Park.
Factor (VIF) (Belsley et al., 1980), shown in Eq. (3). VIFj ¼
1 . 1 R2j
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(3)
R2 is the multiple correlation coefficient of the endpoints in one source area regressed on the endpoints in the remaining source areas. A high VIF indicates that endpoints in that region could be nearly explained by some linear combination of those in other regions, while the correlation matrix alone is only useful for individual pairs of source areas. A VIF greater than 10 is considered strong collinearity. A further indication of multi-collinearity is large standard errors for the regression coefficients. It is often difficult to choose source areas that simultaneously satisfy all criteria and the choice requires some qualitative judgment. Those chosen for this analysis are shown in Fig. 1. 3. Input data 3.1. Sulfate concentrations The sulfate concentrations used in TrMB for BRAVO were the daily median concentrations of all available 24-h average fine (o2.5 mm diameter) particulate sulfur and sulfate concentrations measured at BBNP for 117 days from 5 July to 29 October 1999. Measurements at the primary BRAVO receptor site, K-Bar Ranch, located within BBNP, included 12- and 24-h values of sulfate ion, and 6-, 12-, and 24-h average elemental sulfur
3.2. Perfluorocarbon tracers Four chemically inert, non-depositing perfluorocarbon tracers were released at nearly constant rates from four different sites within Texas during the second half of the BRAVO field study: Eagle Pass (250 km from BBNP), San Antonio (450 km), Houston (750 km), and northeast Texas (750 km). During the first half of the study three of the four tracers were released from Eagle Pass as ‘‘timing’’ tracers with release rates specified to determine transport times from Eagle Pass to BBNP, and the fourth was released from northeast Texas. Details of the tracer release, measurement, analyses, and evaluation can be found in Watson et al. (2000), Pitchford et al. (2001, 2004), White et al. (2001), Green et al. (2003), Gebhart et al. (2005), and Schichtel et al. (2005b). 3.3. Back-trajectories Three back-trajectory models, Atmospheric Transport and Dispersion (ATAD) (Heffter, 1980), HYSPLIT version 4.5 (Draxler and Hess, 1998), and CAPITA Monte Carlo (CMC) (Schichtel and Husar, 1997) were used to generate backtrajectories for input to TrMB. All models were exercised with at least two gridded input meteorological fields. ATAD was also run with its traditional input of North American rawinsonde data (Schwartz and Govett, 1992) supplemented by observations from four BRAVO radar wind profilers. The gridded data included 36 km output from the Mesoscale Meteorological Model (MM5) (Grell et al., 1994) and data from two standard National Oceanic and Atmospheric Administration (NOAA) archives: the ETA Data Assimilation System (EDAS) (Black, 1994) when available and the lower
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Range and Daily Median of Measured Sulfate at K-Bar 10
Jul 1
Aug 1
Sep 1
Oct 1
Nov 1
Median shown for 7/5-10/29
8
6
4
2
0 180
200
220
240 260 Julian Day 1999
280
300
Fig. 2. Range (shaded area) and daily median of 24-h averaged sulfur and sulfate measurements in mg m3 at K-Bar Ranch (line).
resolution FNL (Kanamitsu, 1989) when EDAS results were not available. EDAS data were missing for the entire month of October and for several days in July. The combined EDAS and FNL data set is referred to as EDAS/FNL. There are several fundamental differences in how the trajectory models calculate trajectories and in the input data employed. These details and the results of extensive qualitative and quantitative testing of many combinations of model and input data are described in Gebhart et al. (2005) and summarized in the following section. Tests showed that the choice of wind field was more influential than the trajectory model for source-attribution modeling. Test results also showed that the sparse rawinsonde data alone are probably inadequate for back-trajectory modeling in this area which is frequently downwind of data-poor regions including Mexico and the Gulf of Mexico. Back-trajectories were started from BBNP (29.31N Latitude, 103.181W Longitude) and traced backward in time for 5, 7, and 10 days. Early results from the BRAVO chemical dispersion modeling (Schichtel et al., 2005a, b, 2006; Pitchford et al., 2004, 2005; Barna et al., 2006b) indicated that the lifetime of sulfur in the atmosphere was longer than
5 days on a significant number of days during BRAVO. Trajectory lengths of up to 10 days in length were therefore used in the TrMB modeling. 4. Results 4.1. Summary of model tests 4.1.1. Modeling of known attributions A test of the TrMB model was performed in which measured sulfate concentrations were replaced by simulated values from the Regional Modeling System for Aerosols and Deposition (REMSAD) (Barna et al., 2006a,b), a deterministic chemical transport model. Source attributions of the simulated sulfate were also known from REMSAD and compared to those estimated by TrMB. To be consistent with the meteorological input data employed by REMSAD, only backtrajectories generated using MM5 wind fields were used in this evaluation. A similar test of measured perfluorocarbon tracer concentrations with known release sites and rates allowed testing of both MM5 and EDAS/FNL meteorology. However, the tracers are nonreactive and nondepositing, so influences of chemistry and
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Table 1 Attributions of simulated REMSAD sulfate by TrMB for 6 July–28 October 1999 (115 days) using MM5 Model
Texas
Mexico
Eastern US
Western US
R2
Mean bias (predobs) SO4 (ng m3)
Mean norm. bias (predobs)/obs
REMSAD simulated sulfate (ng m3) REMSAD attrib. CMC 5-day CMC 7-day CMC 10-day HYSPLIT 5-day HYSPLIT 7-day HYSPLIT 10-day ATAD 5-day
351
488
897
195
NA
NA
NA
18% 19% 20% 21% 43% 43% 46% 25%
25% 31% 24% 21% 25% 23% 21% 33%
46% 39% 36% 37% 16% 16% 19% 36%
10% 11% 20% 21% 17% 18% 13% 8%
NA 0.778 0.798 0.775 0.768 0.820 0.801 0.735
NA 23 12 13 11 26 14 24
NA 11% 9% 9% 20% 11% 15% 16%
Top row shows the REMSAD attributions with the boundary conditions (7%) and non-linear components (2%) proportionally redistributed. TrMB attributions within 10 percentage points of the REMSAD attributions are highlighted. The last three columns are statistics comparing the TrMB predictions to REMSAD simulated sulfate concentrations.
Table 2 Results of TrMB modeling (MM5 input, 5-day trajectories) of perfluorocarbon tracers at BBNP, 17 September–28 October 1999 (42 days)
Mean conc. (ppq) Mean percent (%) ATAD Rawinsonde ATAD EDAS/FNL HYSPLIT EDAS/FNL CMC EDAS/FNL ATAD MM5 HYSPLIT MM5 CMC MM5
Eagle Pass
San Antonio
Houston
R2
Mean bias (ppq)
Mean norm. bias
0.15570.024 2074 35712 1678 28712 3079 34712 82718 23716
0.55970.081 72713 65714 3379 67713 43710 60713 18718 77719
0.06270.008 871 079 5179 579 2778 679 0711 0712
NA NA 0.495 0.708 0.640 0.721 0.564 0.484 0.643
NA NA 0.244 0.096 0.078 0.007 0.019 0.044 0.085
NA NA 13% 376% 834% 235% 901% 1159% 372%
The first two rows show the measured concentrations and percents of tracer from each release site. Remaining rows give the modeled attributions. Those accurate to within the uncertainty of the measurement and standard error of the regression coefficients are highlighted.
deposition on model performance could not be tested using the tracers. Also, all tracer release sites were within Texas and tracers were released from two of the sites only during the second half of the study, so the model’s ability to distinguish concentrations arriving from more distant source regions and during summer-time meteorology could not be considered using the tracers. Tables 1 and 2 summarize the results of these tests which are discussed in detail in Gebhart et al. (2005). Mean bias is the mean of (predictedobserved) and mean normalized bias is the mean of the daily (predictedobserved)/observed. High mean normalized biases in the tracer tests are due in part to a few near-zero observations. These also caused the sign of the mean normalized bias to be opposite of the mean bias. Note that high R2 and
low biases between predicted and observed concentrations are poor indicators of whether the TrMB model has reproduced the correct attributions. In the tracer test, the cases with the highest correlations also had the least correct attributions. For example see ATAD EDAS/FNL and CMC EDAS/ FNL in Table 2. These statistics indicate only whether TrMB could fit a model that reproduced the observations, not whether it fit the correct model. As shown in Tables 1 and 2, TrMB reproduced known mean source attributions to within measurement and regression uncertainties using some input trajectories, while other sets of trajectories did not perform well. Furthermore, those that passed one test tended to also pass the other, indicating that the source of error was more likely
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Mexico 10/4
2.0
10/6 10/5
10/9 10/11 8/22
1.5 1.0
10/19 10/22
0.5 10/21
0.0 0
10/5 8/30 8/21 9/23
1.5 ug/m3
ug/m3
Texas 2.5
1.0
7/27 8/28 8/29
9/11
0.5
7/30 8/1 7/31 9/24
0.0
1000 2000 3000 4000 5000 endpoints
0
2000
4000 6000 endpoints
8000
CAPITAMC MM5 5-Day Eastern U.S
5
10/6 9/1 9/15
3 2
10/13
10/12 10/14
1
1.2 10/10
ug/m3
4 ug/m3
Western U.S.
9/2
10/5
0.8
10/8
10/17 9/21 10/18
9/25
10/20 9/30 9/27
0.4
9/26
7/11
0
0.0 0
2000 4000 endpoints
6000
0
2000 4000 8000 6000 10000 endpoints
Fig. 3. Scatter plots of simulated sulfate attributions vs. number of endpoints for each of four large source areas using 5-day backtrajectories from the CAPITA MC model using MM5 meteorology. The solid lines are the ‘‘true’’ mean slopes from the deterministic model simulation; dashed lines are the TrMB modeled mean slopes. The points show the daily values.
incorrect trajectories rather than errors in the concentrations. Collinearity tests showed that incorrect attributions were not associated with collinearity. Based on the results of these tests and some qualitative tests described in Gebhart et al. (2005), trajectories generated by the CMC and ATAD models with MM5 input and by HYSPLIT with EDAS/FNL input were deemed adequate for use in the TrMB attribution of measured sulfate for BRAVO. The remaining sets of trajectories were not used. 4.1.2. Daily deviations from mean The TrMB regression coefficients are estimates of the mean relationships between measured concentrations and the presence of air masses in upwind source regions. BRAVO provided an opportunity to examine the daily deviations from the mean, ðajt a¯ j ÞN jt . Using the simulated sulfate concentrations as described above, the known daily attributions from REMSAD were compared to those estimated from TrMB. Results for one case are shown in Fig. 3. In each scatter plot the solid line shows the ‘‘true’’ mean relationship between endpoints and concentrations as simulated by REMSAD. The dashed line is the mean estimated by TrMB. In this example, the closeness of the dashed
and solid lines illustrates, as can also be seen in Table 1, that all modeled attributions for this case were within 5 percentage points of the correct attributions. TrMB slightly overestimated mean attributions for Texas, Mexico, and the western United States (dashed line above the solid) and underestimated the eastern US. The more interesting aspect of the graphs, however, is the scatter of the points about the lines. The points are the ‘‘true’’ REMSAD-simulated daily endpoint-to-concentration relationships. While TrMB reproduced the means quite accurately, some daily attributions deviated significantly from the mean. For example, on 4 October, the true (simulated) sulfate attribution to Texas was underestimated by TrMB by nearly a factor of 5, even though on average, the mean attribution to Texas was within 1 percentage point of being correct. This is not surprising since daily chemistry, dispersion, emissions, and deposition can all vary significantly from a four-month mean. It does, however, illustrate that the uncertainties in the daily TrMB attributions are much larger than the uncertainties in the mean attributions. In fact, even if the TrMB mean source attributions were perfect, there could still be very large errors in the daily attributions.
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Table 3 Relative attributions of median 24-h sulfur at Big Bend to each source region by each model/wind field combination Percent attribution of sulfate to each source area
CAPITA MC with MM5
HYSPLIT with EDAS & FNL start heights 100–1000 m AGL
ATAD with MM5
Trajectory length (days) North Central States (4) Northeast (5) MO/IL/AR (10) East Central States (11) LA/MS (20) FL/GA (21) Eastern U.S (4,5,10,11,20,21)
5 073 072 573 173 1776 073 23%
7 074 172 974 576 1179 074 26%
10 075 174 1075 977 479 074 24%
5 072 271 073 172 475 072 7%
7 073 371 076 473 776 073 14%
10 074 073 079 674 1078 074 16%
5 072 071 572 072 1775 072 17%
Pacific Northwest (1) Northern Rockies (2) Dakotas (3) Southern California (6) AZ/NM (7) Central Plains (9) Western US (1,2,3,6,7,9)
373 074 374 073 579 3710 14%
373 074 075 073 379 15711 21%
574 075 376 075 7710 10712 25%
073 076 373 072 477 177 8%
073 176 574 072 279 076 8%
073 077 475 273 0712 078 6%
272 073 072 172 074 075 3%
Texas Panhandle (8) West Texas (15) North Central Texas (16) Northeast Texas (17) Southeast Texas (19) Texas (8,15,16,17,19)
074 075 275 474 13710 19%
075 375 075 074 9711 12%
075 075 075 074 12711 12%
076 177 475 573 3578 45%
077 078 176 673 29710 36%
578 0710 177 676 18712 30%
072 173 975 272 878 20%
Baja California (12) Northwest Mexico (13) North Central Mexico (14) Carbo´n I & II (18) West Central Mexico (22) Central Mexico (23) Monterrey Region, MX (24) SW Coast of Mexico (25) Mexico City & Volcano (26) S. Mexico/ Yucatan (27) Mexico
073 174 074 23712 175 073 5710 072 976 675 45%
174 075 074 24712 175 073 079 071 876 775 41%
076 077 175 22711 175 073 079 071 1076 675 40%
173 277 073 24710 073 073 477 171 774 074 39%
075 4710 073 21711 474 073 578 072 874 075 42%
076 578 074 22712 674 074 778 173 675 175 48%
No ends 071 274 33710 072 072 676 071 1075 174 50%
(12,13,14,18,22,23,24,25,26,27) Mean observed S (ng m3) Mean predicted S (ng m3) R2 Number of observations
835.7 832.7 0.622 117
835.7 833.1 0.669 117
835.7 834.6 0.689 117
835.7 807.7 0.478 117
835.7 795.9 0.500 117
835.7 786.9 0.459 117
835.7 823.3 0.585 117
Uncertainties are based on the standard errors of the regression coefficients. Model statistics are shown in the last 4 rows.
4.2. BRAVO sulfate source attributions Table 3 shows a summary of the TrMB results for measured fine particulate sulfur at BBNP for all sets of trajectories that passed the preliminary tests described above. The table includes the four-month mean relative percent attributions for each of the 27 smaller source areas and uncertainties based on the standard errors of the regression coefficients. Table 3 also includes the summed attributions for four larger aggregated regions, eastern US, western US, Texas, and Mexico. Uncertainties for these large
areas were not estimated because it was not possible to ascertain what portions of the estimated uncertainties were due to misattributions within the large region as opposed to misattributions between them. For example, an error in the attribution to southeast Texas could be because some of that sulfur actually arrived from northeast Texas, resulting in no error in the total attribution from Texas; or it could be a miss-allocation between southeast Texas and Louisiana/Mississippi, generating incorrect apportionments to both Texas and the eastern US.
0.14770.114 37.790715.233 0.16370.140 1.20870.764 0.13470.079 0.13270.112 0.21670.334 0.04370.240 0.35970.194 0.02070.331 0.08770.247 0.09170.118 0.04070.507 0.12470.241 0.02370.141 0.24370.110 0.25270.066 0.21870.544 0.49170.884 0.01670.220 0.12770.048 1.38871.071 1.29170.567 0.05770.066 0.28471.898 0.43770.174 0.00270.105
North Central States (4) Northeast (5) MO/IL/AR (10) East Central States (11) LA/MS (20) FL/GA (21) Pacific Northwest (1) Northern Rockies (2) Dakotas (3) Southern California (6) AZ/NM (7) Central Plains (9) Texas Panhandle (8) West Texas (15) North Central Texas (16) Northeast Texas (17) Southeast Texas (19) Baja California (12) Northwest Mexico (13) N Central Mexico (14) Carbo´n I & II (18) W Central Mexico (22) Central Mexico (23) Monterrey Reg., MX (24) SW Coast Mexico (25) Mex City, Volcano (26) S Mexico/ Yucatan (27) 1.29 2.48 1.16 1.58 1.69 1.17 0.65 0.18 1.85 0.06 0.35 0.77 0.08 0.51 0.16 2.21 3.83 0.40 0.56 0.07 2.64 1.30 2.28 0.85 0.15 2.50 0.02
t
0.20 0.02 0.25 0.12 0.09 0.24 0.52 0.86 0.07 0.95 0.73 0.44 0.94 0.61 0.87 0.03 0.00 0.69 0.58 0.94 0.01 0.20 0.03 0.40 0.88 0.01 0.99
P
2.0 1.6 3.2 2.2 3.4 1.4 2.1 3.4 3.2 3.4 17.6 4.0 9.3 10.5 3.9 2.6 3.7 6.5 22.9 2.6 1.8 6.6 2.0 2.4 2.9 2.1 2.0
VIF
179.8 0.7 325.2 31.7 588.9 208.7 71.5 192.6 153.2 48.8 294.6 436.9 113.9 264.9 318.3 246.1 1242.4 70.7 86.1 99.2 1753.1 28.4 44.2 912.4 8.1 197.7 342.4
Mean ends/ day 26720 28711 53746 38724 79747 28723 15724 8746 55730 1716 26773 40752 5758 33764 7745 60727 313782 15738 42776 2722 223784 39730 57725 52760 2715 86734 1736
Pred S (ng m3)7unc 3 3 7 5 10 3 2 1 7 0 3 5 1 4 1 8 39 2 5 0 28 5 7 7 0 11 0
% pred S
073 371 076 473 776 073 073 176 574 072 279 076 077 078 176 673 29710 075 4710 073 21711 474 073 578 072 874 075
Relative %7unc
32 5 47 24 57 54 37 44 38 19 33 55 36 34 49 51 96 18 18 25 99 13 32 88 8 50 55
No. days (max 117)
Trajectories from HYSPLIT with EDAS/FNL input, 7-day trajectories. Order of source areas is the same as in Table 3. ‘‘No. days’’ is the number of days when at least one endpoint was in the source area.
Coef.7SE
Source area (locations in Fig. 1)
Table 4 Sample of detailed statistics from a TrMB model
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Detailed statistics for a single case are shown in Table 4, which includes the regression coefficients, standard errors, t statistics (coefficient/standard error), P values (probability that coefficient could be zero), and VIF. Values of tX2 ðP ¼ 0:05Þ indicate significance at the 95% confidence level. Negative coefficients occurred when the endpoints were inversely correlated with the concentrations so that when more air arrived from the area the concentration at BBNP tended to be lower. No negative coefficients were significant at the 95% level and all had small magnitudes. Sources with VIFs410 are considered significantly collinear with a combination of other areas, causing more difficulty in determining the regression coefficient (higher standard error) so more uncertainty in the attribution. With rare exceptions VIFs410 occurred only for sources to the west and/or north from which airmasses arrived infrequently and from which attributions are also expected to be low due to relatively low emissions. Trajectories also often had higher elevations west of BBNP, thus possibly not interacting with ground-based emissions in those areas. Collinearity could be eliminated by combining sources or readjusting their boundaries. However, for BRAVO, source boundaries were fixed to facilitate comparison of other factors including source apportionment techniques, emissions, meteorological data, trajectory models, trajectory start heights and lengths, etc. Different sets of trajectories had collinearity in different locations. The seventh column of Table 4 gives the daily average particulate sulfur (ng m3) attributed to each source, calculated by multiplying the regression coefficient by the mean endpoints. The uncertainty is estimated by multiplying the mean endpoints by the standard errors of the regression coefficients. The raw percent attribution, shown in column eight, is the mean predicted sulfur attributed to the area divided by the total predicted sulfur. Column nine is relative percent attribution as shown in Table 3, calculated by setting negative values to zero and renormalizing the positive values to 100%. Uncertainties are assumed to be the same as for the raw attributions, though this is likely an underestimate. The final column in Table 4 is the number of days (maximum 117) when airmasses arrived from each area. Attribution results vary somewhat by trajectory model and input data combination, though for most of the 27 smaller sources the differences between combinations are within the standard errors of the regression coefficients. In general, all combinations
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give approximately the same total attribution to Mexico, ranging from 39% to 50% with a median of 42%. With MM5 meteorology in the CMC model, longer trajectories result in somewhat less attribution to Mexico, while the reverse is true for HYSPLIT with EDAS/FNL. The biggest differences were in the mean attributions to Texas. HYSPLIT with EDAS/FNL input attributes approximately twice as much (30–45%) to Texas as predicted using MM5 in ATAD (20%) or CMC (12–19%). Both HYSPLIT and CMC attribute less to Texas as the trajectory length increases. MM5 input in both ATAD and CMC results in more attribution (17–26%) to the eastern US than HYSPLIT with EDAS/FNL (7–16%). Longer HYSPLIT trajectories give greater attribution to the eastern US, while the largest attribution to the eastern United States by CMC was with 7-day trajectories. For all model/wind field combinations the smallest attribution to any of the four large source regions was to the western US, though the percentages attributed by HYSPLIT/EDAS/FNL (6–8%) were only about half that attributed by CMC/MM5 (14–25%). ATAD/MM5 had the lowest attribution to the western US at just 3%. Longer HYSPLIT/EDAS/FNL trajectories caused slightly less attribution to the western US, while the reverse was true for longer CMC/MM5 trajectories.
5. Discussion 5.1. Variations in TrMB results Trajectory heights influence the speeds so trajectories with lower average heights tend to preferentially implicate closer source regions at the expense of those farther upwind. Endpoints generated with CMC/MM5 had a mean height of 1156 m and mean wind speed of 6.2 m s1 while those generated by HYSPLIT/EDAS/FNL had a mean height of 686 m and speed of 5.6 m s1 (Gebhart et al., 2005). TrMB attributions using HYSPLIT/EDAS/FNL trajectories as input generated much higher attributions (30–45%) for close-in Texas than did CMC/MM5 trajectories (12–19%). As might be expected, longer trajectory lengths resulted in lower attributions to Texas and higher attributions to the more distant eastern and western US. The biggest differences were usually, though not always, between the 5- and 7-day lengths. Longer trajectories resulted in higher attributions to Mexico with CMC/MM5 input, but lower
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attributions when HYSPLIT/EDAS/FNL trajectories were used. An assumption of most trajectory analyses is that errors in horizontal placement of trajectories are random, e.g., trajectories that are too far east on some days are balanced by those that are too far west on other days, so that the mean directional error is small when many trajectories are averaged. However, qualitative and quantitative tests of BRAVO back-trajectories showed that there were systematic biases in horizontal placement of trajectories that were dependent mostly on input meteorology and to a lesser extent on the trajectory model. Biases appeared to be both regionally and seasonally dependent (Gebhart et al., 2005). In addition, because of the nature of ordinary least-squares linear regression, the TrMB model is more sensitive to errors in trajectory placement that occur on high concentration days than it is to those on days of lower concentrations. Despite several tests against the BRAVO tracers and simulated data, none of the sets of trajectories shown in Table 3 could be eliminated as obviously inferior. 5.2. TrMB results compared to other BRAVO modeling Comparisons of TrMB results to those from REMSAD (Barna et al., 2006b), shown in Table 5, found that TrMB estimated that larger fractions of sulfur arrived from Mexico and the western US and less from the eastern US than REMSAD. Both CMC and ATAD with MM5 give approximately the same average attribution to Texas as REMSAD, though HYSPLIT/EDAS/FNL attributes much more to Texas. Since MM5 meteorology was used in REMSAD, it is expected that EDAS/FNL meteorology might give results that are more different from MM5. Table 5 Comparison of TrMB sulfate source attribution results to other BRAVO estimates Source region
TrMB (%)
REMSAD (%)
BRAVO best estimate (hybrid model) (%)
Texas Eastern US Western US Mexico Boundary Other
12–45 7–26 3–25 39–50 0 0
16 42 9 23 7 3
16 30 8 40 6 0
Reasons for the differences between TrMB and REMSAD could include problems with either model, including collinearity or inaccurate or inappropriate back-trajectories (e.g. endpoints above the mixed layer) in TrMB. The most likely sources of error in REMSAD include incorrect emissions, especially Mexican emissions (Kuhns et al., 2005) and/or incorrect modeling of precipitation and clouds (Barna et al., 2006a). The final phase of the BRAVO study was model and data reconciliation (Pitchford et al, 2004, 2005; Schichtel et al., 2005a, 2006). Analysis of the results of two chemical transport models (CTMs) revealed systematic geographic and seasonal biases in the source apportionments for BRAVO. For example, during October, the modeled contribution from the eastern US sources nearly always exceeded the measured concentrations in east Texas. Conversely, during July, when transport patterns were most likely to bring air masses from Mexico to BBNP, predicted concentrations at BBNP were underestimated. To correct these biases, a hybrid source apportionment model was developed which adjusted the initial CTM source contributions so the modeled sulfate concentrations optimally fit the measured concentrations, resulting in refined daily source contributions with reduced biases. The refined results reduced the initial study-average eastern US contribution to BBNP from 40% to 30%, while Mexico’s contribution increased from 23–32% to 40%. Contributions from Texas and the western US changed little, with final attributions of 16% and 5–9%, respectively. Besides being more consistent with measured concentrations, these hybrid source attributions also brought the CTM-predicted attributions closer to those estimated by the receptor models, including TrMB. The hybrid results are considered by the study participants to be the best BRAVO estimates of sulfate source attribution. These are also summarized in Table 5. The range of TrMB attributions bound the BRAVO best estimate for three of the four large source regions, Mexico, Texas and the western US. However, all TrMB estimates were lower than the BRAVO best estimate for the eastern US. 6. Conclusions A deterministic back-trajectory-based linear regression model, TrMB, with minimal input requirements, was a useful source apportionment technique for the 1999 BRAVO study. Tests of TrMB using known
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attributions of tracer and synthetic sulfate data showed that this model could reproduce mean source attributions to within expected uncertainty when some sets of trajectories were used and that TrMB results were most sensitive to the trajectories on high concentration days. Those sets of trajectories that failed these tests were then eliminated from the source attribution modeling of the measured data. TrMB source apportionment estimates for sulfate measured at BBNP during BRAVO varied somewhat depending on input meteorological data, trajectory model, and trajectory length, but the ranges of results included the independently generated BRAVO study best estimates for Mexico (39–50% TrMB, 40% best estimate), Texas (12–45% TrMB, 16% best estimate), and the western US (3–25% TrMB, 8% best estimate). TrMB attributions for the eastern US (7–26%) were lower than the best estimate (30%). The analysis and evaluation of TrMB during BRAVO clearly demonstrated some of the benefits and drawbacks of this technique. Source attributions for individual days can be very inaccurate even when the mean attributions are predicted accurately. This was anticipated because deposition, chemistry, and other factors influencing short-term source-receptor relationships can vary significantly from the mean. However, the magnitude of the deviations had not been previously explored for this type of model. It is apparent that the results of TrMB, when taken in isolation, should be viewed cautiously. It is possible to fit a regression model such that the measured and predicted concentrations match closely, yet the resulting source attributions are erroneous. However, when used as part of a robust evaluation process involving other models and analyses, TrMB is valuable and can provide insights into the accuracy of other techniques. It is an advantage of TrMB that emissions data and other factors with large uncertainties such as modeled precipitation and clouds are not required as input and that complex physical processes are not modeled explicitly. This allows the results of TrMB to be a useful comparison for results from CTMs. This was especially valuable for BBNP, which is frequently upwind of Mexico, where emissions data are more uncertain and measured meteorological data are more sparse than in the US. In BRAVO, TrMB results corroborated suspicions that Mexican SO2 emissions were underestimated and that the contributions from eastern US sources to BBNP sulfate had been overestimated by the CTMs.
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Disclaimer: The assumptions, findings, conclusions, judgments, and views presented herein are those of the authors and should not be interpreted as necessarily representing official National Park Service policies. References Barna, M.G., Gebhart, K.A., Schichtel, B.A., Malm, W.C., 2006a. Modeling regional sulfate during the BRAVO study: 1. Base emissions simulation and performance evaluation. Atmospheric Environment, in press doi:10.1016/j.atmosenv.2005.12.040. Barna, M.G., Gebhart, K.A., Schichtel, B.A., Malm, W.C., 2006b. Modeling regional sulfate during the BRAVO study: 2. Emission sensitivity simulations and source apportionment. Atmospheric Environment, in press doi:10.1016/j.atmosenv.2005.12.038. Belsley, D.A., Kuh, E., Welsch, R.E., 1980. Regression Diagnostics—Identifying Influential Data and Sources of Collinearity. Wiley, New York, pp. 92–93. Black, T.L., 1994. The new NMC mesoscale Eta model: description and forecast examples. Weather Forecasting 9, 265–278. Draxler, R.R., Hess, G.D., 1998. An overview of the HYSPLIT_4 modeling system for trajectories, dispersion, and deposition. Australian Meteorological Magazine 47, 295–308. Gebhart, K.A., Malm, W.C., 1989. Source apportionment of particulate sulfate concentrations at three national parks in the eastern United States. In: Mathai, C.V. (Ed.), Transactions of the A&WMA/EPA Specialty Conference—Visibility and Fine Particles. October 15–19, Estes Park, CO, pp. 898–913. Gebhart, K.A., Malm, W.C., 1994. Source attribution and statistical summary of data measured at Grand Canyon National Park during 1989–1991. In: Proceedings of ‘‘Aerosols and Atmospheric Optics’’. Snowbird, UT, pp. 1098–1124. Gebhart, K.A., Alhbrandt, R.A., Malm, W.C., Iyer, H.K., 1988. Estimating the fractional contribution of secondary aerosols from different source areas on a regional scale. Preprints of the 81st Annual APCA Meeting, Dallas, TX, June, Paper No. 88-054.06, available from A&WMA, Pittsburgh. Gebhart, K.A., Schichtel, B.A., Barna, M.G., 2005. Directional biases in back-trajectories caused by model and input data. Journal of the Air and Waste Management Association 55, 1649–1662. Green, M., Kuhns, H., Pitchford, M., Dietz, R., Ashbaugh, L., Watson, T., 2003. Application of the tracer-aerosol gradient interpretive technique to sulfur attribution for the Big Bend Regional Aerosol and Visibility Observational Study. Journal of the Air and Waste Management Association 53 (5), 586–595. Grell, G.A., Dudhia, J., Stauffer, D.R., 1994. A description of the fifth generation Penn State/NCAR Mesoscale Model (MM5). NCAR Technical Note (TN-398STR), NCAR, Boulder, CO. Heffter, J.L., 1980. Air Resources Laboratory Atmospheric Transport and Diffusion Model (ARL-ATAD). National Oceanic and Atmospheric Administration, Technical Memo, ERL-ARL-81. Iyer, H.K., Malm, W.C., Ahlbrandt, R.A., 1987. A mass balance method for estimating the fractional contribution from
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various sources to a receptor site. In: Bhardwaja, P.S. (Ed.), Transactions: Visibility Protection: Research and Policy Aspects, September 1986. Grand Teton National Park, WY, Air Pollution Control Association (now A&WMA), Pittsburgh, pp. 861–869. Kanamitsu, M., 1989. Description of the NMC global data assimilation and forecast system. Weather Forecasting 4, 335–342. Kuhns, H., Knipping, E.M., Vukovich, J.M., 2005. Development of a United States–Mexico emissions inventory for the Big Bend Regional Aerosol and Visibility Observational (BRAVO) study. Journal of the Air and Waste Management Association 55, 677–692. Malm, W.C., 1992. Characteristics and origins of haze in the continental United States. Earth Science Reviews 33, 1–36. Malm, W.C., Day, D.E., Kreidenweis, S.M., Collett, J.L., Lee, T., 2003. Humidity-dependent optical properties of fine particles during the Big Bend Regional Aerosol and Visibility Observational study. Journal Geophysical Research 108 (D9), 4279. Pitchford, M., Pitchford, A., 1985. Analysis of regional visibility in the southwest using principal component and backtrajectory techniques. Atmospheric Environment 19, 1301–1316. Pitchford, M., Green, M., Dietz, R., Watson, T., 2001. Perfluorocarbon tracers used to study transport and dispersion during the BRAVO Study. In: Proceeding of the Regional Haze and Global Radiation Balance–Aerosol Measurements and Models: Closure, Reconciliation, and Evaluation Conference. October 2–5, Bend, OR, A&WMA, Pittsburgh, PA. Pitchford, M.L., Tombach, I.H., Barna, M.G., Gebhart, K.A., Green, M.C., Knipping, E., Kumar, N., Malm, W.C., Pun, B., Schichtel, B.A., Seigneur, C., 2004. Big Bend Regional Aerosol and Visibility Observational (BRAVO) Study. Official Report of the Sponsoring Agencies: US Environmental Protection Agency, National Park Service, Texas Commission on Environmental Quality, EPRI, and National Oceanic and Atmospheric Administration. Available at http:// vista.cira.colostate.edu/improve/Studies/BRAVO/reports/FinalReport/bravofinalreport.htm. Pitchford, M.L., Schichtel, B.A., Gebhart, K.A., Barna, M.G., Malm, W.C., Tombach, I.H., Knipping, E.M., 2005. Re-
conciliation and interpretation of the Big Bend National Park light extinction source apportionment: Results from the Big Bend Regional Aerosol and Visibility Observational study– Part II. Journal of the Air and Waste Management Association 55, 1726–1732. Schichtel, B.A., Husar, R.B., 1997. Regional simulation of atmospheric pollutants with the CAPITA Monte Carlo model. Journal of the Air and Waste Management Association 47, 331–343. Schichtel, B.A., Pitchford, M., Gebhart, K.A., Malm, W.C., Barna, M.G., Knipping, E., Tombach, I., 2005a. Reconciliation and interpretation of the Big Bend National Park particulate sulfur source apportionment: results from the Big Bend Regional Aerosol and Visibility Observational study–Part I. Journal of the Air and Waste Management Association 55, 1709–1725. Schichtel, B.A., Barna, M.G., Gebhart, K.G., Malm, W.C., 2005b. Evaluation of a Eulerian and Lagrangian air quality model using perfluorocarbon tracers released in Texas for the BRAVO haze study. Atmospheric Environment 39, 7044–7062. Schichtel, B.A., Malm, W.C., Gebhart, K.A., Barna, M.G., 2006. A hybrid source apportionment model integrating measured data and air quality model results. Journal of Geophysical Research, in press. Schwartz, B.E., Govett, M., 1992. A Hydrostatically Consistent North American Radiosonde Data Base at the Forecast Systems Laboratory, 1946-present, NOAA Technical Memorandum ERL FSL-4, NOAA/ERL/FSL 325 Broadway, Boulder, CO 80303. Watson, T.B., Johnson, R., Pitchford, M.L., Green, M., Kuhns, H., Etyemezian, V., 2000. The Perflourocarbon Tracer Releases during the Big Bend Regional Aerosol and Visibility Observational (BRAVO) Study. NOAA Technical Memorandum; OAR ARL-237, National Oceanic and Atmospheric Administration: Idaho Falls, ID. White, W.H., Dietz, R.N., Green, M.C., Pitchford, M.L., Watson, T.B., 2001. Preliminary analysis of perfluorocarbon tracer measurements in the Big Bend Regional Aerosol and Visibility Study (BRAVO). In: Proceeding of the Rebional Haze and Global Radiation Balance–Aerosol Measurements and Models: Closure, Reconciliation, and Evaluation Conference. October 2–5, Bend, OR, A&WMA, Pittsburgh, PA.
Atmospheric Environment 40 (2006) 2823–2834 www.elsevier.com/locate/atmosenv
Quantitative back-trajectory apportionment of sources of particulate sulfate at Big Bend National Park, TX Kristi A. Gebhart, Bret A. Schichtel, Michael G. Barna, William C. Malm National Park Service, Air Resources Division, CIRA Building, Colorado State University, Fort Collins, CO 80523, USA Received 2 June 2005; received in revised form 6 January 2006; accepted 6 January 2006
Abstract As part of the Big Bend Regional Aerosol and Visibility Observational (BRAVO) study, a quantitative back-trajectorybased receptor model, Trajectory Mass Balance (TrMB) was used to estimate source apportionment of particulate sulfur measured at Big Bend National Park, Texas, during July–October 1999. The model was exercised using a number of sets of trajectories generated by three different trajectory models, with three different sets of input gridded meteorology, and tracked for 5, 7, and 10 days back in time. The performance of the TrMB model with the different trajectory inputs was first evaluated against perfluorocarbon tracers and synthetically generated sulfate concentrations from a regional air quality model, both of which had known attributions. These tests were used to determine which trajectories were adequate for the TrMB modeling of measured sulfate concentrations, illustrated the magnitude of the daily uncertainties as compared to the uncertainties in the mean attributions, and demonstrated the value of a robust evaluation process. Depending on trajectories, mean sulfate source apportionment results were 39–50% from Mexico, 7–26% from the eastern US, 12–45% from Texas, and 3–25% from the western US. These ranges were inclusive of the best BRAVO attribution estimates for Mexico, Texas, and the western US, but TrMB underestimated the eastern US contribution as compared to the BRAVO best estimates. Published by Elsevier Ltd. Keywords: Receptor modeling; Back-trajectory modeling; Big Bend National Park; Source apportionment; Tracer studies
1. Introduction The Big Bend Regional Aerosol and Visibility Observational (BRAVO) study (Pitchford et al., 2004, 2005; Schichtel et al., 2005a), designed to determine the causes of visibility impairment at Big Bend National Park, Texas (BBNP), was conducted during July–October 1999. A feature of BRAVO Corresponding author. Tel.: +1 970 491 3684; fax: +1 970 491 8598. E-mail address: [email protected] (K.A. Gebhart).
1352-2310/$ - see front matter Published by Elsevier Ltd. doi:10.1016/j.atmosenv.2006.01.018
was the use of several techniques to estimate the attribution of particulate sulfate concentrations measured at the park to sulfur emission sources in the US and Mexico. These techniques included receptor models, chemical dispersion models, qualitative data analyses, and finally, a model reconciliation and assessment, which led to the development of a hybrid source apportionment model to form the final BRAVO estimates. A key feature of the BRAVO study was the release of perfluorocarbon tracers from four sites in Texas, which aided model assessment.
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As part of BRAVO, a quantitative back-trajectory-based receptor model, Trajectory Mass Balance (TrMB), was first tested and then used to estimate the four-month average contributions to fine particulate sulfate measured at BBNP from several source regions. This paper describes that modeling effort, the evaluation of the TrMB model using tracer data and synthetic sulfate concentrations, and finally its application to source attribution at BBNP during BRAVO. 2. Methodology 2.1. Model equations The TrMB model (e.g., Pitchford and Pitchford, 1985; Iyer et al., 1987; Gebhart et al., 1988; Gebhart and Malm, 1989, 1994; Malm, 1992) is a receptor model in which measured concentrations at a receptor are assumed to be linearly related to the frequency of airmass transport from and duration in emission source areas before arriving at the receptor by the following formulation of the conservation of mass: C it ¼
J X
units of concentration per endpoint. These are estimates of the study-long (July–October 1999) mean relationship between airmass residence time in the source area and measured concentration at the receptor. The intercept was fixed at zero, forcing all identified source areas to account for the measured concentrations. When the intercept is allowed to float it often becomes larger than is physically reasonable because it will include the error term as shown in Eq. (2). Although emissions data were available for BRAVO, they were not included explicitly in this modeling, given that sulfur emissions in Mexico are very uncertain (Kuhns et al., 2005). The error in Eq. (2) is due to measurement error and deviations of the daily unknown transfer coefficients from their means, ðajt a¯ j ÞN jt . Additional assumptions inherent in the model include that uncertainties in measured values are random, uncorrelated, and normally distributed and the contributions of the source regions are linearly independent. Also, the number of source regions modeled cannot exceed the number of time periods. 2.2. Source areas
Qijt T ijt N jt .
(1)
j¼1
The subscripts i,j, and t refer to chemical species, source areas, and times, respectively. C are the measured concentrations, Q the emission rates, T the transformation and deposition factors to account for deposition, diffusion, and chemical conversion, and N the number of back-trajectory endpoints. An endpoint is defined as the position of an air parcel that eventually will arrive at the receptor, in this case, BBNP. Endpoints are calculated hourly for up to 10 days back in time. In this application the only variables inputted explicitly were C, the daily measured sulfate concentrations at BBNP; and N, the number of back-trajectory endpoints in each source area for each day. The remaining terms, QT, called the ‘‘transfer coefficients’’ were estimated by ordinary least-squares regression such that Eq. (1) simplifies to C t ¼ a¯ 0 þ
J X
a¯ j N jt þ errort .
(2)
j¼1
The subscript i has been dropped for simplicity since only particulate sulfate was modeled. The values of a ¼ QT are the regression coefficients with
Source areas were chosen based on several criteria including: (1) Location: Understanding the relative influence of sources in Mexico vs. sources in Texas and other areas of the US was a primary goal of BRAVO. (2) Size: Source areas should generally get larger as the distance from the receptor increases to accommodate the increased uncertainty in endpoint locations and increased dispersion around the trajectory center line as distance and travel time increase. However, they should be small enough so that a single regression coefficient is sufficient to explain the mean relationship between source area and receptor. Most trajectories passing through a region should ideally have similar exposure to emissions, dispersion, and transformation en route to the receptor. (3) Emissions: Model performance relies on the contribution from the area being larger than the errors in the model, so source areas should have significant emissions of the pollutant of interest, in this case SO2. (4) Independence: To avoid collinearity between source regions, the timing and number of trajectories passing through each region should be reasonably independent from other regions. Multi-collinearity between source areas was examined by two methods, the correlation matrix of the endpoints and the Variance Inflation
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3
4
2
1
concentrations from two types of samplers. When the higher time resolution data were averaged to 24 h, there were from 1 to 7 daily measurements of fine particulate sulfur or sulfate for each day. The daily range and medians are shown in Fig. 2. Days of particular interest were 1, 14–15 September and 12 October, which, because they had high measured concentrations, were influential points in the TrMB regressions. Details of the particulate measurements are discussed in Malm et al. (2003) and Pitchford et al. (2004). Synthetic sulfate concentrations were also used for testing purposes only. These are discussed in Section 4.1.
5
9 6
12
10
8
7
15 16 17 19 13 14 18
20
11 21
22 23 24 25
26 27
Fig. 1. Source areas used for source attribution of sulfate at Big Bend National Park.
Factor (VIF) (Belsley et al., 1980), shown in Eq. (3). VIFj ¼
1 . 1 R2j
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(3)
R2 is the multiple correlation coefficient of the endpoints in one source area regressed on the endpoints in the remaining source areas. A high VIF indicates that endpoints in that region could be nearly explained by some linear combination of those in other regions, while the correlation matrix alone is only useful for individual pairs of source areas. A VIF greater than 10 is considered strong collinearity. A further indication of multi-collinearity is large standard errors for the regression coefficients. It is often difficult to choose source areas that simultaneously satisfy all criteria and the choice requires some qualitative judgment. Those chosen for this analysis are shown in Fig. 1. 3. Input data 3.1. Sulfate concentrations The sulfate concentrations used in TrMB for BRAVO were the daily median concentrations of all available 24-h average fine (o2.5 mm diameter) particulate sulfur and sulfate concentrations measured at BBNP for 117 days from 5 July to 29 October 1999. Measurements at the primary BRAVO receptor site, K-Bar Ranch, located within BBNP, included 12- and 24-h values of sulfate ion, and 6-, 12-, and 24-h average elemental sulfur
3.2. Perfluorocarbon tracers Four chemically inert, non-depositing perfluorocarbon tracers were released at nearly constant rates from four different sites within Texas during the second half of the BRAVO field study: Eagle Pass (250 km from BBNP), San Antonio (450 km), Houston (750 km), and northeast Texas (750 km). During the first half of the study three of the four tracers were released from Eagle Pass as ‘‘timing’’ tracers with release rates specified to determine transport times from Eagle Pass to BBNP, and the fourth was released from northeast Texas. Details of the tracer release, measurement, analyses, and evaluation can be found in Watson et al. (2000), Pitchford et al. (2001, 2004), White et al. (2001), Green et al. (2003), Gebhart et al. (2005), and Schichtel et al. (2005b). 3.3. Back-trajectories Three back-trajectory models, Atmospheric Transport and Dispersion (ATAD) (Heffter, 1980), HYSPLIT version 4.5 (Draxler and Hess, 1998), and CAPITA Monte Carlo (CMC) (Schichtel and Husar, 1997) were used to generate backtrajectories for input to TrMB. All models were exercised with at least two gridded input meteorological fields. ATAD was also run with its traditional input of North American rawinsonde data (Schwartz and Govett, 1992) supplemented by observations from four BRAVO radar wind profilers. The gridded data included 36 km output from the Mesoscale Meteorological Model (MM5) (Grell et al., 1994) and data from two standard National Oceanic and Atmospheric Administration (NOAA) archives: the ETA Data Assimilation System (EDAS) (Black, 1994) when available and the lower
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Range and Daily Median of Measured Sulfate at K-Bar 10
Jul 1
Aug 1
Sep 1
Oct 1
Nov 1
Median shown for 7/5-10/29
8
6
4
2
0 180
200
220
240 260 Julian Day 1999
280
300
Fig. 2. Range (shaded area) and daily median of 24-h averaged sulfur and sulfate measurements in mg m3 at K-Bar Ranch (line).
resolution FNL (Kanamitsu, 1989) when EDAS results were not available. EDAS data were missing for the entire month of October and for several days in July. The combined EDAS and FNL data set is referred to as EDAS/FNL. There are several fundamental differences in how the trajectory models calculate trajectories and in the input data employed. These details and the results of extensive qualitative and quantitative testing of many combinations of model and input data are described in Gebhart et al. (2005) and summarized in the following section. Tests showed that the choice of wind field was more influential than the trajectory model for source-attribution modeling. Test results also showed that the sparse rawinsonde data alone are probably inadequate for back-trajectory modeling in this area which is frequently downwind of data-poor regions including Mexico and the Gulf of Mexico. Back-trajectories were started from BBNP (29.31N Latitude, 103.181W Longitude) and traced backward in time for 5, 7, and 10 days. Early results from the BRAVO chemical dispersion modeling (Schichtel et al., 2005a, b, 2006; Pitchford et al., 2004, 2005; Barna et al., 2006b) indicated that the lifetime of sulfur in the atmosphere was longer than
5 days on a significant number of days during BRAVO. Trajectory lengths of up to 10 days in length were therefore used in the TrMB modeling. 4. Results 4.1. Summary of model tests 4.1.1. Modeling of known attributions A test of the TrMB model was performed in which measured sulfate concentrations were replaced by simulated values from the Regional Modeling System for Aerosols and Deposition (REMSAD) (Barna et al., 2006a,b), a deterministic chemical transport model. Source attributions of the simulated sulfate were also known from REMSAD and compared to those estimated by TrMB. To be consistent with the meteorological input data employed by REMSAD, only backtrajectories generated using MM5 wind fields were used in this evaluation. A similar test of measured perfluorocarbon tracer concentrations with known release sites and rates allowed testing of both MM5 and EDAS/FNL meteorology. However, the tracers are nonreactive and nondepositing, so influences of chemistry and
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Table 1 Attributions of simulated REMSAD sulfate by TrMB for 6 July–28 October 1999 (115 days) using MM5 Model
Texas
Mexico
Eastern US
Western US
R2
Mean bias (predobs) SO4 (ng m3)
Mean norm. bias (predobs)/obs
REMSAD simulated sulfate (ng m3) REMSAD attrib. CMC 5-day CMC 7-day CMC 10-day HYSPLIT 5-day HYSPLIT 7-day HYSPLIT 10-day ATAD 5-day
351
488
897
195
NA
NA
NA
18% 19% 20% 21% 43% 43% 46% 25%
25% 31% 24% 21% 25% 23% 21% 33%
46% 39% 36% 37% 16% 16% 19% 36%
10% 11% 20% 21% 17% 18% 13% 8%
NA 0.778 0.798 0.775 0.768 0.820 0.801 0.735
NA 23 12 13 11 26 14 24
NA 11% 9% 9% 20% 11% 15% 16%
Top row shows the REMSAD attributions with the boundary conditions (7%) and non-linear components (2%) proportionally redistributed. TrMB attributions within 10 percentage points of the REMSAD attributions are highlighted. The last three columns are statistics comparing the TrMB predictions to REMSAD simulated sulfate concentrations.
Table 2 Results of TrMB modeling (MM5 input, 5-day trajectories) of perfluorocarbon tracers at BBNP, 17 September–28 October 1999 (42 days)
Mean conc. (ppq) Mean percent (%) ATAD Rawinsonde ATAD EDAS/FNL HYSPLIT EDAS/FNL CMC EDAS/FNL ATAD MM5 HYSPLIT MM5 CMC MM5
Eagle Pass
San Antonio
Houston
R2
Mean bias (ppq)
Mean norm. bias
0.15570.024 2074 35712 1678 28712 3079 34712 82718 23716
0.55970.081 72713 65714 3379 67713 43710 60713 18718 77719
0.06270.008 871 079 5179 579 2778 679 0711 0712
NA NA 0.495 0.708 0.640 0.721 0.564 0.484 0.643
NA NA 0.244 0.096 0.078 0.007 0.019 0.044 0.085
NA NA 13% 376% 834% 235% 901% 1159% 372%
The first two rows show the measured concentrations and percents of tracer from each release site. Remaining rows give the modeled attributions. Those accurate to within the uncertainty of the measurement and standard error of the regression coefficients are highlighted.
deposition on model performance could not be tested using the tracers. Also, all tracer release sites were within Texas and tracers were released from two of the sites only during the second half of the study, so the model’s ability to distinguish concentrations arriving from more distant source regions and during summer-time meteorology could not be considered using the tracers. Tables 1 and 2 summarize the results of these tests which are discussed in detail in Gebhart et al. (2005). Mean bias is the mean of (predictedobserved) and mean normalized bias is the mean of the daily (predictedobserved)/observed. High mean normalized biases in the tracer tests are due in part to a few near-zero observations. These also caused the sign of the mean normalized bias to be opposite of the mean bias. Note that high R2 and
low biases between predicted and observed concentrations are poor indicators of whether the TrMB model has reproduced the correct attributions. In the tracer test, the cases with the highest correlations also had the least correct attributions. For example see ATAD EDAS/FNL and CMC EDAS/ FNL in Table 2. These statistics indicate only whether TrMB could fit a model that reproduced the observations, not whether it fit the correct model. As shown in Tables 1 and 2, TrMB reproduced known mean source attributions to within measurement and regression uncertainties using some input trajectories, while other sets of trajectories did not perform well. Furthermore, those that passed one test tended to also pass the other, indicating that the source of error was more likely
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Mexico 10/4
2.0
10/6 10/5
10/9 10/11 8/22
1.5 1.0
10/19 10/22
0.5 10/21
0.0 0
10/5 8/30 8/21 9/23
1.5 ug/m3
ug/m3
Texas 2.5
1.0
7/27 8/28 8/29
9/11
0.5
7/30 8/1 7/31 9/24
0.0
1000 2000 3000 4000 5000 endpoints
0
2000
4000 6000 endpoints
8000
CAPITAMC MM5 5-Day Eastern U.S
5
10/6 9/1 9/15
3 2
10/13
10/12 10/14
1
1.2 10/10
ug/m3
4 ug/m3
Western U.S.
9/2
10/5
0.8
10/8
10/17 9/21 10/18
9/25
10/20 9/30 9/27
0.4
9/26
7/11
0
0.0 0
2000 4000 endpoints
6000
0
2000 4000 8000 6000 10000 endpoints
Fig. 3. Scatter plots of simulated sulfate attributions vs. number of endpoints for each of four large source areas using 5-day backtrajectories from the CAPITA MC model using MM5 meteorology. The solid lines are the ‘‘true’’ mean slopes from the deterministic model simulation; dashed lines are the TrMB modeled mean slopes. The points show the daily values.
incorrect trajectories rather than errors in the concentrations. Collinearity tests showed that incorrect attributions were not associated with collinearity. Based on the results of these tests and some qualitative tests described in Gebhart et al. (2005), trajectories generated by the CMC and ATAD models with MM5 input and by HYSPLIT with EDAS/FNL input were deemed adequate for use in the TrMB attribution of measured sulfate for BRAVO. The remaining sets of trajectories were not used. 4.1.2. Daily deviations from mean The TrMB regression coefficients are estimates of the mean relationships between measured concentrations and the presence of air masses in upwind source regions. BRAVO provided an opportunity to examine the daily deviations from the mean, ðajt a¯ j ÞN jt . Using the simulated sulfate concentrations as described above, the known daily attributions from REMSAD were compared to those estimated from TrMB. Results for one case are shown in Fig. 3. In each scatter plot the solid line shows the ‘‘true’’ mean relationship between endpoints and concentrations as simulated by REMSAD. The dashed line is the mean estimated by TrMB. In this example, the closeness of the dashed
and solid lines illustrates, as can also be seen in Table 1, that all modeled attributions for this case were within 5 percentage points of the correct attributions. TrMB slightly overestimated mean attributions for Texas, Mexico, and the western United States (dashed line above the solid) and underestimated the eastern US. The more interesting aspect of the graphs, however, is the scatter of the points about the lines. The points are the ‘‘true’’ REMSAD-simulated daily endpoint-to-concentration relationships. While TrMB reproduced the means quite accurately, some daily attributions deviated significantly from the mean. For example, on 4 October, the true (simulated) sulfate attribution to Texas was underestimated by TrMB by nearly a factor of 5, even though on average, the mean attribution to Texas was within 1 percentage point of being correct. This is not surprising since daily chemistry, dispersion, emissions, and deposition can all vary significantly from a four-month mean. It does, however, illustrate that the uncertainties in the daily TrMB attributions are much larger than the uncertainties in the mean attributions. In fact, even if the TrMB mean source attributions were perfect, there could still be very large errors in the daily attributions.
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Table 3 Relative attributions of median 24-h sulfur at Big Bend to each source region by each model/wind field combination Percent attribution of sulfate to each source area
CAPITA MC with MM5
HYSPLIT with EDAS & FNL start heights 100–1000 m AGL
ATAD with MM5
Trajectory length (days) North Central States (4) Northeast (5) MO/IL/AR (10) East Central States (11) LA/MS (20) FL/GA (21) Eastern U.S (4,5,10,11,20,21)
5 073 072 573 173 1776 073 23%
7 074 172 974 576 1179 074 26%
10 075 174 1075 977 479 074 24%
5 072 271 073 172 475 072 7%
7 073 371 076 473 776 073 14%
10 074 073 079 674 1078 074 16%
5 072 071 572 072 1775 072 17%
Pacific Northwest (1) Northern Rockies (2) Dakotas (3) Southern California (6) AZ/NM (7) Central Plains (9) Western US (1,2,3,6,7,9)
373 074 374 073 579 3710 14%
373 074 075 073 379 15711 21%
574 075 376 075 7710 10712 25%
073 076 373 072 477 177 8%
073 176 574 072 279 076 8%
073 077 475 273 0712 078 6%
272 073 072 172 074 075 3%
Texas Panhandle (8) West Texas (15) North Central Texas (16) Northeast Texas (17) Southeast Texas (19) Texas (8,15,16,17,19)
074 075 275 474 13710 19%
075 375 075 074 9711 12%
075 075 075 074 12711 12%
076 177 475 573 3578 45%
077 078 176 673 29710 36%
578 0710 177 676 18712 30%
072 173 975 272 878 20%
Baja California (12) Northwest Mexico (13) North Central Mexico (14) Carbo´n I & II (18) West Central Mexico (22) Central Mexico (23) Monterrey Region, MX (24) SW Coast of Mexico (25) Mexico City & Volcano (26) S. Mexico/ Yucatan (27) Mexico
073 174 074 23712 175 073 5710 072 976 675 45%
174 075 074 24712 175 073 079 071 876 775 41%
076 077 175 22711 175 073 079 071 1076 675 40%
173 277 073 24710 073 073 477 171 774 074 39%
075 4710 073 21711 474 073 578 072 874 075 42%
076 578 074 22712 674 074 778 173 675 175 48%
No ends 071 274 33710 072 072 676 071 1075 174 50%
(12,13,14,18,22,23,24,25,26,27) Mean observed S (ng m3) Mean predicted S (ng m3) R2 Number of observations
835.7 832.7 0.622 117
835.7 833.1 0.669 117
835.7 834.6 0.689 117
835.7 807.7 0.478 117
835.7 795.9 0.500 117
835.7 786.9 0.459 117
835.7 823.3 0.585 117
Uncertainties are based on the standard errors of the regression coefficients. Model statistics are shown in the last 4 rows.
4.2. BRAVO sulfate source attributions Table 3 shows a summary of the TrMB results for measured fine particulate sulfur at BBNP for all sets of trajectories that passed the preliminary tests described above. The table includes the four-month mean relative percent attributions for each of the 27 smaller source areas and uncertainties based on the standard errors of the regression coefficients. Table 3 also includes the summed attributions for four larger aggregated regions, eastern US, western US, Texas, and Mexico. Uncertainties for these large
areas were not estimated because it was not possible to ascertain what portions of the estimated uncertainties were due to misattributions within the large region as opposed to misattributions between them. For example, an error in the attribution to southeast Texas could be because some of that sulfur actually arrived from northeast Texas, resulting in no error in the total attribution from Texas; or it could be a miss-allocation between southeast Texas and Louisiana/Mississippi, generating incorrect apportionments to both Texas and the eastern US.
0.14770.114 37.790715.233 0.16370.140 1.20870.764 0.13470.079 0.13270.112 0.21670.334 0.04370.240 0.35970.194 0.02070.331 0.08770.247 0.09170.118 0.04070.507 0.12470.241 0.02370.141 0.24370.110 0.25270.066 0.21870.544 0.49170.884 0.01670.220 0.12770.048 1.38871.071 1.29170.567 0.05770.066 0.28471.898 0.43770.174 0.00270.105
North Central States (4) Northeast (5) MO/IL/AR (10) East Central States (11) LA/MS (20) FL/GA (21) Pacific Northwest (1) Northern Rockies (2) Dakotas (3) Southern California (6) AZ/NM (7) Central Plains (9) Texas Panhandle (8) West Texas (15) North Central Texas (16) Northeast Texas (17) Southeast Texas (19) Baja California (12) Northwest Mexico (13) N Central Mexico (14) Carbo´n I & II (18) W Central Mexico (22) Central Mexico (23) Monterrey Reg., MX (24) SW Coast Mexico (25) Mex City, Volcano (26) S Mexico/ Yucatan (27) 1.29 2.48 1.16 1.58 1.69 1.17 0.65 0.18 1.85 0.06 0.35 0.77 0.08 0.51 0.16 2.21 3.83 0.40 0.56 0.07 2.64 1.30 2.28 0.85 0.15 2.50 0.02
t
0.20 0.02 0.25 0.12 0.09 0.24 0.52 0.86 0.07 0.95 0.73 0.44 0.94 0.61 0.87 0.03 0.00 0.69 0.58 0.94 0.01 0.20 0.03 0.40 0.88 0.01 0.99
P
2.0 1.6 3.2 2.2 3.4 1.4 2.1 3.4 3.2 3.4 17.6 4.0 9.3 10.5 3.9 2.6 3.7 6.5 22.9 2.6 1.8 6.6 2.0 2.4 2.9 2.1 2.0
VIF
179.8 0.7 325.2 31.7 588.9 208.7 71.5 192.6 153.2 48.8 294.6 436.9 113.9 264.9 318.3 246.1 1242.4 70.7 86.1 99.2 1753.1 28.4 44.2 912.4 8.1 197.7 342.4
Mean ends/ day 26720 28711 53746 38724 79747 28723 15724 8746 55730 1716 26773 40752 5758 33764 7745 60727 313782 15738 42776 2722 223784 39730 57725 52760 2715 86734 1736
Pred S (ng m3)7unc 3 3 7 5 10 3 2 1 7 0 3 5 1 4 1 8 39 2 5 0 28 5 7 7 0 11 0
% pred S
073 371 076 473 776 073 073 176 574 072 279 076 077 078 176 673 29710 075 4710 073 21711 474 073 578 072 874 075
Relative %7unc
32 5 47 24 57 54 37 44 38 19 33 55 36 34 49 51 96 18 18 25 99 13 32 88 8 50 55
No. days (max 117)
Trajectories from HYSPLIT with EDAS/FNL input, 7-day trajectories. Order of source areas is the same as in Table 3. ‘‘No. days’’ is the number of days when at least one endpoint was in the source area.
Coef.7SE
Source area (locations in Fig. 1)
Table 4 Sample of detailed statistics from a TrMB model
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Detailed statistics for a single case are shown in Table 4, which includes the regression coefficients, standard errors, t statistics (coefficient/standard error), P values (probability that coefficient could be zero), and VIF. Values of tX2 ðP ¼ 0:05Þ indicate significance at the 95% confidence level. Negative coefficients occurred when the endpoints were inversely correlated with the concentrations so that when more air arrived from the area the concentration at BBNP tended to be lower. No negative coefficients were significant at the 95% level and all had small magnitudes. Sources with VIFs410 are considered significantly collinear with a combination of other areas, causing more difficulty in determining the regression coefficient (higher standard error) so more uncertainty in the attribution. With rare exceptions VIFs410 occurred only for sources to the west and/or north from which airmasses arrived infrequently and from which attributions are also expected to be low due to relatively low emissions. Trajectories also often had higher elevations west of BBNP, thus possibly not interacting with ground-based emissions in those areas. Collinearity could be eliminated by combining sources or readjusting their boundaries. However, for BRAVO, source boundaries were fixed to facilitate comparison of other factors including source apportionment techniques, emissions, meteorological data, trajectory models, trajectory start heights and lengths, etc. Different sets of trajectories had collinearity in different locations. The seventh column of Table 4 gives the daily average particulate sulfur (ng m3) attributed to each source, calculated by multiplying the regression coefficient by the mean endpoints. The uncertainty is estimated by multiplying the mean endpoints by the standard errors of the regression coefficients. The raw percent attribution, shown in column eight, is the mean predicted sulfur attributed to the area divided by the total predicted sulfur. Column nine is relative percent attribution as shown in Table 3, calculated by setting negative values to zero and renormalizing the positive values to 100%. Uncertainties are assumed to be the same as for the raw attributions, though this is likely an underestimate. The final column in Table 4 is the number of days (maximum 117) when airmasses arrived from each area. Attribution results vary somewhat by trajectory model and input data combination, though for most of the 27 smaller sources the differences between combinations are within the standard errors of the regression coefficients. In general, all combinations
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give approximately the same total attribution to Mexico, ranging from 39% to 50% with a median of 42%. With MM5 meteorology in the CMC model, longer trajectories result in somewhat less attribution to Mexico, while the reverse is true for HYSPLIT with EDAS/FNL. The biggest differences were in the mean attributions to Texas. HYSPLIT with EDAS/FNL input attributes approximately twice as much (30–45%) to Texas as predicted using MM5 in ATAD (20%) or CMC (12–19%). Both HYSPLIT and CMC attribute less to Texas as the trajectory length increases. MM5 input in both ATAD and CMC results in more attribution (17–26%) to the eastern US than HYSPLIT with EDAS/FNL (7–16%). Longer HYSPLIT trajectories give greater attribution to the eastern US, while the largest attribution to the eastern United States by CMC was with 7-day trajectories. For all model/wind field combinations the smallest attribution to any of the four large source regions was to the western US, though the percentages attributed by HYSPLIT/EDAS/FNL (6–8%) were only about half that attributed by CMC/MM5 (14–25%). ATAD/MM5 had the lowest attribution to the western US at just 3%. Longer HYSPLIT/EDAS/FNL trajectories caused slightly less attribution to the western US, while the reverse was true for longer CMC/MM5 trajectories.
5. Discussion 5.1. Variations in TrMB results Trajectory heights influence the speeds so trajectories with lower average heights tend to preferentially implicate closer source regions at the expense of those farther upwind. Endpoints generated with CMC/MM5 had a mean height of 1156 m and mean wind speed of 6.2 m s1 while those generated by HYSPLIT/EDAS/FNL had a mean height of 686 m and speed of 5.6 m s1 (Gebhart et al., 2005). TrMB attributions using HYSPLIT/EDAS/FNL trajectories as input generated much higher attributions (30–45%) for close-in Texas than did CMC/MM5 trajectories (12–19%). As might be expected, longer trajectory lengths resulted in lower attributions to Texas and higher attributions to the more distant eastern and western US. The biggest differences were usually, though not always, between the 5- and 7-day lengths. Longer trajectories resulted in higher attributions to Mexico with CMC/MM5 input, but lower
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attributions when HYSPLIT/EDAS/FNL trajectories were used. An assumption of most trajectory analyses is that errors in horizontal placement of trajectories are random, e.g., trajectories that are too far east on some days are balanced by those that are too far west on other days, so that the mean directional error is small when many trajectories are averaged. However, qualitative and quantitative tests of BRAVO back-trajectories showed that there were systematic biases in horizontal placement of trajectories that were dependent mostly on input meteorology and to a lesser extent on the trajectory model. Biases appeared to be both regionally and seasonally dependent (Gebhart et al., 2005). In addition, because of the nature of ordinary least-squares linear regression, the TrMB model is more sensitive to errors in trajectory placement that occur on high concentration days than it is to those on days of lower concentrations. Despite several tests against the BRAVO tracers and simulated data, none of the sets of trajectories shown in Table 3 could be eliminated as obviously inferior. 5.2. TrMB results compared to other BRAVO modeling Comparisons of TrMB results to those from REMSAD (Barna et al., 2006b), shown in Table 5, found that TrMB estimated that larger fractions of sulfur arrived from Mexico and the western US and less from the eastern US than REMSAD. Both CMC and ATAD with MM5 give approximately the same average attribution to Texas as REMSAD, though HYSPLIT/EDAS/FNL attributes much more to Texas. Since MM5 meteorology was used in REMSAD, it is expected that EDAS/FNL meteorology might give results that are more different from MM5. Table 5 Comparison of TrMB sulfate source attribution results to other BRAVO estimates Source region
TrMB (%)
REMSAD (%)
BRAVO best estimate (hybrid model) (%)
Texas Eastern US Western US Mexico Boundary Other
12–45 7–26 3–25 39–50 0 0
16 42 9 23 7 3
16 30 8 40 6 0
Reasons for the differences between TrMB and REMSAD could include problems with either model, including collinearity or inaccurate or inappropriate back-trajectories (e.g. endpoints above the mixed layer) in TrMB. The most likely sources of error in REMSAD include incorrect emissions, especially Mexican emissions (Kuhns et al., 2005) and/or incorrect modeling of precipitation and clouds (Barna et al., 2006a). The final phase of the BRAVO study was model and data reconciliation (Pitchford et al, 2004, 2005; Schichtel et al., 2005a, 2006). Analysis of the results of two chemical transport models (CTMs) revealed systematic geographic and seasonal biases in the source apportionments for BRAVO. For example, during October, the modeled contribution from the eastern US sources nearly always exceeded the measured concentrations in east Texas. Conversely, during July, when transport patterns were most likely to bring air masses from Mexico to BBNP, predicted concentrations at BBNP were underestimated. To correct these biases, a hybrid source apportionment model was developed which adjusted the initial CTM source contributions so the modeled sulfate concentrations optimally fit the measured concentrations, resulting in refined daily source contributions with reduced biases. The refined results reduced the initial study-average eastern US contribution to BBNP from 40% to 30%, while Mexico’s contribution increased from 23–32% to 40%. Contributions from Texas and the western US changed little, with final attributions of 16% and 5–9%, respectively. Besides being more consistent with measured concentrations, these hybrid source attributions also brought the CTM-predicted attributions closer to those estimated by the receptor models, including TrMB. The hybrid results are considered by the study participants to be the best BRAVO estimates of sulfate source attribution. These are also summarized in Table 5. The range of TrMB attributions bound the BRAVO best estimate for three of the four large source regions, Mexico, Texas and the western US. However, all TrMB estimates were lower than the BRAVO best estimate for the eastern US. 6. Conclusions A deterministic back-trajectory-based linear regression model, TrMB, with minimal input requirements, was a useful source apportionment technique for the 1999 BRAVO study. Tests of TrMB using known
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attributions of tracer and synthetic sulfate data showed that this model could reproduce mean source attributions to within expected uncertainty when some sets of trajectories were used and that TrMB results were most sensitive to the trajectories on high concentration days. Those sets of trajectories that failed these tests were then eliminated from the source attribution modeling of the measured data. TrMB source apportionment estimates for sulfate measured at BBNP during BRAVO varied somewhat depending on input meteorological data, trajectory model, and trajectory length, but the ranges of results included the independently generated BRAVO study best estimates for Mexico (39–50% TrMB, 40% best estimate), Texas (12–45% TrMB, 16% best estimate), and the western US (3–25% TrMB, 8% best estimate). TrMB attributions for the eastern US (7–26%) were lower than the best estimate (30%). The analysis and evaluation of TrMB during BRAVO clearly demonstrated some of the benefits and drawbacks of this technique. Source attributions for individual days can be very inaccurate even when the mean attributions are predicted accurately. This was anticipated because deposition, chemistry, and other factors influencing short-term source-receptor relationships can vary significantly from the mean. However, the magnitude of the deviations had not been previously explored for this type of model. It is apparent that the results of TrMB, when taken in isolation, should be viewed cautiously. It is possible to fit a regression model such that the measured and predicted concentrations match closely, yet the resulting source attributions are erroneous. However, when used as part of a robust evaluation process involving other models and analyses, TrMB is valuable and can provide insights into the accuracy of other techniques. It is an advantage of TrMB that emissions data and other factors with large uncertainties such as modeled precipitation and clouds are not required as input and that complex physical processes are not modeled explicitly. This allows the results of TrMB to be a useful comparison for results from CTMs. This was especially valuable for BBNP, which is frequently upwind of Mexico, where emissions data are more uncertain and measured meteorological data are more sparse than in the US. In BRAVO, TrMB results corroborated suspicions that Mexican SO2 emissions were underestimated and that the contributions from eastern US sources to BBNP sulfate had been overestimated by the CTMs.
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Disclaimer: The assumptions, findings, conclusions, judgments, and views presented herein are those of the authors and should not be interpreted as necessarily representing official National Park Service policies. References Barna, M.G., Gebhart, K.A., Schichtel, B.A., Malm, W.C., 2006a. Modeling regional sulfate during the BRAVO study: 1. Base emissions simulation and performance evaluation. Atmospheric Environment, in press doi:10.1016/j.atmosenv.2005.12.040. Barna, M.G., Gebhart, K.A., Schichtel, B.A., Malm, W.C., 2006b. Modeling regional sulfate during the BRAVO study: 2. Emission sensitivity simulations and source apportionment. Atmospheric Environment, in press doi:10.1016/j.atmosenv.2005.12.038. Belsley, D.A., Kuh, E., Welsch, R.E., 1980. Regression Diagnostics—Identifying Influential Data and Sources of Collinearity. Wiley, New York, pp. 92–93. Black, T.L., 1994. The new NMC mesoscale Eta model: description and forecast examples. Weather Forecasting 9, 265–278. Draxler, R.R., Hess, G.D., 1998. An overview of the HYSPLIT_4 modeling system for trajectories, dispersion, and deposition. Australian Meteorological Magazine 47, 295–308. Gebhart, K.A., Malm, W.C., 1989. Source apportionment of particulate sulfate concentrations at three national parks in the eastern United States. In: Mathai, C.V. (Ed.), Transactions of the A&WMA/EPA Specialty Conference—Visibility and Fine Particles. October 15–19, Estes Park, CO, pp. 898–913. Gebhart, K.A., Malm, W.C., 1994. Source attribution and statistical summary of data measured at Grand Canyon National Park during 1989–1991. In: Proceedings of ‘‘Aerosols and Atmospheric Optics’’. Snowbird, UT, pp. 1098–1124. Gebhart, K.A., Alhbrandt, R.A., Malm, W.C., Iyer, H.K., 1988. Estimating the fractional contribution of secondary aerosols from different source areas on a regional scale. Preprints of the 81st Annual APCA Meeting, Dallas, TX, June, Paper No. 88-054.06, available from A&WMA, Pittsburgh. Gebhart, K.A., Schichtel, B.A., Barna, M.G., 2005. Directional biases in back-trajectories caused by model and input data. Journal of the Air and Waste Management Association 55, 1649–1662. Green, M., Kuhns, H., Pitchford, M., Dietz, R., Ashbaugh, L., Watson, T., 2003. Application of the tracer-aerosol gradient interpretive technique to sulfur attribution for the Big Bend Regional Aerosol and Visibility Observational Study. Journal of the Air and Waste Management Association 53 (5), 586–595. Grell, G.A., Dudhia, J., Stauffer, D.R., 1994. A description of the fifth generation Penn State/NCAR Mesoscale Model (MM5). NCAR Technical Note (TN-398STR), NCAR, Boulder, CO. Heffter, J.L., 1980. Air Resources Laboratory Atmospheric Transport and Diffusion Model (ARL-ATAD). National Oceanic and Atmospheric Administration, Technical Memo, ERL-ARL-81. Iyer, H.K., Malm, W.C., Ahlbrandt, R.A., 1987. A mass balance method for estimating the fractional contribution from
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