Appendix A: Trajectory Analysis Methods Page A-1

Appendix A: Application of Trajectory Analysis 

Methods to Sulfate Source Attribution Studies in 

the Northeast U.S. 

Gary Kleiman, Iyad Kheirbek, and John Graham 

Northeast States for Coordinated Air Use Management (NESCAUM) 

Boston, MA 02114. 

ABSTRACT 

Back trajectories have been calculated (8 per day) for the five-year period including 2000 

through 2004 using the HYSPLIT modeling system for 13 Eastern sites including 10 

rural locations near Class 1 areas subject to EPA’s Regional Haze Rule and 7 urban 

location which have annual average PM2.5 concentrations above or near the National 

Ambient Air Quality Standard (NAAQS). The back trajectories have been clustered 

based on 3-dimensional similarity to identify the predominant meteorological pathways 

influencing each site. Trajectories have also been associated with the nearest temporal 

value of 24-hr average concentration of PM2.5 and IMPROVE sulfate values measured at 

or near each site. Individual trajectories and clustered probability fields are utilized in a 

variety of ways to apportion geographic contribution to meteorological transport of 

sulfate. Results are compared with quantitative methods of apportioning state-specific 

contributions to observed sulfate and serve as an independent check on contribution 

assessments developed through these alternative techniques. 
Appendix A: Trajectory Analysis Methods Page A-2

Appendix A: Application of Trajectory Analysis Methods to 

Sulfate Source Attribution Studies in the Northeast U.S. 

A.1. Introduction 

The 1999 Regional Haze Rule (RHR) contains requirements for a site-specific 

pollution apportionment as part of each mandatory Federal Class I area’s long-term 

emissions management strategy. A variety of techniques have been explored for 

conducting such pollution apportionments, but tagged chemical transport modeling is one 

of the few techniques which provide quantitative assessments of individual state or 

regional contributions to ambient concentrations. Given the importance of accurate 

pollution apportionment assessments, it is highly desirable to have several independent 

techniques provide confirmation of transport model results. 

Traditional trajectory analyses that associate an ambient measurement of air 

quality with the geographical region upwind prior to the observation are limited in that 

they demonstrate the relationship between ambient air quality and the integrated path 

along the length of a back trajectory. It is difficult to distinguish the contribution of a 

specific point along a single back trajectory from the contribution of other points along 

that path. Large numbers of back trajectories have been used in a variety of ways to try 

to “triangulate” by taking advantage of the variation in meteorology and paths that an 

ensemble of back trajectories offers.1-5 Combining results from multiple receptor sites 

offers a more robust method of triangulation and can yield very specific source regions 

associated with unique chemical signatures available with source apportionment 

techniques. These methods – which include ensemble trajectory analysis and factor 

analysis methods – all select based on chemical signatures. That is, they identify 

geographic regions on the basis of a unique chemical characteristic, such as high levels of 

an observed pollutant or high levels of a specific combination of pollutants. 

Moody et al.,6 following methods of Dorling,7 have applied the Patterns in 

Atmospheric Transport History (PATH) clustering algorithm, to large numbers of back 

trajectories in order to group trajectories by three-dimensional similarity. Calculation of 

average pollution levels corresponding to the members of a cluster of back trajectories of 

similar three-dimensional structure provides a robust technique of associating air 

pollutants with typical meteorological pathways,8,9 but remains limited in its ability to 

distinguish individual points along an atmospheric pathway defined by a cluster of back 

trajectories. The cluster methods provide a way of identifying geographic regions based 

primarily on meteorological – rather than chemical – characteristics. The 

meteorologically selected regions can then be analyzed with respect to their chemical 

associations. 

The definition of an individual cluster of back trajectories in PATH analysis is 

dependent on a subjective choice of the “Radius of Proximity.” This threshold defines 

the limiting difference between the three-dimensional coordinates of two back trajectories 

and determines if they are in the same cluster or different clusters. Selection of a smaller 

radius of proximity, in effect, will split clusters into component sub-clusters. Thus in the 

limiting case (radius of proximity = 0) the analysis reverts to a traditional trajectory 
Appendix A: Trajectory Analysis Methods Page A-3

analysis with each trajectory representing its own cluster. In this sense, PATH analysis 

offers a trade-off between uncertainty and fine scale structure of a trajectory analysis. By 

defining a radius of proximity and back-trajectory length, 10,000+ back trajectories for 

each site over the 5 year period can be represented by approximately 10-20 clusters. 

Using these trajectory and cluster data bases, as well as the associated receptorbased pollution data, we have carried out analyses using the incremental probability 

method, and two PATH-derived techniques method for attributing pollution transport to 

geographic areas. 

These qualitative methods support and enhance the conclusions derived through 

alternative methods (independent of back-trajectories) of associating emissions with 

downwind air quality impacts (i.e. the use of chemical transport models, or source

modeling, rather than the receptor based approaches used in trajectory analysis). Here 

we use our large database of back trajectories and corresponding air pollution 

measurements to develop multiple metrics related to Wishinski and Poirot’s “incremental 

probability”10 which is reflective of the increase in probability – relative to the everyday 

probability – of a geographic region being associated with a predominant meteorological 

pathway for sulfate transport (as opposed to a source region itself). The results are used 

to bolster the conceptual model of visibility impairment at Class I sites presented in 

Chapter 2. 

A.2. Trajectory Approaches 

The Hybrid Single Particle Lagrangian Integrated Trajectory (HYSPLIT) 

model11,12 was used to calculate back trajectories for 13 sites in the Northeast and Eastern 

U.S. The locations correspond to Class I areas subject to the RHR as well as several sites 

where potential nonattainment issues with the PM2.5 NAAQS warranted analysis. Results 

are presented primarily for three rural sites which geographically span the MANE-VU 

class I domain: Acadia National Park, Maine, Lye Brook Wilderness Area, Vermont, and 

Brigantine Wilderness Area, New Jersey. 

Back trajectories were calculated eight times per day for starting heights of 200, 

500 and 1000m above ground level using meteorological wind fields for the five year 

period 2000-2004. NOAA ARL archives analyzed meteorological products for use with 

the HYSPLIT model including the Eta Data Assimilation System (EDAS) wind fields, 

which cover North America with an 80 km spatial resolution and are based on 3-hourly 

variational analyses.13 These back-trajectories -- and the underlying wind fields used to 

generate them -- provide the primary dataset used to explore meteorological patterns in 

the Northeast. Figure A-1 shows a single EDAS back-trajectory representing the path that 

a particle of air has traveled prior to arriving at Acadia National Park. 

The back trajectories with corresponding pollutant measurements and emissions 

data can be combined in a number of ways to yield various metrics which may help 

identify specific meteorological pathways that are more likely than others to contribute to 

sulfate transport to a specific receptor site. 
Appendix A: Trajectory Analysis Methods Page A-4

Figure A-1. Single HYSPLIT Calculated back-trajectory, Acadia National Park 

A common method of analysis requires the calculation of residence-time 

probabilities, which are a measure of the time spent in a specific grid cell relative to the 

total time spent in any grid cell.14 When calculated for all trajectories considered in an 

analysis, this defines the everyday probability as shown in Equation 1. 

Equation 1. Everyday Residence-time Probability

total endpoints passing through all grid cellsfrom all trajectories

total endpoints passing through grid cell i, j

=

=













=

N

n

N

n

EP

ij

ij

These residence time probabilities provide an indication of the fractional time 

spent in a specific grid cell relative to time spent anywhere in the domain by air parcels 

that eventually pass over a given receptor. They can be calculated for any subset of 

trajectories, including all the days within a time frame, yielding the “everyday” 

probability, or a subset corresponding to days with high measured concentrations of 

pollutants at a receptor site. Figure A-2 shows trajectories from the 10% of days with the 

highest sulfate concentrations during the 2000-2004 time period. The plot on the left 

shows the actual trajectories while on the plot on the right shows the resulting residencetime probability field for high sulfate days. 

Figure A-2. Trajectories from the highest sulfate days at Acadia National Park. The highest 10% 

sulfate trajectories (left) and corresponding residence-time probability (right) are shown. 
Appendix A: Trajectory Analysis Methods Page A-5

When the residence-time probability field is calculated for the subset of days 

corresponding to high concentrations of pollutants (as shown in Figure A-2) the result is 

called a high-day probability as shown in Equation 2. 

Equation 2. High Day Residence-time Probability 

total high day endpoints passing through all grid cellsfrom high day trajectories

total high day endpoints passing through grid cell i, j

=

=













=

M

m

M

m

HP

ij

ij

The difference between the everyday probability (Equation 1, all days during 

2000-2004) and the high day probability (Equation 2, high pollution days during 2000-

2004) has been referred to as the incremental probability and identifies areas where the 

probability of poor air quality is greater than the average probability associated with 

typical meteorological patterns (see Equation 3). 

Equation 3. Incremental Probability 

IP = HP − EP

When calculated in this way for each trajectory with its individual pollutant 

concentration value, a standard incremental probability analysis results and can serve as a 

basis for comparison to alternate metrics. Figure A-3 shows the 5-year incremental 

probability field for days corresponding to the top 10 percent of observed sulfate values 

at two sites: Acadia National Park in Maine and Lye Brook Wilderness in Vermont. 

These figures are based on available 500 meter start height HYSPLIT-EDAS back 

trajectories and monitoring data for those sites. Incremental probabilities have been 

calculated for 7 sites in the MANE-VU region and 3 nearby sites in the VISTAS region. 

Plots for all sites (and several different percentile groupings) are presented at the end of 

this Appendix. 

Figure A-3. Incremental Probability (Top 10% observed sulfate days) 

at Acadia, ME and Lye Brook, VT during 2000-2004. 

Acadia Lye Brook
Appendix A: Trajectory Analysis Methods Page A-6

A.3. Cluster-Based Approaches 

Trajectories can be used individually or grouped to create another dataset based 

on the PATH approach.6

 Trajectory clusters are based on the calculated Euclidean 

distance between three-dimensional normalized coordinates of the respective trajectories. 

These clusters are formed by finding the “central” trajectory which has the greatest 

number of neighboring trajectories within a subjectively selected “radius of proximity.” 

There is a trade-off between the “resolution” of various modes of atmospheric transport 

identified by PATH and the number of clusters. Using a narrow radius of proximity, 

more defined clusters that are easily associated with a specific class of meteorological 

transport result (e.g. fast flow from the Northwest, shallow coastal flow, etc.); however, it 

also results in a large number of clusters at each site. 

In order to better define specific meteorological pathways that might be 

associated with pollutant transport, we used a radius of proximity of 12 (this is a unit-less 

value since the coordinates have all been normalized prior to clustering) and a backtrajectory time of 120 hours. This typically resulted in approximately 100-200 frequency 

based clusters at each site, but relatively few clusters contain the majority of the 

trajectory population. Figure A-4 shows typical meteorological patterns among the most 

frequent clusters calculated for Brigantine Wilderness Area, New Jersey. Results are 

plotted as a residence-time probability for each cluster (see Equation 1). Clusters in the 

figure have been associated with specific atmospheric “modes” or meteorological 

patterns that are commonly observed at multiple sites. The modes pictured correspond to 

Northwest Fast flow (NWF), Southwest Interior (SWI), Southwest Coastal (SWC), 

Southeast Maritime (SEM), Upper Midwest (UMW), and Northerly flow (N). Whereas 

each cluster is unique to a specific site and the specific group of trajectories clustered, the 

modes represent patterns which are often observed year after year, and from site to site. 

In this sense, the clusters provide a means of identifying modes of transport which can be 

used for identifying pollution transport mechanisms. 

Figure A-4. Residence-time probability for 6 frequency-based clusters observed at 

Brigantine Wilderness Area, New Jersey between 2000 and 2004. 

NWF SWI SWC

SEM UMW N

Note: Codes reflect atmospheric “modes” or typical patterns of transport which consistently 

appear at multiple sites.
Appendix A: Trajectory Analysis Methods Page A-7

While these frequency-based clusters are useful, a variant method of grouping 

these trajectories was developed to redistribute trajectories into the most common modes. 

This alternate method of clustering relies on the frequency-based cluster groups described 

in the preceding paragraphs, but forms trajectory groups based on proximity rather than 

frequency. In the first step, the frequency-based approach is used to identify the central 

trajectories that represent the most populated frequency-based clusters (approximately 10 

clusters typically contain at least 98 percent of the trajectories in the dataset using R=12 

and 120 hour back-trajectory time). These 10 central trajectories are then used to 

develop 10 proximity-based clusters by assigning every trajectory in the dataset to its 

nearest central trajectories (calculated back to 72 hours). The main advantage of these 

proximity-based clusters is that they more uniformly distribute the population of 

trajectories amongst the most frequently observed atmospheric modes and result in more 

defined clusters than the frequency-based approach. Figure A-5 shows the proximitybased clusters resulting from the frequency-based clusters shown in Figure A-1. In this 

proximity-based approach, trajectories are more evenly distributed, as the entire 

trajectory dataset are assigned to only 10 modes. 

Each trajectory, frequency-based cluster, and proximity-based cluster was 

associated with corresponding monitoring data (or averaged monitoring data in the case 

of clusters) measured as close in time as possible to the “start” time of the back trajectory 

calculation. Associations were made for PM2.5, sulfate ion, organic carbon, and aerosol 

extinction as PM components routinely measured as part of the IMPROVE program, 

although results are presented here only for 24-hr integrated sulfate ion mass. 

A.3.1. Cluster-weighted Probability 

Everyday probabilities can be calculated for any subset of trajectories. When 

calculated for the trajectories within a given cluster, that cluster’s everyday probability 

results. This is essentially a normalized version of the residence-time probabilities shown 

in Figure A-4 and Figure A-5. Everyday probabilities for clusters at 13 sites are 

Figure A-5. Residence-time probability for 6 proximity-based clusters observed at 

Brigantine Wilderness Area, New Jersey between 2000 and 2004. 

NWF SWI SWC

SEM UMW

N

Note: Codes reflect atmospheric “modes” or typical patterns of transport which consistently appear at multiple sites.
Appendix A: Trajectory Analysis Methods Page A-8

presented at the conclusion of this appendix. The everyday probabilities for clusters at an 

individual site and the associated average pollution information corresponding to each 

cluster is combined through a method identified here as the cluster-weighted probability 

(CWP). 

Each PATH-derived cluster’s residence-time probability is weighted by the 

average sulfate value for any measurements corresponding to a trajectory which is a 

member of that cluster. The weighted residence-time probability is summed over all

clusters calculated for a site (as opposed to just the highest probability for a specific 

pollutant as was the case with the incremental probability metrics). The everyday 

probability is subtracted from the sum of cluster-weighted probabilities to identify areas 

of increased (or in the case of negative values, decreased) probability of being associated 

with a meteorological pathway for pollutant transport. Equation 5 presents the clusterweighted probability. 

Equation 5. Cluster-weighted Probability 

Average pollutant concentration (based on all days)

( ) Average pollutant concentration (based on observations associated with cluster i)

 total number of clusters calculated

( )

1

1

=

=

=













= ∑ ⋅ − ⋅

=

C

C

L

C RP C EP

C

CWP

i

i

L

i

i

Here, (C )i represents the average sulfate value for all trajectories within cluster i 

which had an associated SO4

2- measurement (roughly 25-30 percent, given 1-in-3 day 

sampling schedules). By weighting the residence-time probability for cluster i by this 

quantity, we are implicitly assuming that similar trajectories (i.e. traversing similar source 

regions under similar meteorological conditions) will have similar resulting ambient 

concentrations at the receptor. The quantity (C ) represents the average value for sulfate 

measurements associated with trajectories in any of the clusters and acts to normalize the 

sum of the residence-time probabilities. 

As we have examined two alternate methods for assigning trajectories to clusters 

– frequency-based clustering and proximity-based clustering – two methods for 

calculating cluster weighted probabilities exist. The first uses the frequency-based 

clusters as the dataset, while the second uses the more distributed, proximity-based 

clusters as the dataset. Figure A-6 shows the CWP calculated for both methods at 

Brigantine Wilderness Area, New Jersey. 

While calculated from the same underlying trajectory files and sulfate 

observations, this metric is calculated in a fundamentally different way than the 

incremental probability approach presented. The CWP uses trajectory clusters (as 

opposed individual trajectories) to develop a weighted probability field which is then 

compared to the everyday probability. The fact that the results are similar to those 

calculated for the IP technique provides reassurance that these approaches are reasonable 

for identifying areas that are associated with sulfate transport. 
Appendix A: Trajectory Analysis Methods Page A-9

A.4. Results 

Regions of transport to different sites can be determined using the trajectory (nonclustered) technique, incremental probability. In this method, pollution values are 

assigned to individual trajectories (as opposed to clusters) and regions associated with 

high sulfate transport are determined by looking at the difference of the high day 

trajectory probabilities from the everyday trajectory probabilities. Figure A-7 shows the 

top 10% sulfate incremental probability at three sites, Acadia, Brigantine, and Lye Brook. 

In these incremental probability plots, trajectories with higher pollution 

concentrations generally follow a path from the Midwest across the Northeast region 

prior to arriving at Acadia. Transport paths from the Southeast and the Midwest are 

evident at Brigantine, and a combination of Midwest transport and transport from the 

Southeast along the industrial I-95 Corridor affect Lye Brook. 

Incremental probability can also be used to look at the regions contributing to the 

best pollution days at a site. Figure A-8 shows the 10% lowest sulfate incremental 

probability. Best-day incremental probability shows that trajectories arriving to the sites 

Figure A-6. Cluster-weighted Probability methods associated to sulfate transport using 

frequency based clusters on left and proximity-based clusters on the right at Brigantine 

Wilderness Area, New Jersey. 

Note: Areas of increased (yellow/red) or decreased (cyan/blue) 

Figure A-7. Incremental Probability (Top 10% Sulfate) at three sites, 

Acadia, Brigantine and Lye Brook 2000-2004. 

Acadia Brigantine Lye Brook
Appendix A: Trajectory Analysis Methods Page A-10

on days with low sulfate levels tend to follow a path from the north in Canada or off the 

Atlantic Ocean. This is an expected result as fewer sources are located in this region. 

By examining pollution levels associated with different clusters, we can gain 

insight into which atmospheric modes are associated with transport to sites in the MANEVU region. Figure A-9 compares the proximity-based cluster with the highest sulfate 

value at three sites, Lye Brook Wilderness Area, Brigantine Wilderness Area, and Acadia 

National Park. 

Figure A-9 demonstrates that the clusters showing the highest pollution values 

show similar meteorological characteristics at different sites. The three sites show that in 

the higher average pollution clusters, the air follows the path from the Midwest to the site 

in question. Lye Brook shows an east coast component contributing as an area of 

transport on the worst average sulfate days. Using this method, we have grouped 

trajectories purely based on meteorological characteristics and can examine pollution 

levels within these groupings. Thus agreement between this method and the incremental 

probability results shown earlier suggest that whether you select trajectories based on 

meteorology or chemistry, similar regions are identified as being associated with sulfate 

transport. Figures at the end of this appendix show the clusters and average pollution 

values for all the sites in the region analyzed. 

Figure A-10 displays the proximity-based clusters with the lowest average sulfate 

concentrations. They show which meteorological mode contributes to the best pollution 

days at three different sites, Acadia, Lye Brook, and Brigantine. This provides a method 

that is comparable to Figure A-8 where incremental probability for the lowest sulfate 

trajectories is shown. Again, the comparison is made between this clustering technique 

where trajectories are grouped solely on meteorological characteristics and the 

incremental probability technique that looks at trajectories with similar pollution 

characteristics. 

Much like the atmospheric modes that contribute to the highest sulfate levels at 

our three sites, very similar atmospheric patterns contribute to the best sulfate days across 

multiple sites in the region. Air masses moving in from the north and off the Atlantic 

Ocean contribute to the best days at Acadia, Brigantine, and Lye Brook. Similar modes 

affect the best days at many other sites, seen in the section following this appendix. 

Figure A-8. Incremental Probability (Bottom 10% Sulfate) at three sites, Acadia, 

Brigantine and Lye Brook 2000-2004. 

Acadia Brigantine Lye Brook
Appendix A: Trajectory Analysis Methods Page A-11

Cluster weighted probabilities are used to combine cluster information with 

pollution information and the following CWP plots show regions with greater probability 

of sulfate transport in red/yellow and regions of decreased probability of sulfate transport 

in blue. We have presented the CWP based on proximity-based clusters in Figure A-11, 

which shows results similar to Figure A-9 since the clusters weighted by the highest 

pollution values tend to enhance the regions they cover, consistent with a greater 

probability of contributing to sulfate transport. However, the CWP plots in Figure A-11 

now contain information from all the clusters (and thus all the trajectories) in the dataset. 

Figure A-9. Proximity based cluster with the highest associated sulfate value for three sites 

in the MANE-VU region, Acadia (sulf=3.19μg/m3), Brigantine (sulf=6.79μg/m3), and Lye 

Brook (sulf=4.56μg/m3). 

Acadia Brigantine

Figure A-10. Proximity based cluster with the lowest associated sulfate value for three sites 

in the MANE-VU region, Acadia (sulf=1.41μg/m3), Brigantine (sulf=2.23μg/m3), and Lye 

Brook (sulf=1.16μg/m3). 

Acadia Brigantine Lye Brook

Figure A-11. Cluster Weighted Probability at three sites, Acadia, Brigantine and Lye Brook 2000-2004.

Acadia Brigantine Lye Brook
Appendix A: Trajectory Analysis Methods Page A-12

By averaging the various probability fields across sites, we can gain insight into 

which regions are most likely to be associated with sulfate transport to multiple sites in 

the MANE-VU region. A region that is associated with transport to several sites in 

different locations is far more likely to be associated with large emission sources. Figure 

A-12 show a multi-site averages of incremental probability for the top 10 percent worst 

days at five northern sites, Acadia, Lye Brook, Camp Dodge, Moosehorn, and Mohawk 

Mountain. Figure A-13 shows the multi-site average CWP which includes all proximitybased clusters for the same sites. 

Figure A-12. Multi-site average probabilities showing areas of increased (yellow/red) or 

decreased (cyan/blue) probability of being associated with sulfate transport to Acadia, Lye 

Brook, Camp Dodge, Moosehorn, and Mohawk Mountain on the ten percent worst sulfate 

days. 

Figure A-13. Multi-site average CWP showing areas of increased (yellow/red) or decreased

(cyan/blue) probability of being associated with sulfate transport to Acadia, Lye Brook, 

Camp Dodge, Moosehorn, and Mohawk Mountain. 
Appendix A: Trajectory Analysis Methods Page A-13

From a qualitative perspective, the two metrics (IP and CWP) are quite similar 

showing significant sulfate transport (on an annual average basis) along the Eastern 

corridor from Virginia up through Maryland and Eastern Pennsylvania. A second area of 

influence along the Ohio River valley between Ohio, Pennsylvania and West Virginia 

seems to play a significant role as well. 

These averages can also be applied to different geographical regions as well. 

Figure A-14 shows the average IP while Figure A-15 shows the average CWP for four 

southern sites, Brigantine, Shenandoah, Dolly Sods, and Great Smokey Mountains. The 

figure highlights specific regions of higher probability of sulfate transport affecting a 

large area along the east coast. 

Figure A-14. Multi-site average IP showing areas of increased (yellow/red) or decreased 

(cyan/blue) probability of being associated with sulfate transport to Brigantine, 

Shenandoah, Dolly Sods, and Great Smokey Mountains.

Figure A-15. Multi-site average CWP showing areas of increased (yellow/red) or decreased 

(cyan/blue) probability of being associated with sulfate transport to Brigantine, 

Shenandoah, Dolly Sods, and Great Smokey Mountains.
Appendix A: Trajectory Analysis Methods Page A-14

A.5. Conclusions 

A large database of back trajectories and corresponding air pollution 

measurements have been used with trajectory cluster analysis techniques to apportion 

observed sulfate mass concentrations as an independent check on source modeling 

results. Clusters have been used here to develop metrics related to Wishinski and 

Poirot’s “incremental probability”10 which provides the relative increase in probability of 

a geographic region being associated with a predominant meteorological pathway 

associated with pollutant transport. 

Several techniques have identified state-specific contributions of SO2 emission 

sources to sulfate formation. Results indicate that cluster-based trajectory techniques can 

provide a semi-quantitative check on chemical transport model results. This analysis 

demonstrates a potentially novel way of identifying regions that play a role in pollutant 

transport (and may host source emissions as well). Combined with meteorological 

information and source apportionment model results, the approach may yield a more 

comprehensive picture of source emissions and the circumstances under which they are 

transported to specific receptor sites. 

A.5.1. Acknowledgements 

The U.S. EPA has made this work possible through their support of the MANEVU Regional Planning Organization. The HYSPLIT4 model was provided by NOAA. 

(HYbrid Single-Particle Lagrangian Integrated Trajectory Model, 1997. Web address: 

http://www.arl.noaa.gov/ready/hysplit4.html, NOAA Air Resources Laboratory, Silver 

Spring, MD). The authors would also like to thank Nicolas Hamel, who developed the 

“clustermaker” code which allowed us to perform the analysis in an efficient manner, 

Ingrid Ulbrich who set up and calculated the trajectory database for many early years in 

the analysis and Jamie Lehner who assisted with many early data analyses on which this 

work has built. 
Appendix A: Trajectory Analysis Methods Page A-15

References 

1. Seibert, P.; Kromp-Kolb, H; Baltensperger, U.; Jost, D.T.; Schwikowski, M.; Kaspar, 

A.; Puxbaum, H., “Trajectory Analysis of Aerosol Measurements at High Alpine 

Sites,” in Transport and Transformation of Pollutants in the Troposphere, eds. 

Borell, P.M.; Borell, P.; Cvitas, T.; Seiler, W., Academic Publishing, Den Haag, 

1994, 689-693. 

2. Hopke, P.K.; Li, C.L.; Cizek, W.; Landsberger, S., “The Use of Bootstrapping to 

Estimate Conditional Probability Fields for Source Locations of Airborne Pollutants,” 

Chemom. Intell. Lab. Syst. 1995, 30, 69-79. 

3. Stohl, A., “Trajectory statistics: A new method to establish source-receptor 

relationships of air pollutants and its application to the transport of particulate sulfate 

in Europe,” Atmos. Environ., 1996, 30, 579-587. 

4. Kleiman, G.; Prinn, R.G., “Measurement and Deduction of emissions of 

trichloroethene, tetrachloroethene, and trichloromethane (chloroform) in the 

northeastern United States and southeastern Canada,” J. Geophys. Res., 2000, 105, 

28875-28893. 

5. Hsu, Y.K.; Holsen, T.M.; Hopke, P.K., “Comparison of hybrid receptor models to 

locate PCB sources in Chicago,” Atmos. Env., 2003, 37, 545-562. 

6. Moody, J.L.; Munger, J.W.; Goldstein, A.H.; Jacob, D.J.; Wofsy, S.C., “Harvard 

Forest regional-scale air mass composition by Patterns in Atmospheric Transport 

History (PATH),” J. Geophys. Res., 1998, 103, 13181-13194. 

7. Dorling, S.R.; Davies, T.D.; Pierce, C.E., “Cluster analysis: A technique for 

estimating synoptic meteorological controls on air and precipitation chemistry – 

Method and Application,” Atmos. Env., 1992, 26A, 2575-2581. 

8. Dorling, S.R.; Davies, T.D.; Pierce, C.E., “Cluster analysis: A technique for 

estimating synoptic meteorological controls on air and precipitation chemistry – 

results from Eskdalemuir, south Scotland,” Atmos. Env., 1992, 26A, 2583-2602. 

9. Kahl, J.D.W.; Liu, D.; White, W.H.; Macias, E.W.; Vasconselos, L., “The 

Relationship Between Atmospheric Transport and the Particle Scattering Coefficient 

at the Grand Canyon,” J. Air & Waste Manage. Assoc., 1997, 47, 419-425. 

10. Wishinski, P.R.; Poirot, R. L., “Long-Term Ozone Trajectory Climatology for the 

Eastern US, Part I: Methods,” paper 98-A613, Vermont Dept. of Env. Conservation 

(1998). 
Appendix A: Trajectory Analysis Methods Page A-16

11. Draxler, R.D.; Hess, G.D., “Description of the HYSPLIT-4 Modeling System,” 

NOAA Technical Memorandum ERL, ARL-224, Air Resources Laboratory, Silver 

Springs, Maryland, 24 pgs., 1997. 

12. Draxler, R.D.; Hess, G.D., “An Overview of the HYSPLIT-4 Modeling System for 

Trajectories, Dispersion, and Deposition,” Australian Meteorological Magazine, 

1998, 47, 295-308. 

13. Rolph, G.D., Real-time Environmental Applications and Display sYstem (READY) 

Website (http://www.arl.noaa.gov/ready/hysplit4.html). NOAA Air Resources 

Laboratory, Silver Spring, MD., 2003. 

14. Poirot, R. L.; Wishinski, P.R., “Visibility, sulfate and air mass history associated with 

the summertime aerosol in Northern Vermont,” Atmos. Environ. 1986, 20, 1457-

1469.