Appendix A- Pittsburgh 

Supplement

Trajectory analysis results at 

Pittsburgh, PA.
Equations for Different Metrics 

Everyday Residence-time Probability

from all trajectories

total endpoints passing through all grid cells

total endpoints passing through grid celli, j

=

=





=

N

n

N

n EP

ij

ij

High Day Residence-time Probabili

from high day trajectories

total high day endpoints passing th

total high day endpoints passing th

=

=





=

M

m

M

m HP

ij

ij

Incremental Probability

IP

= HP

− EP

Cluster-Weighted Probability

Average pollutant concentration (based on 

associated with cluster i)

( ) Average pollutant concentration (based 

 total number of clusters calculated

( )

1

1

=

=

=





=

∑ ⋅ − ⋅

=

C

C

L

C RP

C EP

C

CWP

i

i

L

i

i
Description of Figures

• Central Trajectory (CT)- Trajectory with the largest number of nearest 

the dataset.

• Frequency Based Clusters- These clusters are formed by finding the “

trajectory which has the greatest number of neighboring trajectories wsubjectively selected radius of proximity (R). These trajectories are thfrom the dataset and the process is applied to the remaining trajectorie

• Proximity Based Clusters- Clustering relies on the frequency-based clu

but forms trajectory groups based on proximity rather than frequency. step, the frequency-based approach is used to identify the central trajerepresent the most populated frequency-based clusters (approximately typically contain at least 98% of the trajectories in the dataset using R=hour back-trajectory (BT) time). These 10 central trajectories are then develop 10 proximity-based clusters by assigning every trajectory in thits nearest central trajectories (calculated back to 72 hours). 

• Incremental Probability- Difference between the everyday probability (

derived from all the trajectories in the dataset) and high day probability derived from trajectories arriving at the site on the subset of high pollu

• Cluster Weighted Probability- Each PATH-derived cluster’s residence-

probability is weighted by the average sulfate (or other pollutant) value measurements corresponding to a trajectory which is a member of thaThe weighted residence-time probability is summed over all clusters ca

a site. The everyday probability is subtracted from the sum of cluster-probabilities to identify areas of increased (or in the case of negative vdecreased) probability of being associated with a meteorological pathwpollutant transport. 
Pittsburgh All Trajectories 00-04, Top 10 Cluste

Modes defined at: R=12, 120hr BT, 500m Start ht, 7852 Valid Trajectories, 63

Reassigned Trajectories Based on 72hr BT, 500m Start Ht, 11330 Valid Traj

Cluster 1 Cluster 2 Cluster 3 Cluster 4 Cluste

Frequency Based Cluster Frequency Based Cluster Frequency Based Cluster Frequency Based Cluster Frequency B

Proximity Based Cluster Proximity Based Cluster Proximity Based Cluster Proximity Based Cluster Proximity B

Central Trajectory Central Trajectory Central Trajectory Central Trajectory Centra

Frequency Proximity

Sulfate 7.64 8.12PM 20.81 22.32# Trajs 5383 1887# Trajs w. Poll 1187 418

Sulfate PM # Trajs # Trajs w. 

Frequency Proximity

Sulfate 5.19 6.02PM 16.17 18.23# Trajs 1506 761# Trajs w. Poll 331 171

Frequency Proximity

Sulfate 5.71 6.18PM 16.88 17.65# Trajs 1048 1275# Trajs w. Poll 228 237

Frequency Proximity

Sulfate 4.25 4.67PM 13.06 14.49# Trajs 661 1263# Trajs w. Poll 152 307
Cluster 6 Cluster 7 Cluster 8 Cluster 9 Clus

Pittsburgh All Trajectories 00-04, Top 10 Cluste

Modes defined at: R=12, 120hr BT, 500m Start ht, 7852 Valid Trajectories, 63

Reassigned Trajectories Based on 72hr BT, 500m Start Ht, 11330 Valid Traj

Frequency Based Cluster Frequency Based Cluster Frequency Based Cluster Frequency Based Cluster Freque

Proximity Based Cluster Proximity Based Cluster Proximity Based Cluster Proximity Based Cluster Proximi

Central Trajectory Central Trajectory Central Trajectory Central Trajectory Centra

Sulfate PM # Trajs # Trajs w

Frequency Proximity

Sulfate 2.89 5.95PM 11.30 17.74# Trajs 386 792# Trajs w. Poll 79 212

Frequency Proximity

Sulfate 10.53 7.23PM 26.70 20.13# Trajs 301 2168# Trajs w. Poll 91 482

Frequency Proximity

Sulfate 4.24 5.94PM 14.82 16.56# Trajs 199 631# Trajs w. Poll 51 153

Frequency Proximity

Sulfate 2.78 3.28PM 10.12 12.83# Trajs 186 569# Trajs w. Poll 39 160
Pittsburgh All Trajectories 00-04, Top 10 Cluste

Modes defined at: R=12, 120hr BT, 500m Start ht, 7852 Valid Trajectories, 63

Reassigned Trajectories Based on 72hr BT, 500m Start Ht, 11330 Valid Traj

Highest Sulfate(Proximity)Lowest Sulfate(Proximity) Sulfate- Sulfate ion C

Bext- Extinction (MmPM- Particulate MattOC- Organic Carbon Num Trajs- Number clusterNum Trajs w. Poll- Nin cluster with associmeasurement (Based samples taken during 

Frequency Proximity

Sulfate 7.64 8.12PM 20.81 22.32# Trajs 5383 1887# Trajs w. Poll 1187 418

Frequency Proximity

Sulfate 10.53 7.23PM 26.70 20.13# Trajs 301 2168# Trajs w. Poll 91 482

Frequency Proximity

Sulfate 2.78 3.28PM 10.12 12.83# Trajs 186 569# Trajs w. Poll 39 160

Frequency Proximity

Sulfate 6.80 3.47PM 19.56 12.82# Trajs 560 1538# Trajs w. Poll 107 324
Pittsburgh All Trajectories 00-04, Incremental Prob

IP Based on Top10%, 500m

Sulfate PM
Pittsburgh All Trajectories 00-04, Cluster Weighted Pr

Calculated using Proximity Based Clusters, 500m

Sulfate PM
Pittsburgh All Trajectories 00-04, Cluster Weighted Pr

Calculated using Frequency Based Clusters, 500m

Sulfate PM