Appendix A- Washington D

Supplement

Trajectory analysis results at 

Washington D.C.
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. 
Cluster 1 Cluster 2 Cluster 3 Cluster 4 Clu

Washington All Trajectories 00-04, Top 10 Clust

Modes defined at: R=12, 120hr BT, 500m Start ht, 7438 Valid Trajectories, 67

Reassigned Trajectories Based on 72hr BT, 500m Start Ht, 11020 Valid Traj

Frequency Based Cluster Frequency Based Cluster Frequency Based Cluster Frequency Based Cluster Frequ

Proximity Based Cluster Proximity Based Cluster Proximity Based Cluster Proximity Based Cluster Pro

Central Trajectory Central Trajectory Central Trajectory Central Trajectory Centra

SuBePM OC # T# T

Frequency Proximity

Sulfate 6.75 7.94Bext 120.54 134.78PM 17.04 18.88OC 4.12 4.47# Trajs 5229 1297# Trajs w. Poll 1584 374

Frequency Proximity

Sulfate 4.09 5.70Bext 87.13 105.95PM 12.11 15.17OC 3.17 3.82# Trajs 1760 1344# Trajs w. Poll 572 365

Frequency Proximity

Sulfate 5.62 4.26Bext 105.20 87.39PM 16.08 12.06OC 4.62 3.24# Trajs 806 1090# Trajs w. Poll 275 296

Frequency Proximity

Sulfate 3.26 5.28Bext 75.57 100.34PM 10.13 13.76OC 2.62 3.05# Trajs 673 1081# Trajs w. Poll 216 294
Cluster 6 Cluster 7 Cluster 8 Cluster 9 C

Washington All Trajectories 00-04, Top 10 Clust

Modes defined at: R=12, 120hr BT, 500m Start ht, 7438 Valid Trajectories, 67

Reassigned Trajectories Based on 72hr BT, 500m Start Ht, 11020 Valid Traj

Frequency Based Cluster Frequency Based Cluster Frequency Based Cluster Frequency Based Cluster Freq

Proximity Based Cluster Proximity Based Cluster Proximity Based Cluster Proximity Based Cluster Pro

Central Trajectory Central Trajectory Central Trajectory Central Trajectory Centra

Frequency Proximity

Sulfate 3.82 4.41Bext 72.29 87.88PM 10.13 12.18OC 2.43 3.18# Trajs 423 1958# Trajs w. Poll 106 527

SBPO# # 

Frequency Proximity

Sulfate 3.48 3.44Bext 74.25 73.24PM 10.39 10.06OC 2.93 2.69# Trajs 287 912# Trajs w. Poll 92 259

Frequency Proximity

Sulfate 5.85 6.43Bext 106.34 117.19PM 16.18 17.74OC 3.93 4.79# Trajs 218 655# Trajs w. Poll 71 214

Frequency Proximity

Sulfate 3.91 5.74Bext 68.44 106.14PM 10.90 15.66OC 2.97 3.87# Trajs 142 702# Trajs w. Poll 36 191
Washington All Trajectories 00-04, Top 10 Clust

Modes defined at: R=12, 120hr BT, 500m Start ht, 7438 Valid Trajectories, 67

Reassigned Trajectories Based on 72hr BT, 500m Start Ht, 11020 Valid Traj

Best and Worst Days

Highest Sulfate(Proximate)Lowest Sulfate(Proximate)

Frequency Proximity

Sulfate 5.85 6.43Bext 106.34 117.19PM 16.18 17.74OC 3.93 4.79# Trajs 218 655# Trajs w. Poll 71 214

Frequency Proximity

Sulfate 6.75 7.94Bext 120.54 134.78PM 17.04 18.88OC 4.12 4.47# Trajs 5229 1297# Trajs w. Poll 1584 374

Frequency Proximity

Sulfate 3.48 3.44Bext 74.25 73.24PM 10.39 10.06OC 2.93 2.69# Trajs 287 912# Trajs w. Poll 92 259

Frequency Proximity

Sulfate 5.62 4.26Bext 105.20 87.39PM 16.08 12.06OC 4.62 3.24# Trajs 806 1090# Trajs w. Poll 275 296

Sulfate- Sulfate ion Bext- Extinction (MPM- Particulate MOC- Organic CarbNum Trajs- NumbeclusterNum Trajs w. Poll- in cluster with assomeasurement (Bassamples taken duri
Washington All Trajectories 00-04, Incremental Prob

IP Based on Top10%, 500m

Sulfate PM

OC B-ext
Washington All Trajectories 00-04, Cluster Weighted P

Calculated using Proximity Based Clusters, 500m

Sulfate PM

OC B-ext
Washington All Trajectories 00-04, Cluster Weighted P

Calculated using Frequency Based Clusters, 500m

Sulfate PM

OC B-ext