Appendix A- Brigantine 

Supplement

Trajectory analysis results at 

Brigantine National Park.
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

Brigantine All Trajectories 00-04, Top 10 Clust

Modes defined at: R=12, 120hr BT, 500m Start ht, 6934 Valid Trajectories, 73

Reassigned Trajectories Based on 72hr BT, 500m Start Ht, 10514 Valid Tra

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 Cent

Frequency Proximity

Sulfate 6.04 6.18Bext 100.96 101.29PM 13.55 13.85OC 2.94 2.97# Trajs 4865 1019# Trajs w. Poll 1386 272

SulfatBext PM OC # Traj# Traj

Frequency Proximity

Sulfate 3.97 5.55Bext 80.55 97.42PM 10.48 13.65OC 2.33 2.68# Trajs 1667 1056# Trajs w. Poll 451 291

Frequency Proximity

Sulfate 3.86 3.79Bext 71.94 74.00PM 10.12 9.67OC 1.68 2.29# Trajs 915 1748# Trajs w. Poll 240 510

Frequency Proximity

Sulfate 2.14 3.48Bext 46.86 67.02PM 6.49 8.53OC 1.72 1.83# Trajs 640 815# Trajs w. Poll 195 249
Cluster 6 Cluster 7 Cluster 8 Cluster 9 Clu

Brigantine All Trajectories 00-04, Top 10 Clust

Modes defined at: R=12, 120hr BT, 500m Start ht, 6934 Valid Trajectories, 73

Reassigned Trajectories Based on 72hr BT, 500m Start Ht, 10514 Valid Tra

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 Cent

Frequency Proximity

Sulfate 3.48 6.79Bext 67.72 111.17PM 8.64 15.06OC 1.63 3.70# Trajs 405 925# Trajs w. Poll 100 259

SulfatBext PM OC # Traj# Traj

Frequency Proximity

Sulfate 4.88 3.31Bext 89.86 61.73PM 11.65 8.39OC 2.42 1.15# Trajs 363 588# Trajs w. Poll 107 142

Frequency Proximity

Sulfate 2.74 2.24Bext 63.07 48.68PM 7.95 6.72OC 1.87 1.91# Trajs 261 886# Trajs w. Poll 80 215

Frequency Proximity

Sulfate 3.89 5.53Bext 65.80 98.54PM 8.54 13.18OC 1.44 2.48# Trajs 129 773# Trajs w. Poll 30 198
Brigantine All Trajectories 00-04, Best/Worst Su

Modes defined at: R=12, 120hr BT, 500m Start ht, 6934 Valid Trajectories, 73

Reassigned Trajectories Based on 72hr BT, 500m Start Ht, 10514 Valid Tra

Highest Sulfate

Lowest Sulfate

Sulfate- Sulfate ion Bext- Extinction (MPM- Particulate MOC- Organic CarbNum Trajs- NumbeclusterNum Trajs w. Poll- in cluster with assomeasurement (Bassamples taken duri

Frequency Proximity

Sulfate 5.83 6.43Bext 103.11 105.64PM 14.33 14.64OC 3.02 2.93# Trajs 432 801# Trajs w. Poll 128 222

Frequency Proximity

Sulfate 3.48 6.79Bext 67.72 111.17PM 8.64 15.06OC 1.63 3.70# Trajs 405 925# Trajs w. Poll 100 259

Frequency Proximity

Sulfate 4.88 3.31Bext 89.86 61.73PM 11.65 8.39OC 2.42 1.15# Trajs 363 588# Trajs w. Poll 107 142

Frequency Proximity

Sulfate 2.74 2.24Bext 63.07 48.68PM 7.95 6.72OC 1.87 1.91# Trajs 261 886# Trajs w. Poll 80 215
Brigantine All Trajectories 00-04, Incremental Prob

IP Based on Top10%, 500m

Sulfate PM

OC B-ext
Brigantine All Trajectories 00-04, Cluster Weighted Pr

Calculated using Proximity Based Clusters, 500m

Sulfate PM

OC B-ext
Brigantine All Trajectories 00-04, Cluster Weighted Pr

Calculated using Frequency Based Clusters, 500m

Sulfate PM

OC B-ext