Appendix A- Acadia 

Supplement

Trajectory analysis results at 

Acadia 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

Acadia All Trajectories 00-04, Top 10 Cluster

Modes defined at: R=12, 120hr BT, 500m Start ht, 5111 Valid Trajectories, 92

Reassigned Trajectories Based on 72hr BT, 500m Start Ht, 8274 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 Cent

SulfaBext PM OC # Tra# Tra

Frequency Proximity

Sulfate 1.30 1.40Bext 29.89 30.83PM 4.04 4.09OC 1.21 1.04# Trajs 487 1032# Trajs w. Poll 137 245

Frequency Proximity

Sulfate 2.76 1.79Bext 54.39 39.91PM 6.92 5.42OC 1.36 1.49# Trajs 817 1058# Trajs w. Poll 221 302

Frequency Proximity

Sulfate 2.17 3.14Bext 44.79 59.88PM 6.01 7.92OC 1.55 1.52# Trajs 1302 738# Trajs w. Poll 324 195

Frequency Proximity

Sulfate 2.60 2.45Bext 52.19 50.35PM 6.91 6.54OC 1.63 1.57# Trajs 3811 1347# Trajs w. Poll 1056 373
Cluster 6

Frequency Based Cluster

Cluster 7 Cluster 8 Cluster 9 Clu

Acadia All Trajectories 00-04, Top 10 Cluster

Modes defined at: R=12, 120hr BT, 500m Start ht, 5111 Valid Trajectories, 92

Reassigned Trajectories Based on 72hr BT, 500m Start Ht, 8274 Valid Traj

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 1.07 3.19Bext 22.28 64.16PM 2.85 8.19OC 0.75 1.91# Trajs 264 805# Trajs w. Poll 78 222

Frequency Proximity

Sulfate 3.28 1.70Bext 59.81 33.20PM 8.02 4.25OC 1.46 0.81# Trajs 235 543# Trajs w. Poll 75 137

Frequency Proximity

Sulfate 1.03 2.21Bext 23.62 44.48PM 3.23 6.11OC 1.10 1.52# Trajs 168 1177# Trajs w. Poll 23 331

Frequency Proximity

Sulfate 1.50 2.10Bext 31.53 44.05PM 4.05 5.95OC 0.62 1.52# Trajs 122 1358# Trajs w. Poll 29 324

SBPO# # 
Acadia All Trajectories 00-04, Best/Worst Sulfa

Modes defined at: R=12, 120hr BT, 500m Start ht, 5111 Valid Trajectories, 92

Reassigned Trajectories Based on 72hr BT, 500m Start Ht, 8274 Valid Traj

Lowest Sulfate(Proximity Based)Highest Sulfate(Proximity Based)

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 1.07 3.19Bext 22.28 64.16PM 2.85 8.19OC 0.75 1.91# Trajs 264 805# Trajs w. Poll 78 222

Frequency Proximity

Sulfate 2.17 3.14Bext 44.79 59.88PM 6.01 7.92OC 1.55 1.52# Trajs 1302 738# Trajs w. Poll 324 195

Frequency Proximity

Sulfate 1.30 1.40Bext 29.89 30.83PM 4.04 4.09OC 1.21 1.04# Trajs 487 1032# Trajs w. Poll 137 245

Frequency Proximity

Sulfate 1.99 1.41Bext 46.99 28.96PM 5.59 3.78OC 1.25 0.89# Trajs 105 699# Trajs w. Poll 20 208
Acadia All Trajectories 00-04, Incremental Probab

IP Based on Top10%

500m

Sulfate PM OC 

Sulfate PM OC 

1000m
Acadia All Trajectories 00-04, Cluster Weighted Pro

Calculated using Proximity Based Clusters, 500m

Sulfate PM

OC B-ext
Acadia All Trajectories 00-04, Cluster Weighted Pro

Calculated using Frequency Based Clusters, 500m

Sulfate PM

OC B-ext