Appendix A-Great Gulf 

Supplement

Trajectory analysis results at 

Great Gulf Wilderness Area.
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

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 Cen

Great Gulf All Trajectories 00-04, Top 9 Clus

Modes defined at: R = 12, 120hr BT, 500m Start Height, 6110 Valid, 8271 Inv

Reassigned Trajectories Based on 72hr BT, 500m Start Height, 9352 Vali

Sulfate Bext PM OC # Trajs # Trajs 

Frequency Proximity

Sulfate 2.29 3.04Bext 40.64 51.94PM 6.09 7.45OC 1.66 1.92# Trajs 4514 1195# Trajs w. Poll 1086 290

Frequency Proximity

Sulfate 1.02 3.94Bext 21.03 58.59PM 2.98 8.77OC 0.89 1.86# Trajs 952 712# Trajs w. Poll 240 171

Frequency Proximity

Sulfate 3.71 1.42Bext 64.02 27.76PM 8.69 4.11OC 1.98 1.22# Trajs 871 2011# Trajs w. Poll 206 513

Frequency Proximity

Sulfate 1.44 2.05Bext 26.61 37.60PM 3.62 5.07OC 1.10 1.38# Trajs 734 738# Trajs w. Poll 205 191
Great Gulf All Trajectories 00-04, Top 9 Clus

Modes defined at: R = 12, 120hr BT, 500m Start Height, 6110 Valid, 8271 Inv

Reassigned Trajectories Based on 72hr BT, 500m Start Height, 9352 Vali

Cluster 6 Cluster 7 Cluster 8 Cluster 9

Frequency Based Cluster Frequency Based Cluster Frequency Based Cluster Frequency Based Cluster

Proximity Based Cluster Proximity Based Cluster Proximity Based Cluster Proximity Based ClusterCentral Trajectory Central Trajectory Central Trajectory Central Trajectory

Frequency Proximity

Sulfate 1.58 3.11Bext 31.90 48.28PM 4.42 7.49OC 1.45 1.74# Trajs 346 1379# Trajs w. Poll 96 329

Frequency Proximit

Sulfate 1.25 1.3Bext 25.09 28.9PM 3.43 4.3OC 1.11 1.5# Trajs 171 113# Trajs w. Poll 59 29

Frequency Proximity

Sulfate 2.25 3.40Bext 42.50 58.13PM 5.79 7.75OC 1.50 1.66# Trajs 223 792# Trajs w. Poll 58 207

Frequency Proximity

Sulfate 1.96 3.28Bext 34.98 58.24PM 5.13 7.81OC 1.42 1.97# Trajs 191 419# Trajs w. Poll 42 101
Great Gulf All Trajectories 00-04, Top 9 Clus

Modes defined at: R = 12, 120hr BT, 500m Start Height, 6110 Valid, 8271 Inv

Reassigned Trajectories Based on 72hr BT, 500m Start Height, 9352 Valid 

Best/Worst Days

Highest Sulfate(Proximity)Lowest Sulfate(Proximity) 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 1.02 3.94Bext 21.03 58.59PM 2.98 8.77OC 0.89 1.86# Trajs 952 712# Trajs w. Poll 240 171

Frequency Proximity

Sulfate 2.25 3.40Bext 42.50 58.13PM 5.79 7.75OC 1.50 1.66# Trajs 223 792# Trajs w. Poll 58 207

Frequency Proximity

Sulfate 3.48 0.97Bext 54.84 21.48PM 8.11 3.23OC 1.77 1.12# Trajs 560 1309# Trajs w. Poll 142 278

Frequency Proximity

Sulfate 1.25 1.39Bext 25.09 28.95PM 3.43 4.33OC 1.11 1.54# Trajs 171 1134# Trajs w. Poll 59 296
Great Gulf All Trajectories 00-04, Incremental Prob

IP Based on Top10%, 500m

Sulfate PM

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

Calculated using Proximity Based Clusters, 500m

Sulfate PM

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

Calculated using Frequency Based Clusters, 500m

Sulfate PM

OC B-ext