Appendix A- Dolly Sods 

Supplement

Trajectory analysis results at Dol

Sods 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. 
Dolly Sods All Trajectories 00-04, Top 9 Clust

Modes defined at: R = 12, 120hr BT, 500m Start Height,8954 Valid, 5421 Inva

Reassigned Trajectories Based on 72hr BT, 500m Start Height, 12177 Valid 

Cluster 1 Cluster 2 Cluster 3 Cluster 4 C

Frequency Based Cluster Frequency Based Cluster Frequency Based Cluster Frequency Based Cluster FreqProximity Based Cluster Proximity Based Cluster Proximity Based Cluster Proximity Based Cluster Pro

Central Trajectory Central Trajectory Central Trajectory Central Trajectory Cent

Frequency Proximity

Sulfate 5.76 6.21Bext 93.59 100.66PM 12.49 13.65OC 2.37 2.62# Trajs 6263 1820# Trajs w. Poll 1780 505

SuBePM OC # T# T

Frequency Proximity

Sulfate 2.86 5.54Bext 54.24 89.60PM 7.05 12.19OC 2.11 2.48# Trajs 1353 834# Trajs w. Poll 420 220

Frequency Proximity

Sulfate 3.58 4.55Bext 63.26 76.80PM 8.25 10.38OC 1.88 2.14# Trajs 880 1208# Trajs w. Poll 222 376

Frequency Proximity

Sulfate 4.09 4.78Bext 70.99 78.82PM 9.12 10.32OC 2.21 2.05# Trajs 759 1686# Trajs w. Poll 214 425
Dolly Sods All Trajectories 00-04, Top 9 Clus

Modes defined at: R = 12, 120hr BT, 500m Start Height,8954 Valid, 5421 Inva

Reassigned Trajectories Based on 72hr BT, 500m Start Height, 12177 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 Cluster

Central Trajectory Central Trajectory Central Trajectory Central Trajectory

Frequency Proximity

Sulfate 4.54 5.16Bext 76.59 84.18PM 10.11 10.95OC 1.83 1.89# Trajs 286 1008# Trajs w. Poll 91 278

Frequency Proximity

Sulfate 4.41 4.48Bext 72.35 76.78PM 9.86 9.92OC 1.89 2.10# Trajs 199 2584# Trajs w. Poll 58 721

Frequency Proximity

Sulfate 3.23 4.03Bext 55.31 69.20PM 7.02 9.20OC 1.22 2.07# Trajs 226 1053# Trajs w. Poll 56 303

Frequency Proximity

Sulfate 3.55 2.60Bext 68.90 51.45PM 8.76 6.67OC 2.01 2.09# Trajs 220 1272# Trajs w. Poll 80 438
Dolly Sods All Trajectories 00-04, Top 9 Clust

Modes defined at: R = 12, 120hr BT, 500m Start Height,8954 Valid, 5421 Inva

Reassigned Trajectories Based on 72hr BT, 500m Start Height, 12177 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 5.76 6.21Bext 93.59 100.66PM 12.49 13.65OC 2.37 2.62# Trajs 6263 1820# Trajs w. Poll 1780 505

Frequency Proximity

Sulfate 4.13 5.81Bext 71.82 93.76PM 9.51 12.93OC 2.06 2.33# Trajs 753 712# Trajs w. Poll 241 196

Frequency Proximity

Sulfate 3.23 4.03Bext 55.31 69.20PM 7.02 9.20OC 1.22 2.07# Trajs 226 1053# Trajs w. Poll 56 303

Frequency Proximity

Sulfate 3.55 2.60Bext 68.90 51.45PM 8.76 6.67OC 2.01 2.09# Trajs 220 1272# Trajs w. Poll 80 438
Dolly Sods All Trajectories 00-04, Incremental Prob

IP Based on Top10%, 500m

Sulfate PM

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

Calculated using Proximity Based Clusters, 500m

Sulfate PM

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

Calculated using Frequency Based Clusters, 500m

Sulfate PM

OC B-ext