Appendix A- Shenandoa

Supplement

Trajectory analysis results at 

Shenandoah 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 Clus

Shenandoah All Trajectories 00-04, Top 10 Cl

Modes defined at: R= 12, 120hr BT, 500m start height, 8272 valid trajectori

Reassign Trajectories Based on 72hr BT, 500m start height, 12005 Valid 

Frequency Based Cluster Frequency Based Cluster Frequency Based Cluster Frequency Based Cluster FrequeProximity Based Cluster Proximity Based Cluster Proximity Based Cluster Proximity Based Cluster Proximi

Central Trajectory Central Trajectory Central Trajectory Central Trajectory Central 

Sulfate Bext PM OC # Trajs # Trajs w. P

Frequency Proximity

Sulfate 5.57 5.82Bext 92.97 94.38PM 12.43 12.93OC 2.20 2.28# Trajs 6091 1715# Trajs w. Poll 1569 425

Frequency Proximity

Sulfate 3.78 3.80Bext 65.93 67.79PM 8.79 8.65OC 1.60 1.58# Trajs 1512 1746# Trajs w. Poll 410 480

Frequency Proximity

Sulfate 4.26 4.70Bext 71.64 79.66PM 10.08 10.05OC 2.21 1.67# Trajs 901 1305# Trajs w. Poll 302 344

Frequency Proximity

Sulfate 2.96 4.57Bext 53.12 74.17PM 6.36 10.95OC 1.25 2.44# Trajs 686 979# Trajs w. Poll 144 320
Shenandoah All Trajectories 00-04, Top 10 Cl

Modes defined at: R= 12, 120hr BT, 500m start height, 8272 valid trajectori

Reassign Trajectories Based on 72hr BT, 500m start height, 12005 Valid 

Cluster 6 Cluster 7 Cluster 8 Cluster 9 ClusteFrequency Based Cluster Frequency Based Cluster Frequency Based Cluster Frequency Based Cluster Frequenc

Proximity Based Cluster Proximity Based Cluster Proximity Based Cluster Proximity Based Cluster Proximity 

Central Trajectory Central Trajectory Central Trajectory Central Trajectory Central 

Sulfate Bext PM OC # Trajs # Trajs w. Pol

Frequency Proximity

Sulfate 2.42 5.76Bext 49.41 96.51PM 6.12 13.24OC 1.28 2.41# Trajs 384 996# Trajs w. Poll 128 274

Frequency Proximity

Sulfate 3.88 4.59Bext 59.42 75.51PM 8.49 10.55OC 1.45 2.06# Trajs 325 975# Trajs w. Poll 80 253

Frequency Proximity

Sulfate 4.45 4.90Bext 77.59 86.33PM 10.31 11.11OC 2.13 2.22# Trajs 244 973# Trajs w. Poll 61 263

Frequency Proximity

Sulfate 2.31 2.60Bext 43.76 50.03PM 5.51 6.21OC 1.15 1.37# Trajs 176 751# Trajs w. Poll 44 208
Shenandoah All Trajectories 00-04, Top 10 Cl

Modes defined at: R= 12, 120hr BT, 500m start height, 8272 valid trajectori

Reassign Trajectories Based on 72hr BT, 500m start height, 12005 Valid 

Best and 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 5.57 5.82Bext 92.97 94.38PM 12.43 12.93OC 2.20 2.28# Trajs 6091 1715# Trajs w. Poll 1569 425

Frequency Proximity

Sulfate 3.54 5.57Bext 62.10 93.26PM 8.34 12.73OC 1.75 2.40# Trajs 161 506# Trajs w. Poll 45 121

Frequency Proximity

Sulfate 2.31 2.60Bext 43.76 50.03PM 5.51 6.21OC 1.15 1.37# Trajs 176 751# Trajs w. Poll 44 208

Frequency Proximity

Sulfate 3.78 3.80Bext 65.93 67.79PM 8.79 8.65OC 1.60 1.58# Trajs 1512 1746# Trajs w. Poll 410 480
Shenandoah All Trajectories 00-04, Incremental Prob

IP Based on Top10%, 500m

Sulfate PM

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

Calculated using Proximity Based Clusters, 500m

Sulfate PM

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

Calculated using Frequency Based Clusters, 500m

Sulfate PM

OC B-ext