Appendix A- James Rive

Face Supplement

Trajectory analysis results at 

James River Face 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. 
James River Face All Trajectories 00-04, Top 10 

Modes defined at: R= 12, 120hr BT, 500m start height, 8915 valid trajectorie

Reassign Trajectories Based on 72hr BT, 500m start height,12103 Valid T

Cluster 1 Cluster 2 Cluster 3 Cluster 4 Clus

Frequency Based Cluster Frequency Based Cluster Frequency Based Cluster Frequency Based Cluster Freque

Proximity Based Cluster Proximity Based Cluster Proximity Based Cluster Proximity Based Cluster Proxim

Central Trajectory Central Trajectory Central Trajectory Central Trajectory Central 

Sulfate Bext PM OC # Trajs # Trajs 

Frequency Proximity

Sulfate 5.87 6.27Bext 102.71 108.01PM 14.64 15.81OC 3.70 4.17# Trajs 6290 1397# Trajs w. Poll 1805 405

Frequency Proximity

Sulfate 4.06 4.35Bext 73.65 78.57PM 10.27 10.68OC 2.63 2.64# Trajs 1398 1386# Trajs w. Poll 446 439

Frequency Proximity

Sulfate 4.26 4.45Bext 76.57 80.93PM 11.51 11.99OC 3.19 3.29# Trajs 793 1338# Trajs w. Poll 292 459

Frequency Proximity

Sulfate 3.71 5.71Bext 70.53 99.25PM 9.11 13.31OC 2.31 3.17# Trajs 724 1331# Trajs w. Poll 179 339
James River Face All Trajectories 00-04, Top 10 

Modes defined at: R= 12, 120hr BT, 500m start height, 8915 valid trajectorie

Reassign Trajectories Based on 72hr BT, 500m start height,12103 Valid T

Cluster 6 Cluster 7 Cluster 8 Cluster 9Frequency Based Cluster Frequency Based Cluster Frequency Based Cluster Frequency Based ClusterProximity Based Cluster Proximity Based Cluster Proximity Based Cluster Proximity Based Cluster

Central Trajectory Central Trajectory Central Trajectory Central Trajectory

Frequency Proximity

Sulfate 3.45 5.38Bext 67.24 95.14PM 9.41 13.37OC 2.90 3.43# Trajs 156 819# Trajs w. Poll 40 263

Frequency Proximity

Sulfate 2.53 3.46Bext 47.66 64.27PM 6.31 8.80OC 1.61 2.37# Trajs 315 1792# Trajs w. Poll 107 498

Frequency Proximity

Sulfate 4.02 5.06Bext 68.45 87.42PM 10.69 12.92OC 2.94 3.34# Trajs 234 906# Trajs w. Poll 60 252

Frequency Proximity

Sulfate 5.69 5.06Bext 102.07 90.44PM 14.29 12.57OC 3.88 3.18# Trajs 208 1963# Trajs w. Poll 66 545
James River Face All Trajectories 00-04, Best/Wor

Modes defined at: R= 12, 120hr BT, 500m start height, 8915 valid trajectorie

Reassign Trajectories Based on 72hr BT, 500m start height,12103 Valid T

Highest Sulfate(Proximity)Lowest Sulfate(Proximity)

Frequency Proximity

Sulfate 5.87 6.27Bext 102.71 108.01PM 14.64 15.81OC 3.70 4.17# Trajs 6290 1397# Trajs w. Poll 1805 405

Frequency Proximity

Sulfate 4.58 5.95Bext 81.17 104.85PM 11.20 15.28OC 2.87 3.79# Trajs 662 1086# Trajs w. Poll 178 288

Frequency Proximity

Sulfate 2.53 3.46Bext 47.66 64.27PM 6.31 8.80OC 1.61 2.37# Trajs 315 1792# Trajs w. Poll 107 498

Frequency Proximity

Sulfate 4.06 4.35Bext 73.65 78.57PM 10.27 10.68OC 2.63 2.64# Trajs 1398 1386# Trajs w. Poll 446 439

Sulfate- Sulfate ion Bext- Extinction (MPM- Particulate MOC- Organic CarbNum Trajs- NumbeclusterNum Trajs w. Poll- in cluster with assomeasurement (Bassamples taken duri
James River Face All Trajectories 00-04, Incremental P

IP Based on Top10%, 500m

Sulfate PM

OC B-ext
James River Face All Trajectories 00-04, Cluster Weighte

CWP calculated using Proximity Based Clusters, 500m

Sulfate PM

OC B-ext
James River Face All Trajectories 00-04, Cluster Weighte

Calculated using Frequency Based Clusters, 500m

Sulfate PM

OC B-ext