Appendix A- Great Smok

Mountains Supplement

Trajectory analysis results at 

Great Smokey Mountains Nation

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 Cl

GRSM All Trajectories 00-04, Top 10 Cluster

Modes defined at: R=12, 120hr BT, 500m Start ht, 9827 Valid Trajectories, 45

Reassigned Trajectories Based on 72hr BT, 500m Start Ht, 12557 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

Frequency Proximity

Sulfate 5.45 6.08Bext 101.65 112.58PM 13.62 15.08OC 3.23 3.38# Trajs 7141 1648# Trajs w. Poll 2099 494

Sulfate Bext PM OC # Trajs # Trajs 

Frequency Proximity

Sulfate 4.47 6.37Bext 89.30 113.89PM 10.78 14.14OC 2.58 2.96# Trajs 1330 392# Trajs w. Poll 396 130

Frequency Proximity

Sulfate 4.26 4.17Bext 77.11 78.79PM 10.85 10.96OC 2.44 2.38# Trajs 787 1515# Trajs w. Poll 251 476

Frequency Proximity

Sulfate 4.23 4.95Bext 75.88 93.00PM 10.39 12.19OC 2.33 2.70# Trajs 483 1032# Trajs w. Poll 141 260
Cluster 6 Cluster 7 Cluster 8 Cluster 9 C

GRSM All Trajectories 00-04, Top 10 Cluster

Modes defined at: R=12, 120hr BT, 500m Start ht, 9827 Valid Trajectories, 45

Reassigned Trajectories Based on 72hr BT, 500m Start Ht, 12557 Valid Traj

Frequency Based Cluster Frequency Based Cluster Frequency Based Cluster Frequency Based Cluster F

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

Central Trajectory Central Trajectory Central Trajectory Central Trajectory Ce

Frequency Proximity

Sulfate 3.05 4.71Bext 71.00 89.15PM 8.74 12.70OC 2.41 3.25# Trajs 396 1168# Trajs w. Poll 122 336

SBPO# # 

Frequency Proximity

Sulfate 1.94 2.70Bext 50.52 62.65PM 6.02 7.48OC 1.56 2.14# Trajs 292 2103# Trajs w. Poll 97 648

Frequency Proximity

Sulfate 6.52 4.52Bext 116.58 80.59PM 15.83 11.60OC 3.06 2.85# Trajs 221 944# Trajs w. Poll 61 259

Frequency Proximity

Sulfate 1.78 6.17Bext 54.67 114.09PM 6.13 14.21OC 1.99 3.08# Trajs 144 1448# Trajs w. Poll 42 362
Highest Sulfate

(Proximity)Lowest Sulfate(Proximity)

GRSM All Trajectories 00-04, Best/Worst Sulfa

Modes defined at: R=12, 120hr BT, 500m Start ht, 9827 Valid Trajectories, 45

Reassigned Trajectories Based on 72hr BT, 500m Start Ht, 12557 Valid Traj

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 4.47 6.37Bext 89.30 113.89PM 10.78 14.14OC 2.58 2.96# Trajs 1330 392# Trajs w. Poll 396 130

Frequency Proximity

Sulfate 1.78 6.17Bext 54.67 114.09PM 6.13 14.21OC 1.99 3.08# Trajs 144 1448# Trajs w. Poll 42 362

Frequency Proximity

Sulfate 4.26 4.17Bext 77.11 78.79PM 10.85 10.96OC 2.44 2.38# Trajs 787 1515# Trajs w. Poll 251 476

Frequency Proximity

Sulfate 1.94 2.70Bext 50.52 62.65PM 6.02 7.48OC 1.56 2.14# Trajs 292 2103# Trajs w. Poll 97 648
GRSM All Trajectories 00-04, Incremental Probab

IP Based on Top10%, 500m

Sulfate PM

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

CWP calculated using Proximity Based Clusters, 500m

Sulfate PM

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

Calculated using Frequency Based Clusters, 500m

Sulfate PM

OC B-ext