Appendix A- Mohawk 

Mountain Supplement

Trajectory analysis results at 

Mohawk Mountain.
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

Mohawk Mt All Trajectories 00-04, Top 9 Clust

Modes defined at: R=12, 120hr BT, 500m Start ht, 6456 Valid Trajectories, 77

Reassigned Trajectories Based on 72hr BT, 500m Start Ht, 10161 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 Central 

Frequency Proximity

Sulfate 4.00 4.25Bext 74.59 77.74PM 9.83 10.12OC 2.85 3.03# Trajs 4562 1286# Trajs w. Poll 931 293

Frequency Proximity

Sulfate 1.62 5.10Bext 35.40 91.95PM 4.55 11.78OC 1.41 3.19# Trajs 1318 917# Trajs w. Poll 254 205

Frequency Proximity

Sulfate 4.85 2.01Bext 89.55 41.43PM 10.99 5.35OC 2.87 1.50# Trajs 925 1130# Trajs w. Poll 196 200

SulfBext PM OC # Tr# Tr

Frequency Proximity

Sulfate 1.75 2.65Bext 36.74 49.81PM 5.12 6.45OC 1.66 1.73# Trajs 812 698# Trajs w. Poll 168 141
Cluster 6 Cluster 7 Cluster 8 Cluster 9

Mohawk Mt All Trajectories 00-04, Top 9 Clust

Modes defined at: R=12, 120hr BT, 500m Start ht, 6456 Valid Trajectories, 77

Reassigned Trajectories Based on 72hr BT, 500m Start Ht, 10161 Valid Traj

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 

Sulfate 2.34 Bext 45.33 PM 5.49 OC 1.63 # Trajs 188 # Trajs w. Poll 37 

Frequency Proximity

Sulfate 1.96 1.53Bext 38.83 40.71PM 5.53 6.44OC 1.62 2.95# Trajs 301 1141# Trajs w. Poll 41 239

Frequency Proximity

Sulfate 2.38 4.62Bext 47.70 83.40PM 6.37 10.99OC 1.69 2.80# Trajs 270 1061# Trajs w. Poll 48 217

Frequency Proximity

Sulfate 2.51 2.26Bext 49.09 47.14PM 6.52 6.32OC 1.60 1.87# Trajs 253 2161# Trajs w. Poll 58 369
Mohawk Mt All Trajectories 00-04, Best/Worst Su

Modes defined at: R=12, 120hr BT, 500m Start ht, 6456 Valid Trajectories, 77

Reassigned Trajectories Based on 72hr BT, 500m Start Ht, 10161 Valid Traj

Highest Sulfate

Lowest Sulfate

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 1.62 5.10Bext 35.40 91.95PM 4.55 11.78OC 1.41 3.19# Trajs 1318 917# Trajs w. Poll 254 205

Frequency Proximity

Sulfate 5.04 4.84Bext 89.33 83.57PM 12.38 10.98OC 3.31 2.58# Trajs 641 1135# Trajs w. Poll 110 220

Frequency Proximity

Sulfate 4.85 2.01Bext 89.55 41.43PM 10.99 5.35OC 2.87 1.50# Trajs 925 1130# Trajs w. Poll 196 200

Frequency Proximity

Sulfate 1.96 1.53Bext 38.83 40.71PM 5.53 6.44OC 1.62 2.95# Trajs 301 1141# Trajs w. Poll 41 239
Mohawk Mt All Trajectories 00-04, Incremental Prob

IP Based on Top10%, 500m

Sulfate PM

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

Calculated using Proximity Based Clusters, 500m

Sulfate PM

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

Calculated using Frequency Based Clusters. 500m

Sulfate PM

OC B-ext