Appendix A- New York C

Supplement

Trajectory analysis results at 

Queens College, New York City
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. 
NYC All Trajectories 00-04, Top 10 Cluste

Modes defined at: R= 12, 120hr BT, 500m start height, 6488 valid trajectori

Reassign Trajectories Based on 72hr BT, 500m start height,10116 Valid 

Cluster 1 Cluster 2 Cluster 3 Cluster 4 Clus

Frequency Based Cluster Frequency Based Cluster Frequency Based Cluster Frequency Based Cluster Frequ

Proximity Based Cluster Proximity Based Cluster Proximity Based Cluster Proximity Based Cluster ProxCentral Trajectory Central Trajectory Central Trajectory Central Trajectory Central 

SulfatBextPM OC # Traj# Traj

Frequency Proximity

Sulfate 5.87 6.44BextPM 18.30 18.86OC 3.02 3.14# Trajs 4617 1180# Trajs w. Poll 1105 284

Frequency Proximity

Sulfate 3.42 5.86BextPM 13.10 17.27OC 2.30 2.44# Trajs 1638 1134# Trajs w. Poll 339 276

Frequency Proximity

Sulfate 4.41 3.32BextPM 12.98 13.48OC 1.93 3.10# Trajs 851 976# Trajs w. Poll 182 226

Frequency Proximity

Sulfate 2.26 5.63BextPM 9.15 18.32OC 2.42 3.07# Trajs 687 927# Trajs w. Poll 146 230
NYC All Trajectories 00-04, Top 10 Cluste

Modes defined at: R= 12, 120hr BT, 500m start height, 6488 valid trajectori

Reassign Trajectories Based on 72hr BT, 500m start height, 10116 Valid 

Cluster 6 Cluster 7 Cluster 8 Cluster 9 Clus

Frequency Based Cluster Frequency Based Cluster Frequency Based Cluster Frequency Based Cluster Frequ

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

Central Trajectory Central Trajectory Central Trajectory Central Trajectory Centra

SulBexPM OC # T# T

Frequency Proximity

Sulfate 4.53 6.05BextPM 15.47 19.79OC 2.89 3.22# Trajs 317 770# Trajs w. Poll 72 167

Frequency Proximity

Sulfate 4.97 3.95BextPM 18.04 14.50OC 2.56 2.33# Trajs 305 2119# Trajs w. Poll 69 470

Frequency Proximity

Sulfate 2.75 3.46BextPM 12.05 12.63OC 2.73 2.39# Trajs 278 775# Trajs w. Poll 49 150

Frequency Proximity

Sulfate 3.01 7.20BextPM 9.26 20.90OC 1.53 3.26# Trajs 150 658# Trajs w. Poll 37 123
NYC All Trajectories 00-04, Top 10 Cluste

Modes defined at: R= 12, 120hr BT, 500m start height, 6488 valid trajectori

Reassign Trajectories Based on 72hr BT, 500m start height, 10116 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 6.44 5.87BextPM 18.86 18.30OC 3.14 3.02# Trajs 1180 4617# Trajs w. Poll 284 1105

Frequency Proximity

Sulfate 3.48 6.42BextPM 10.73 19.36OC 1.97 3.60# Trajs 775 438# Trajs w. Poll 190 85

Frequency Proximity

Sulfate 5.63 2.26BextPM 18.32 9.15OC 3.07 2.42# Trajs 927 687# Trajs w. Poll 230 146

Frequency Proximity

Sulfate 2.67 2.44BextPM 10.10 9.15OC 2.21 1.21# Trajs 812 110# Trajs w. Poll 166 17
NYC All Trajectories 00-04, Incremental Probab

IP Based on Top10%, 500m

Sulfate PM
NYC All Trajectories 00-04, Cluster Weighted Prob

CWP calculated using Proximity Based Clusters, 500m

Sulfate PM
NYC All Trajectories 00-04, Cluster Weighted Prob

Calculated using Frequency Based Clusters, 500m

Sulfate PM