Appendix A- Moosehorn

Supplement

Trajectory analysis results at 

Moosehorn National Wildlife 

Refuge.
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. 
Moosehorn All Trajectories 00-04, Top 10 Clu

Modes defined at: R= 12, 120hr BT, 500m start height, 4804 valid trajectori

Reassign Trajectories Based on 72hr BT, 500m start height,7894 Valid 

Cluster 1 Cluster 2 Cluster 3 Cluster 4 Clu

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 Centra

SulfBexPM OC # Tr# Tr

Frequency Proximity

Sulfate 2.47 2.55Bext 51.08 53.59PM 6.87 7.21OC 1.98 2.13# Trajs 3666 1106# Trajs w. Poll 1141 299

Frequency Proximity

Sulfate 1.67 3.30Bext 37.55 64.22PM 5.22 8.29OC 1.79 1.73# Trajs 974 434# Trajs w. Poll 273 109

Frequency Proximity

Sulfate 2.86 1.42Bext 55.21 34.94PM 7.05 4.71OC 1.59 1.69# Trajs 742 1052# Trajs w. Poll 208 313

Frequency Proximity

Sulfate 1.63 2.83Bext 36.00 54.84PM 5.15 7.38OC 1.68 1.95# Trajs 508 1382# Trajs w. Poll 166 332
Moosehorn All Trajectories 00-04, Top 10 Clu

Modes defined at: R= 12, 120hr BT, 500m start height, 4804 valid trajectori

Reassign Trajectories Based on 72hr BT, 500m start height,7894 Valid 

Cluster 6 Cluster 7 Cluster 8 Cluster 9 Clust

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 Tra

Sulfate Bext PM OC # Trajs # Trajs w

Frequency Proximity

Sulfate 2.91 1.85Bext 58.09 40.18PM 7.65 5.59OC 1.90 1.82# Trajs 301 1547# Trajs w. Poll 88 410

Frequency Proximity

Sulfate 1.12 3.68Bext 27.26 68.86PM 3.74 8.95OC 1.48 2.08# Trajs 257 485# Trajs w. Poll 67 167

Frequency Proximity

Sulfate 0.95 3.32Bext 24.11 64.52PM 3.33 8.44OC 1.31 2.18# Trajs 147 781# Trajs w. Poll 28 243

Frequency Proximity

Sulfate 1.94 2.07Bext 43.02 37.93PM 5.98 5.31OC 1.78 1.04# Trajs 120 318# Trajs w. Poll 39 87
Moosehorn All Trajectories 00-04, Top 10 Clu

Modes defined at: R= 12, 120hr BT, 500m start height, 4804 valid trajectori

Reassign Trajectories Based on 72hr BT, 500m start height,7894 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 1.12 3.68Bext 27.26 68.86PM 3.74 8.95OC 1.48 2.08# Trajs 257 485# Trajs w. Poll 67 167

Frequency Proximity

Sulfate 1.26 1.28Bext 26.61 27.63PM 3.70 3.91OC 1.20 1.25# Trajs 378 492# Trajs w. Poll 121 142

Frequency Proximity

Sulfate 2.86 1.42Bext 55.21 34.94PM 7.05 4.71OC 1.59 1.69# Trajs 742 1052# Trajs w. Poll 208 313

Frequency Proximity

Sulfate 0.95 3.32Bext 24.11 64.52PM 3.33 8.44OC 1.31 2.18# Trajs 147 781# Trajs w. Poll 28 243
Moosehorn All Trajectories 00-04, Incremental Prob

IP Based on Top10%, 500m

Sulfate PM

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

Calculated using Proximity Based Clusters, 500m

Sulfate PM

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

Calculated using Frequency Based Clusters, 500m

Sulfate PM

OC B-ext