Appendix A- Lye Brook 

Supplement

Trajectory analysis results at Ly

Brook 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. 
Cluster 1 Cluster 2 Cluster 3 Cluster 4 Clu

Lye Brook All Trajectories 00-04, Top 10 Clust

Modes defined at: R=12, 120hr BT, 500m Start ht, 6282 Valid Trajectories, 80

Reassigned Trajectories Based on 72hr BT, 500m Start Ht, 9859 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 

SuBePO# 

# 

Frequency Proximity

Sulfate 2.47 3.14Bext 46.2 56.48PM 6.26 7.69OC 1.4 1.75# Trajs 4505 896

# Trajs w. Poll 1226 196

Frequency Proximity

Sulfate 4.14 3.67Bext 68.71 66.52PM 9.56 8.79OC 1.76 1.63# Trajs 1229 802

# Trajs w. Poll 355 246

Frequency Proximity

Sulfate 1.79 1.43Bext 35.8 30.80PM 4.82 4.00OC 1.13 0.99# Trajs 986 1623

# Trajs w. Poll 284 358

Frequency Proximity

Sulfate 1.7 1.56Bext 30.48 29.28PM 4.22 4.07OC 0.88 0.91# Trajs 636 929

# Trajs w. Poll 194 254
Lye Brook All Trajectories 00-04, Top 10 Clust

Modes defined at: R=12, 120hr BT, 500m Start ht, 6282 Valid Trajectories, 80

Reassigned Trajectories Based on 72hr BT, 500m Start Ht, 9859 Valid Traj

Cluster 6 Cluster 7 Cluster 8 Cluster 9 Clus

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 Proxim

Central Trajectory Central Trajectory Central Trajectory Central Trajectory Central 

Frequency Proximity

Sulfate 3.58 1.16Bext 62.5 24.77PM 8.73 3.70OC 1.78 1.07# Trajs 360 1592

# Trajs w. Poll 94 361

Frequency Proximity

Sulfate 0.93 3.75Bext 19.79 57.79PM 2.74 7.81OC 0.7 1.07# Trajs 301 500

# Trajs w. Poll 68 131

Frequency Proximity

Sulfate 2.36 2.76Bext 44.72 50.56PM 6.09 6.79OC 1.45 1.37# Trajs 218 656

# Trajs w. Poll 62 193

Frequency Proximity

Sulfate 5.83 3.97Bext 90.51 67.64PM 12.95 9.13OC 2.22 1.73# Trajs 157 586

# Trajs w. Poll 47 192

SBPO# 

# 
Highest Sulfate

(Proximity)Lowest Sulfate(Proximity)

Lye Brook All Trajectories 00-04, Best/Worst Su

Modes defined at: R=12, 120hr BT, 500m Start ht, 6282 Valid Trajectories, 80

Reassigned Trajectories Based on 72hr BT, 500m Start Ht, 9859 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 5.83 3.97Bext 90.51 67.64PM 12.95 9.13OC 2.22 1.73# Trajs 157 586

# Trajs w. Poll 47 192

Frequency Proximity

Sulfate 0.87 4.56Bext 17.41 72.69PM 2.09 10.89OC 0.39 2.27# Trajs 129 492

# Trajs w. Poll 36 130

Frequency Proximity

Sulfate 1.79 1.43Bext 35.8 30.80PM 4.82 4.00OC 1.13 0.99# Trajs 986 1623

# Trajs w. Poll 284 358

Frequency Proximity

Sulfate 3.58 1.16Bext 62.5 24.77PM 8.73 3.70OC 1.78 1.07# Trajs 360 1592

# Trajs w. Poll 94 361
Cluster 1 Cluster 2 Cluster 3 Cluster 4 Clu

Lye Brook All Trajectories 00-04, Top 10 Clust

Modes defined at: R=12, 120hr BT, 1000m Start ht, 6282 Valid Trajectories, 8

Reassigned Trajectories Based on 72hr BT, 500m Start Ht, 9859 Valid Traj

Proximity Based Cluster Statistics Shown

Sulfate= 3.20Bext= 58.59PM =7.60OC = 1.47Num trajs = 633Num Trajs w. Poll = 171

Sulfate= 1.55Bext= 31.60PM =4.52OC = 1.22Num trajs = 2154Num Trajs w. Poll = 538

Sulfate= 3.91Bext= 63.84PM =9.29OC =1.93Num trajs = 796Num Trajs w. Poll = 223

Sulfate= 1.30Bext= 25.92PM =3.62OC = 0.90Num trajs = 1367Num Trajs w. Poll = 384

SulfBexPM OC Num Num 

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
Cluster 6 Cluster 7 Cluster 8 Cluster 9 Clus

Sulfate= 2.07Bext= 41.31PM =5.12OC = 1.03Num trajs = 289Num Trajs w. Poll = 75

Sulfate= 3.92Bext= 68.67PM =9.11OC = 1.72Num trajs = 633Num Trajs w. Poll = 191

Sulfate= 1.74Bext= 35.57PM =4.62OC =1.07Num trajs = 656Num Trajs w. Poll = 192

Sulfate= 3.39Bext= 56.78PM =7.78OC = 1.32Num trajs = 736Num Trajs w. Poll = 200

SulfBexPM OC Num Num 

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 Pro

Central Trajectory Central Trajectory Central Trajectory Central Trajectory Centra

Lye Brook All Trajectories 00-04, Top 10 Clust

Modes defined at: R=12, 120hr BT, 1000m Start ht, 6282 Valid Trajectories, 8

Reassigned Trajectories Based on 72hr BT, 500m Start Ht, 9859 Valid Traj

Proximity Based Cluster Statistics Shown
Highest Sulfate

(Proximity)Lowest Sulfate(Proximity)

Lye Brook All Trajectories 00-04, Best/Worst Su

Modes defined at: R=12, 120hr BT, 1000m Start ht, 6282 Valid Trajectories, 8

Reassigned Trajectories Based on 72hr BT, 500m Start Ht, 9859 Valid Traj

Sulfate= 3.92Bext= 68.67PM =9.11OC = 1.72Num trajs = 633Num Trajs w. Poll = 191

Sulfate= 3.91Bext= 63.84PM =9.29OC =1.93Num trajs = 796Num Trajs w. Poll = 223Sulfate= 1.55Bext= 31.60PM =4.52OC = 1.22Num trajs = 2154Num Trajs w. Poll = 538

Sulfate= 1.30Bext= 25.92PM =3.62OC = 0.90Num trajs = 1367Num Trajs w. Poll = 384

Sulfate- Sulfate ion Bext- Extinction (MPM- Particulate MOC- Organic CarbNum Trajs- NumbeclusterNum Trajs w. Poll- in cluster with assomeasurement (Bassamples taken duri
Cluster 1 Cluster 2 Cluster 3 Cluster 4 Clu

Lye Brook All Trajectories 00-04, Top 10 Clust

Modes defined at: R=12, 120hr BT, 500m(winter)-1000m(summer) Sta

Reassigned Trajectories Based on 72hr BT, 500m Start Ht, 9859 Valid Trajecto

Proximity Based Cluster Statistics Shown

Sulfate= 1.74Bext= 35.04PM =4.65OC = 1.10Num trajs = 1498Num Trajs w. Poll = 422

Sulfate= 3.62Bext= 63.93PM =8.64OC = 1.64Num trajs = 828Num Trajs w. Poll = 223

Sulfate= 2.37Bext= 41.55PM =5.52OC =1.03Num trajs = 969Num Trajs w. Poll = 297

Sulfate= 1.89Bext= 39.62PM =5.19OC = 1.17Num trajs = 1442Num Trajs w. Poll = 363

SulfBexPM OC Num Num 

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
Cluster 6 Cluster 7 Cluster 8 Cluster 9 Clus

Sulfate= 4.44Bext= 70.63PM =10.42OC = 2.12Num trajs = 509Num Trajs w. Poll = 140

Sulfate= 3.91Bext= 67.74PM =9.07OC = 1.63Num trajs = 664Num Trajs w. Poll = 192

Sulfate= 3.58Bext= 59.50PM =8.35OC =1.68Num trajs = 1455Num Trajs w. Poll = 402

Sulfate= 2.34Bext= 42.33PM =5.84OC = 1.17Num trajs = 467Num Trajs w. Poll = 124

SulfBexPM OC Num Num 

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

Lye Brook All Trajectories 00-04, Top 10 Clust

Modes defined at: R=12, 120hr BT, 500m(winter)-1000m(summer) Sta

Reassigned Trajectories Based on 72hr BT, 500m Start Ht, 9859 Valid Trajecto

Proximity Based Cluster Statistics Shown
Lye Brook All Trajectories 00-04, Best/Worst Sul

Modes defined at: R=12, 120hr BT, 500m(winter)-1000m(summer) Sta

Reassigned Trajectories Based on 72hr BT, 500m Start Ht, 9859 Valid Trajecto

Sulfate= 4.44Bext= 70.63PM =10.42OC = 2.12Num trajs = 509Num Trajs w. Poll = 140

Sulfate= 3.91Bext= 67.74PM =9.07OC = 1.63Num trajs = 664Num Trajs w. Poll = 192

Sulfate= 1.74Bext= 35.04PM =4.65OC = 1.10Num trajs = 1498Num Trajs w. Poll = 422

Sulfate= 1.27Bext= 26.64PM =3.97OC = 1.16Num trajs = 1352Num Trajs w. Poll = 329

Sulfate- Sulfate ion Bext- Extinction (MPM- Particulate MOC- Organic CarbNum Trajs- NumbeclusterNum Trajs w. Poll- in cluster with assomeasurement (Bassamples taken duri

Highest Sulfate(Proximity)Lowest Sulfate(Proximity)
Lye Brook All Trajectories 00-04, Incremental Prob

IP Based on Top10%, 500m

Sulfate PM

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

Calculated using Proximity Based Clusters, 500m

Sulfate PM

OC B-ext
Lye Brook All Trajectories 00-04, Cluster Weighted Pr

Calculated using Frequency Based Clusters, 500m

Sulfate PM

OC B-ext
Lye Brook All Trajectories 00-04, Incremental Prob

IP at 500m

Top 5% IP Top 10% IP Top 
Lye Brook All Trajectories 00-04, Incremental Prob

IP at 1000m

Top 5% IP Top 10% IP Top 
Lye Brook Top 20% Sulfate Incremental Proba

1998-2002, Calculated at 500m, 1000m, and an average using the two 

500 meters 1000 meter

Mixed Height Calculation:All Day Weighted Average = (((500m Sept thru May Allday_Prob)*1365)+(1000m Jun thru Aug Allday Prob)*46

High Day Weighted Average = (((500m Sept thru May Hiday_Prob)*1365)+(1000m Jun thru Aug Hiday Prob)*46

IncProb_mixed_ht = High Day Weighted Average – All Day Weighted Average1365 = Number of days Sept – May

460 = Number of days Jun - Aug

Mixed Height