Appendix A- Lye BrookSupplementTrajectory analysis results at LyeBrook Wilderness Area.Equations for Different MetricsEveryday Residence-time Probabilityiestrajectorallfromcellsgridallthroughpassingendpointstotalji,cellgridthroughpassingendpointstotal===NnNnEPijijHigh Day Residence-time Probabilitytoriesday trajechighfromcellsgridallthroughpassingendpointsdayhightotalji,cellgridthroughpassingendpointsdayhightotal===MmMmHPijijIncremental ProbabilityEPHPIP−=Cluster-Weighted Probabilitydays)allon(basedionconcentratpollutantAveragei)clusterwithassociatednsobservatioon(basedionconcentratpollutantAverage)(calculatedclustersofnumbertotal)(11===⋅−⋅=∑=CCLEPCRPCCCWPiiLiiDescription of Figures• Central Trajectory (CT)- Trajectory with the largest number of nearest neighbors inthe dataset.• Frequency Based Clusters- These clusters are formedby finding the “central”trajectory which has the greatest number of neighboring trajectories within asubjectively selected radius of proximity (R). These trajectories are then removedfrom the dataset and the process is applied to theremaining trajectories.• Proximity Based Clusters- Clustering relies on thefrequency-based cluster groups,but forms trajectory groups based on proximity rather than frequency. In the firststep, the frequency-based approach is used to identify the central trajectories thatrepresent the most populated frequency-based clusters (approximately 10 clusterstypically contain at least 98% of the trajectoriesin the dataset using R=12 and 120hour back-trajectory (BT) time). These 10 centraltrajectories are then used todevelop 10 proximity-based clusters by assigning every trajectory in the dataset toits nearest central trajectories (calculated back to 72 hours).• Incremental Probability- Difference between the everyday probability (probabilityderived from all the trajectories in the dataset) and high day probability (probabilityderived from trajectories arriving at the site on the subset of high pollution days).• Cluster Weighted Probability- Each PATH-derived cluster’s residence-timeprobability is weighted by the average sulfate (orother pollutant) value for anymeasurements corresponding to a trajectory which isa member of that cluster.The weighted residence-time probability is summed overallclusters calculated fora site. The everyday probability is subtracted from the sum of cluster-weightedprobabilities to identify areas of increased (or inthe case of negative values,decreased) probability of being associated with a meteorological pathway forpollutant transport.Cluster 1 Cluster 2 Cluster 3 Cluster 4Cluster 5Lye Brook All Trajectories 00-04, Top 10 ClustersModes defined at: R=12, 120hr BT,500mStart ht, 6282 Valid Trajectories, 8041 InvalidReassigned Trajectories Based on72hr BT,500m Start Ht, 9859 Valid Trajectories Frequency Based Cluster Proximity Based ClusterFrequency Based Cluster Frequency Based Cluster Frequency Based Cluster Frequency Based Cluster FrequencyBased ClusterProximity Based Cluster Proximity Based Cluster Proximity Based Cluster Proximity Based Cluster ProximityBased ClusterCentral TrajectoryCentral Trajectory Central Trajectory Central Trajectory Central TrajectoryFrequency ProximitySulfate 2.07 2.87Bext 36.91 50.45PM 5.57 7.08OC 1.43 1.55# Trajs 427 1775# Trajs w. Poll115 478Frequency ProximitySulfate 2.47 3.14Bext 46.2 56.48PM 6.26 7.69OC 1.4 1.75# Trajs 4505 896# Trajs w. Poll1226 196Frequency ProximitySulfate 4.14 3.67Bext 68.71 66.52PM 9.56 8.79OC 1.76 1.63# Trajs 1229 802# Trajs w. Poll355 246Frequency ProximitySulfate 1.79 1.43Bext 35.8 30.80PM 4.82 4.00OC 1.13 0.99# Trajs 986 1623# Trajs w. Poll284 358Frequency ProximitySulfate 1.7 1.56Bext 30.48 29.28PM 4.22 4.07OC 0.88 0.91# Trajs 636 929# Trajs w. Poll194 254Lye Brook All Trajectories 00-04, Top 10 ClustersModes defined at: R=12, 120hr BT,500mStart ht, 6282 Valid Trajectories, 8041 InvalidReassigned Trajectories Based on72hr BT,500m Start Ht, 9859 Valid TrajectoriesCluster 6 Cluster 7Cluster 8 Cluster 9 Cluster 10 Frequency Based Cluster Proximity Based ClusterFrequency Based Cluster Frequency Based Cluster Frequency Based Cluster Frequency Based Cluster FrequencyBased ClusterProximity Based Cluster Proximity Based Cluster Proximity Based Cluster Proximity Based Cluster ProximityBased ClusterCentral TrajectoryCentral Trajectory Central Trajectory Central Trajectory Central TrajectoryFrequency ProximitySulfate 3.58 1.16Bext 62.5 24.77PM 8.73 3.70OC 1.78 1.07# Trajs 360 1592# Trajs w. Poll94 361Frequency ProximitySulfate 0.93 3.75Bext 19.79 57.79PM 2.74 7.81OC 0.7 1.07# Trajs 301 500# Trajs w. Poll68 131Frequency ProximitySulfate 2.36 2.76Bext 44.72 50.56PM 6.09 6.79OC 1.45 1.37# Trajs 218 656# Trajs w. Poll62 193Frequency ProximitySulfate 5.83 3.97Bext 90.51 67.64PM 12.95 9.13OC 2.22 1.73# Trajs 157 586# Trajs w. Poll47 192Frequency ProximitySulfate 0.87 4.56Bext 17.41 72.69PM 2.09 10.89OC 0.39 2.27# Trajs 129 492# Trajs w. Poll36 130Highest Sulfate(Proximity)Lowest Sulfate(Proximity)Lye Brook All Trajectories 00-04, Best/Worst SulfateModes defined at: R=12, 120hr BT,500mStart ht, 6282 Valid Trajectories, 8041 InvalidReassigned Trajectories Based on72hr BT,500m Start Ht, 9859 Valid TrajectoriesSulfate- Sulfate ion Conc. (ug/m3)Bext- Extinction (Mm-1)PM- Particulate Matter Conc. (ug/m3)OC- Organic Carbon Conc. (ug/m3)Num Trajs- Number of trajectories inclusterNum Trajs w. Poll- Number of trajectoriesin cluster with associated pollutionmeasurement (Based on number of IMPROVEsamples taken during the 2000-2004 period).Frequency ProximitySulfate 5.83 3.97Bext 90.51 67.64PM 12.95 9.13OC 2.22 1.73# Trajs 157 586# Trajs w. Poll47 192Frequency ProximitySulfate 0.87 4.56Bext 17.41 72.69PM 2.09 10.89OC 0.39 2.27# Trajs 129 492# Trajs w. Poll36 130Frequency ProximitySulfate 1.79 1.43Bext 35.8 30.80PM 4.82 4.00OC 1.13 0.99# Trajs 986 1623# Trajs w. Poll284 358Frequency ProximitySulfate 3.58 1.16Bext 62.5 24.77PM 8.73 3.70OC 1.78 1.07# Trajs 360 1592# Trajs w. Poll94 361Cluster 1 Cluster 2 Cluster 3 Cluster 4 Cluster 5Lye Brook All Trajectories 00-04, Top 10 ClustersModes defined at: R=12, 120hr BT,1000mStart ht, 6282 Valid Trajectories, 8041 InvalidReassigned Trajectories Based on72hr BT,500m Start Ht, 9859 Valid TrajectoriesProximity Based Cluster Statistics ShownSulfate= 3.20Bext= 58.59PM =7.60OC = 1.47Num trajs = 633Num Trajs w. Poll = 171Sulfate= 1.55Bext= 31.60PM =4.52OC = 1.22Num trajs = 2154Num Trajs w. Poll = 538Sulfate= 3.91Bext= 63.84PM =9.29OC =1.93Num trajs = 796Num Trajs w. Poll = 223Sulfate= 1.30Bext= 25.92PM =3.62OC = 0.90Num trajs = 1367Num Trajs w. Poll = 384Sulfate= 3.70Bext= 61.83PM =8.67OC = 1.73Num trajs = 1722Num Trajs w. Poll = 469 Frequency Based Cluster Proximity Based ClusterFrequency Based Cluster Frequency Based Cluster Frequency Based Cluster Frequency Based Cluster FrequencyBased ClusterProximity Based Cluster Proximity Based Cluster Proximity Based Cluster Proximity Based Cluster ProximityBased ClusterCentral TrajectoryCentral Trajectory Central Trajectory Central Trajectory Central TrajectoryCluster 6 Cluster 7 Cluster 8 Cluster 9 Cluster 10Sulfate= 2.07Bext= 41.31PM =5.12OC = 1.03Num trajs = 289Num Trajs w. Poll = 75Sulfate= 3.92Bext= 68.67PM =9.11OC = 1.72Num trajs = 633Num Trajs w. Poll = 191Sulfate= 1.74Bext= 35.57PM =4.62OC =1.07Num trajs = 656Num Trajs w. Poll = 192Sulfate= 3.39Bext= 56.78PM =7.78OC = 1.32Num trajs = 736Num Trajs w. Poll = 200Sulfate= 2.40Bext= 45.28PM =5.90OC = 1.17Num trajs = 663Num Trajs w. Poll = 167 Frequency Based Cluster Proximity Based ClusterFrequency Based Cluster Frequency Based Cluster Frequency Based Cluster Frequency Based Cluster FrequencyBased ClusterProximity Based Cluster Proximity Based Cluster Proximity Based Cluster Proximity Based Cluster ProximityBased ClusterCentral TrajectoryCentral Trajectory Central Trajectory Central Trajectory Central TrajectoryLye Brook All Trajectories 00-04, Top 10 ClustersModes defined at: R=12, 120hr BT,1000mStart ht, 6282 Valid Trajectories, 8041 InvalidReassigned Trajectories Based on72hr BT,500m Start Ht, 9859 Valid TrajectoriesProximity Based Cluster Statistics ShownHighest Sulfate(Proximity)Lowest Sulfate(Proximity)Lye Brook All Trajectories 00-04, Best/Worst SulfateModes defined at: R=12, 120hr BT,1000mStart ht, 6282 Valid Trajectories, 8041 InvalidReassigned Trajectories Based on72hr BT,500m Start Ht, 9859 Valid TrajectoriesSulfate= 3.92Bext= 68.67PM =9.11OC = 1.72Num trajs = 633Num Trajs w. Poll = 191Sulfate= 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 = 538Sulfate= 1.30Bext= 25.92PM =3.62OC = 0.90Num trajs = 1367Num Trajs w. Poll = 384Sulfate- Sulfate ion Conc. (ug/m3)Bext- Extinction (Mm-1)PM- Particulate Matter Conc. (ug/m3)OC- Organic Carbon Conc. (ug/m3)Num Trajs- Number of trajectories inclusterNum Trajs w. Poll- Number of trajectoriesin cluster with associated pollutionmeasurement (Based on number of IMPROVEsamples taken during the 2000-2004 period).Cluster 1 Cluster 2 Cluster 3 Cluster 4 Cluster 5Lye Brook All Trajectories 00-04, Top 10 ClustersModes defined at: R=12, 120hr BT,500m(winter)-1000m(summer)Start htReassigned Trajectories Based on72hr BT,500m Start Ht, 9859 Valid Trajectories10 BinsProximity Based Cluster Statistics ShownSulfate= 1.74Bext= 35.04PM =4.65OC = 1.10Num trajs = 1498Num Trajs w. Poll = 422Sulfate= 3.62Bext= 63.93PM =8.64OC = 1.64Num trajs = 828Num Trajs w. Poll = 223Sulfate= 2.37Bext= 41.55PM =5.52OC =1.03Num trajs = 969Num Trajs w. Poll = 297Sulfate= 1.89Bext= 39.62PM =5.19OC = 1.17Num trajs = 1442Num Trajs w. Poll = 363Sulfate= 1.27Bext= 26.64PM =3.97OC = 1.16Num trajs = 1352Num Trajs w. Poll = 329 Frequency Based Cluster Proximity Based ClusterFrequency Based Cluster Frequency Based Cluster Frequency Based Cluster Frequency Based Cluster FrequencyBased ClusterProximity Based Cluster Proximity Based Cluster Proximity Based Cluster Proximity Based Cluster ProximityBased ClusterCentral TrajectoryCentral Trajectory Central Trajectory Central Trajectory Central TrajectoryCluster 6 Cluster 7 Cluster 8 Cluster 9 Cluster 10Sulfate= 4.44Bext= 70.63PM =10.42OC = 2.12Num trajs = 509Num Trajs w. Poll = 140Sulfate= 3.91Bext= 67.74PM =9.07OC = 1.63Num trajs = 664Num Trajs w. Poll = 192Sulfate= 3.58Bext= 59.50PM =8.35OC =1.68Num trajs = 1455Num Trajs w. Poll = 402Sulfate= 2.34Bext= 42.33PM =5.84OC = 1.17Num trajs = 467Num Trajs w. Poll = 124Sulfate= 2.52Bext= 45.99PM =6.60OC = 1.52Num trajs = 465Num Trajs w. Poll = 128 Frequency Based Cluster Proximity Based ClusterFrequency Based Cluster Frequency Based Cluster Frequency Based Cluster Frequency Based Cluster FrequencyBased ClusterProximity Based Cluster Proximity Based Cluster Proximity Based Cluster Proximity Based Cluster ProximityBased ClusterCentral TrajectoryCentral Trajectory Central Trajectory Central Trajectory Central TrajectoryLye Brook All Trajectories 00-04, Top 10 ClustersModes defined at: R=12, 120hr BT,500m(winter)-1000m(summer)Start htReassigned Trajectories Based on72hr BT,500m Start Ht, 9859 Valid Trajectories10 BinsProximity Based Cluster Statistics ShownLye Brook All Trajectories 00-04, Best/Worst SulfateModes defined at: R=12, 120hr BT,500m(winter)-1000m(summer)Start htReassigned Trajectories Based on72hr BT,500m Start Ht, 9859 Valid Trajectories10 BinsSulfate= 4.44Bext= 70.63PM =10.42OC = 2.12Num trajs = 509Num Trajs w. Poll = 140Sulfate= 3.91Bext= 67.74PM =9.07OC = 1.63Num trajs = 664Num Trajs w. Poll = 192Sulfate= 1.74Bext= 35.04PM =4.65OC = 1.10Num trajs = 1498Num Trajs w. Poll = 422Sulfate= 1.27Bext= 26.64PM =3.97OC = 1.16Num trajs = 1352Num Trajs w. Poll = 329Sulfate- Sulfate ion Conc. (ug/m3)Bext- Extinction (Mm-1)PM- Particulate Matter Conc. (ug/m3)OC- Organic Carbon Conc. (ug/m3)Num Trajs- Number of trajectories inclusterNum Trajs w. Poll- Number of trajectoriesin cluster with associated pollutionmeasurement (Based on number of IMPROVEsamples taken during the 2000-2004 period).Highest Sulfate(Proximity)Lowest Sulfate(Proximity)Lye Brook All Trajectories 00-04, Incremental ProbabilityIP Based on Top10%, 500mSulfate PMOCB-extLye Brook All Trajectories 00-04, Cluster WeightedProbabilityCalculated using Proximity Based Clusters, 500mSulfate PMOCB-extLye Brook All Trajectories 00-04, Cluster WeightedProbabilityCalculated using Frequency Based Clusters, 500mSulfate PMOCB-extLye Brook All Trajectories 00-04, Incremental ProbabilityIP at 500mTop 5% IP Top 10% IP Top 20% IPLye Brook All Trajectories 00-04, Incremental ProbabilityIP at 1000mTop 5% IP Top 10% IP Top 20% IPLye Brook Top 20% Sulfate Incremental Probability1998-2002, Calculated at 500m, 1000m, and an average using the two heights500 meters1000 metersMixed Height Calculation:All Day Weighted Average = (((500m Sept thru May Allday_Prob)*1365)+(1000m Jun thru Aug Allday Prob)*460)))/(1365+460)High Day Weighted Average = (((500m Sept thru May Hiday_Prob)*1365)+(1000m Jun thru Aug Hiday Prob)*460)))/(1365+460)IncProb_mixed_ht = High Day Weighted Average – All Day Weighted Average1365 = Number of days Sept – May460 = Number of days Jun-AugMixed Height