Appendix A- ShenandoahSupplementTrajectory analysis results atShenandoah National Park.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 2Cluster 3 Cluster 4Cluster 5Shenandoah All Trajectories 00-04, Top 10 ClustersModes defined at: R= 12, 120hr BT,500mstart height, 8272 valid trajectories, 5637 invalidReassign Trajectories Based on72hrBT, 500m start height, 12005 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 4.22 4.28Bext 75.53 72.36PM 9.88 9.67OC 1.81 1.66# Trajs 491 2069# Trajs w. Poll 102 542Frequency ProximitySulfate 5.57 5.82Bext 92.97 94.38PM 12.43 12.93OC 2.20 2.28# Trajs 6091 1715# Trajs w. Poll 1569 425Frequency ProximitySulfate 3.78 3.80Bext 65.93 67.79PM 8.79 8.65OC 1.60 1.58# Trajs 1512 1746# Trajs w. Poll 410 480Frequency ProximitySulfate 4.26 4.70Bext 71.64 79.66PM 10.08 10.05OC 2.21 1.67# Trajs 901 1305# Trajs w. Poll 302 344Frequency ProximitySulfate 2.96 4.57Bext 53.12 74.17PM 6.36 10.95OC 1.25 2.44# Trajs 686 979# Trajs w. Poll 144 320Shenandoah All Trajectories 00-04, Top 10 ClustersModes defined at: R= 12, 120hr BT,500mstart height, 8272 valid trajectories, 5637 invalidReassign Trajectories Based on72hrBT, 500m start height, 12005 Valid TrajectoriesCluster 6 Cluster 7Cluster 8 Cluster 9Cluster 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 3.54 5.57Bext 62.10 93.26PM 8.34 12.73OC 1.75 2.40# Trajs 161 506# Trajs w. Poll 45 121Frequency ProximitySulfate 2.42 5.76Bext 49.41 96.51PM 6.12 13.24OC 1.28 2.41# Trajs 384 996# Trajs w. Poll 128 274Frequency ProximitySulfate 3.88 4.59Bext 59.42 75.51PM 8.49 10.55OC 1.45 2.06# Trajs 325 975# Trajs w. Poll 80 253Frequency ProximitySulfate 4.45 4.90Bext 77.59 86.33PM 10.31 11.11OC 2.13 2.22# Trajs 244 973# Trajs w. Poll 61 263Frequency ProximitySulfate 2.31 2.60Bext 43.76 50.03PM 5.51 6.21OC 1.15 1.37# Trajs 176 751# Trajs w. Poll 44 208Shenandoah All Trajectories 00-04, Top 10 ClustersModes defined at: R= 12, 120hr BT,500mstart height, 8272 valid trajectories, 5637 invalidReassign Trajectories Based on72hrBT, 500m start height, 12005 Valid TrajectoriesBest and Worst DaysHighest Sulfate(Proximity)Lowest Sulfate(Proximity)Sulfate- 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 5.57 5.82Bext 92.97 94.38PM 12.43 12.93OC 2.20 2.28# Trajs 6091 1715# Trajs w. Poll 1569 425Frequency ProximitySulfate 3.54 5.57Bext 62.10 93.26PM 8.34 12.73OC 1.75 2.40# Trajs 161 506# Trajs w. Poll 45 121Frequency ProximitySulfate 2.31 2.60Bext 43.76 50.03PM 5.51 6.21OC 1.15 1.37# Trajs 176 751# Trajs w. Poll 44 208Frequency ProximitySulfate 3.78 3.80Bext 65.93 67.79PM 8.79 8.65OC 1.60 1.58# Trajs 1512 1746# Trajs w. Poll 410 480Shenandoah All Trajectories 00-04, Incremental ProbabilityIP Based on Top10%, 500mSulfate PMOCB-extShenandoah All Trajectories 00-04, Cluster WeightedProbabilityCalculated using Proximity Based Clusters, 500mSulfate PMOCB-extShenandoah All Trajectories 00-04, Cluster WeightedProbabilityCalculated using Frequency Based Clusters, 500mSulfate PMOCB-ext