Appendix A- James RiverFace SupplementTrajectory analysis results atJames River Face WildernessArea.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.James River Face All Trajectories 00-04, Top 10 ClustersModes defined at: R= 12, 120hr BT,500mstart height, 8915 valid trajectories, 5456 invalidReassign Trajectories Based on72hrBT, 500m start height,12103 Valid TrajectoriesCluster 1 Cluster 2 Cluster 3 Cluster 4 Cluster 5 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 4.58 5.95Bext 81.17 104.85PM 11.20 15.28OC 2.87 3.79# Trajs 662 1086# Trajs w. Poll 178 288Frequency ProximitySulfate 5.87 6.27Bext 102.71 108.01PM 14.64 15.81OC 3.70 4.17# Trajs 6290 1397# Trajs w. Poll 1805 405Frequency ProximitySulfate 4.06 4.35Bext 73.65 78.57PM 10.27 10.68OC 2.63 2.64# Trajs 1398 1386# Trajs w. Poll 446 439Frequency ProximitySulfate 4.26 4.45Bext 76.57 80.93PM 11.51 11.99OC 3.19 3.29# Trajs 793 1338# Trajs w. Poll 292 459Frequency ProximitySulfate 3.71 5.71Bext 70.53 99.25PM 9.11 13.31OC 2.31 3.17# Trajs 724 1331# Trajs w. Poll 179 339James River Face All Trajectories 00-04, Top 10 ClustersModes defined at: R= 12, 120hr BT,500mstart height, 8915 valid trajectories, 5456 invalidReassign Trajectories Based on72hrBT, 500m start height,12103 Valid TrajectoriesCluster 6 Cluster 7 Cluster 8 Cluster 9 Frequency Based Cluster Proximity Based ClusterFrequency Based Cluster Frequency Based Cluster Frequency Based Cluster Frequency Based ClusterProximity Based Cluster Proximity Based Cluster Proximity Based Cluster Proximity Based ClusterCentral TrajectoryCentral Trajectory Central Trajectory Central TrajectoryFrequency ProximitySulfate 3.45 5.38Bext 67.24 95.14PM 9.41 13.37OC 2.90 3.43# Trajs 156 819# Trajs w. Poll 40 263Frequency ProximitySulfate 2.53 3.46Bext 47.66 64.27PM 6.31 8.80OC 1.61 2.37# Trajs 315 1792# Trajs w. Poll 107 498Frequency ProximitySulfate 4.02 5.06Bext 68.45 87.42PM 10.69 12.92OC 2.94 3.34# Trajs 234 906# Trajs w. Poll 60 252Frequency ProximitySulfate 5.69 5.06Bext 102.07 90.44PM 14.29 12.57OC 3.88 3.18# Trajs 208 1963# Trajs w. Poll 66 545James River Face All Trajectories 00-04, Best/WorstSulfateModes defined at: R= 12, 120hr BT,500mstart height, 8915 valid trajectories, 5456 invalidReassign Trajectories Based on72hrBT, 500m start height,12103 Valid TrajectoriesHighest Sulfate(Proximity)Lowest Sulfate(Proximity)Frequency ProximitySulfate 5.87 6.27Bext 102.71 108.01PM 14.64 15.81OC 3.70 4.17# Trajs 6290 1397# Trajs w. Poll 1805 405Frequency ProximitySulfate 4.58 5.95Bext 81.17 104.85PM 11.20 15.28OC 2.87 3.79# Trajs 662 1086# Trajs w. Poll 178 288Frequency ProximitySulfate 2.53 3.46Bext 47.66 64.27PM 6.31 8.80OC 1.61 2.37# Trajs 315 1792# Trajs w. Poll 107 498Frequency ProximitySulfate 4.06 4.35Bext 73.65 78.57PM 10.27 10.68OC 2.63 2.64# Trajs 1398 1386# Trajs w. Poll 446 439Sulfate- 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).James River Face All Trajectories 00-04, IncrementalProbabilityIP Based on Top10%, 500mSulfate PMOCB-extJames River Face All Trajectories 00-04, Cluster Weighted ProbabilityCWP calculated using Proximity Based Clusters, 500mSulfate PMOCB-extJames River Face All Trajectories 00-04, Cluster Weighted ProbabilityCalculated using Frequency Based Clusters, 500mSulfate PMOCB-ext