Appendix A- PittsburghSupplementTrajectory analysis results atPittsburgh, PA.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.Pittsburgh All Trajectories 00-04, Top 10 ClustersModes defined at: R=12, 120hr BT,500mStart ht, 7852 Valid Trajectories, 6394 InvalidReassigned Trajectories Based on72hr BT,500m Start Ht, 11330 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 7.64 8.12PM 20.81 22.32# Trajs 5383 1887# Trajs w. Poll 1187 418Frequency ProximitySulfate 6.80 3.47PM 19.56 12.82# Trajs 560 1538# Trajs w. Poll 107 324Frequency ProximitySulfate 5.19 6.02PM 16.17 18.23# Trajs 1506 761# Trajs w. Poll 331 171Frequency ProximitySulfate 5.71 6.18PM 16.88 17.65# Trajs 1048 1275# Trajs w. Poll 228 237Frequency ProximitySulfate 4.25 4.67PM 13.06 14.49# Trajs 661 1263# Trajs w. Poll 152 307Cluster 6 Cluster 7 Cluster 8 Cluster 9 Cluster 10Pittsburgh All Trajectories 00-04, Top 10 ClustersModes defined at: R=12, 120hr BT,500mStart ht, 7852 Valid Trajectories, 6394 InvalidReassigned Trajectories Based on72hr BT,500m Start Ht, 11330 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 5.08 6.13PM 13.91 19.03# Trajs 179 456# Trajs w. Poll 42 127Frequency ProximitySulfate 2.89 5.95PM 11.30 17.74# Trajs 386 792# Trajs w. Poll 79 212Frequency ProximitySulfate 10.53 7.23PM 26.70 20.13# Trajs 301 2168# Trajs w. Poll 91 482Frequency ProximitySulfate 4.24 5.94PM 14.82 16.56# Trajs 199 631# Trajs w. Poll 51 153Frequency ProximitySulfate 2.78 3.28PM 10.12 12.83# Trajs 186 569# Trajs w. Poll 39 160Pittsburgh All Trajectories 00-04, Top 10 ClustersModes defined at: R=12, 120hr BT,500mStart ht, 7852 Valid Trajectories, 6394 InvalidReassigned Trajectories Based on72hr BT,500m Start Ht, 11330 Valid TrajectoriesHighest 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 AQS ASPDsamples taken during the 2000-2004 period).Frequency ProximitySulfate 7.64 8.12PM 20.81 22.32# Trajs 5383 1887# Trajs w. Poll 1187 418Frequency ProximitySulfate 10.53 7.23PM 26.70 20.13# Trajs 301 2168# Trajs w. Poll 91 482Frequency ProximitySulfate 2.78 3.28PM 10.12 12.83# Trajs 186 569# Trajs w. Poll 39 160Frequency ProximitySulfate 6.80 3.47PM 19.56 12.82# Trajs 560 1538# Trajs w. Poll 107 324Pittsburgh All Trajectories 00-04, Incremental ProbabilityIP Based on Top10%, 500mSulfate PMPittsburgh All Trajectories 00-04, Cluster WeightedProbabilityCalculated using Proximity Based Clusters, 500mSulfate PMPittsburgh All Trajectories 00-04, Cluster WeightedProbabilityCalculated using Frequency Based Clusters, 500mSulfate PM