Appendix A- Washington D.C.SupplementTrajectory analysis results atWashington D.C.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 4 Cluster 5Washington All Trajectories 00-04, Top 10 ClustersModes defined at: R=12, 120hr BT,500mStart ht, 7438 Valid Trajectories, 6778 InvalidReassigned Trajectories Based on72hr BT,500m Start Ht, 11020 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 5.02 6.16Bext 93.63 113.55PM 13.95 16.11OC 3.46 4.21# Trajs 545 768# Trajs w. Poll 172 234Frequency ProximitySulfate 6.75 7.94Bext 120.54 134.78PM 17.04 18.88OC 4.12 4.47# Trajs 5229 1297# Trajs w. Poll 1584 374Frequency ProximitySulfate 4.09 5.70Bext 87.13 105.95PM 12.11 15.17OC 3.17 3.82# Trajs 1760 1344# Trajs w. Poll 572 365Frequency ProximitySulfate 5.62 4.26Bext 105.20 87.39PM 16.08 12.06OC 4.62 3.24# Trajs 806 1090# Trajs w. Poll 275 296Frequency ProximitySulfate 3.26 5.28Bext 75.57 100.34PM 10.13 13.76OC 2.62 3.05# Trajs 673 1081# Trajs w. Poll 216 294Cluster 6 Cluster 7 Cluster 8 Cluster 9 Cluster 10Washington All Trajectories 00-04, Top 10 ClustersModes defined at: R=12, 120hr BT,500mStart ht, 7438 Valid Trajectories, 6778 InvalidReassigned Trajectories Based on72hr BT,500m Start Ht, 11020 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 3.82 4.41Bext 72.29 87.88PM 10.13 12.18OC 2.43 3.18# Trajs 423 1958# Trajs w. Poll 106 527Frequency ProximitySulfate 2.90 5.31Bext 58.47 103.23PM 8.60 15.43OC 2.63 3.96# Trajs 140 1223# Trajs w. Poll 48 340Frequency ProximitySulfate 3.48 3.44Bext 74.25 73.24PM 10.39 10.06OC 2.93 2.69# Trajs 287 912# Trajs w. Poll 92 259Frequency ProximitySulfate 5.85 6.43Bext 106.34 117.19PM 16.18 17.74OC 3.93 4.79# Trajs 218 655# Trajs w. Poll 71 214Frequency ProximitySulfate 3.91 5.74Bext 68.44 106.14PM 10.90 15.66OC 2.97 3.87# Trajs 142 702# Trajs w. Poll 36 191Washington All Trajectories 00-04, Top 10 ClustersModes defined at: R=12, 120hr BT,500mStart ht, 7438 Valid Trajectories, 6778 InvalidReassigned Trajectories Based on72hr BT,500m Start Ht, 11020 Valid TrajectoriesBest and Worst DaysHighest Sulfate(Proximate)Lowest Sulfate(Proximate)Frequency ProximitySulfate 5.85 6.43Bext 106.34 117.19PM 16.18 17.74OC 3.93 4.79# Trajs 218 655# Trajs w. Poll 71 214Frequency ProximitySulfate 6.75 7.94Bext 120.54 134.78PM 17.04 18.88OC 4.12 4.47# Trajs 5229 1297# Trajs w. Poll 1584 374Frequency ProximitySulfate 3.48 3.44Bext 74.25 73.24PM 10.39 10.06OC 2.93 2.69# Trajs 287 912# Trajs w. Poll 92 259Frequency ProximitySulfate 5.62 4.26Bext 105.20 87.39PM 16.08 12.06OC 4.62 3.24# Trajs 806 1090# Trajs w. Poll 275 296Sulfate- 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).Washington All Trajectories 00-04, Incremental ProbabilityIP Based on Top10%, 500mSulfate PMOCB-extWashington All Trajectories 00-04, Cluster WeightedProbabilityCalculated using Proximity Based Clusters, 500mSulfate PMOCB-extWashington All Trajectories 00-04, Cluster WeightedProbabilityCalculated using Frequency Based Clusters, 500mSulfate PMOCB-ext