Appendix A- New York CitySupplementTrajectory analysis results atQueens College, New York City.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.NYC All Trajectories 00-04, Top 10 ClustersModes defined at: R= 12, 120hr BT,500mstart height, 6488 valid trajectories, 7698 invalidReassign Trajectories Based on72hrBT, 500m start height,10116 Valid TrajectoriesCluster 1 Cluster 2 Cluster 3 Cluster 4 Cluster 5 Frequency Based Cluster Proximity Based ClusterFrequency Based Cluster Frequency Based ClusterFrequency Based ClusterFrequency Based Cluster Frequency Based ClusterProximity Based Cluster Proximity Based ClusterProximity Based ClusterProximity Based Cluster Proximity Based ClusterCentral Trajectory Central TrajectoryCentral TrajectoryCentral Trajectory Central TrajectoryFrequency ProximitySulfate 6.42 3.48BextPM 19.36 10.73OC 3.60 1.97# Trajs 438 775# Trajs w. Poll 85 190Frequency ProximitySulfate 5.87 6.44BextPM 18.30 18.86OC 3.02 3.14# Trajs 4617 1180# Trajs w. Poll 1105 284Frequency ProximitySulfate 3.42 5.86BextPM 13.10 17.27OC 2.30 2.44# Trajs 1638 1134# Trajs w. Poll 339 276Frequency ProximitySulfate 4.41 3.32BextPM 12.98 13.48OC 1.93 3.10# Trajs 851 976# Trajs w. Poll 182 226Frequency ProximitySulfate 2.26 5.63BextPM 9.15 18.32OC 2.42 3.07# Trajs 687 927# Trajs w. Poll 146 230NYC All Trajectories 00-04, Top 10 ClustersModes defined at: R= 12, 120hr BT,500mstart height, 6488 valid trajectories, 7698 invalidReassign Trajectories Based on72hrBT, 500m start height, 10116 Valid TrajectoriesCluster 6 Cluster 7 Cluster 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 Trajectory Central Trajectory Central Trajectory Central Trajectory Central TrajectoryFrequency ProximitySulfate 2.44 2.67BextPM 9.15 10.10OC 1.21 2.21# Trajs 110 812# Trajs w. Poll 17 166Frequency ProximitySulfate 4.53 6.05BextPM 15.47 19.79OC 2.89 3.22# Trajs 317 770# Trajs w. Poll 72 167Frequency ProximitySulfate 4.97 3.95BextPM 18.04 14.50OC 2.56 2.33# Trajs 305 2119# Trajs w. Poll 69 470Frequency ProximitySulfate 2.75 3.46BextPM 12.05 12.63OC 2.73 2.39# Trajs 278 775# Trajs w. Poll 49 150Frequency ProximitySulfate 3.01 7.20BextPM 9.26 20.90OC 1.53 3.26# Trajs 150 658# Trajs w. Poll 37 123NYC All Trajectories 00-04, Top 10 ClustersModes defined at: R= 12, 120hr BT,500mstart height, 6488 valid trajectories, 7698 invalidReassign Trajectories Based on72hrBT, 500m start height, 10116 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 AQS ASPDsamples taken during the 2000-2004 period).Frequency ProximitySulfate 6.44 5.87BextPM 18.86 18.30OC 3.14 3.02# Trajs 1180 4617# Trajs w. Poll 284 1105Frequency ProximitySulfate 3.48 6.42BextPM 10.73 19.36OC 1.97 3.60# Trajs 775 438# Trajs w. Poll 190 85Frequency ProximitySulfate 5.63 2.26BextPM 18.32 9.15OC 3.07 2.42# Trajs 927 687# Trajs w. Poll 230 146Frequency ProximitySulfate 2.67 2.44BextPM 10.10 9.15OC 2.21 1.21# Trajs 812 110# Trajs w. Poll 166 17NYC All Trajectories 00-04, Incremental ProbabilityIP Based on Top10%, 500mSulfate PMNYC All Trajectories 00-04, Cluster Weighted ProbabilityCWP calculated using Proximity Based Clusters, 500mSulfatePMNYC All Trajectories 00-04, Cluster Weighted ProbabilityCalculated using Frequency Based Clusters, 500mSulfate PM