Appendix A- BrigantineSupplementTrajectory analysis results atBrigantine 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 2 Cluster 3 Cluster 4 Cluster 5Brigantine All Trajectories 00-04, Top 10 ClustersModes defined at: R=12, 120hr BT,500mStart ht, 6934 Valid Trajectories, 7374 InvalidReassigned Trajectories Based on72hr BT,500m Start Ht, 10514 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 6.04 6.18Bext 100.96 101.29PM 13.55 13.85OC 2.94 2.97# Trajs 4865 1019# Trajs w. Poll 1386 272Frequency ProximitySulfate 5.83 6.43Bext 103.11 105.64PM 14.33 14.64OC 3.02 2.93# Trajs 432 801# Trajs w. Poll 128 222Frequency ProximitySulfate 3.97 5.55Bext 80.55 97.42PM 10.48 13.65OC 2.33 2.68# Trajs 1667 1056# Trajs w. Poll 451 291Frequency ProximitySulfate 3.86 3.79Bext 71.94 74.00PM 10.12 9.67OC 1.68 2.29# Trajs 915 1748# Trajs w. Poll 240 510Frequency ProximitySulfate 2.14 3.48Bext 46.86 67.02PM 6.49 8.53OC 1.72 1.83# Trajs 640 815# Trajs w. Poll 195 249Cluster 6 Cluster 7 Cluster 8 Cluster 9 Cluster 10Brigantine All Trajectories 00-04, Top 10 ClustersModes defined at: R=12, 120hr BT,500mStart ht, 6934 Valid Trajectories, 7374 InvalidReassigned Trajectories Based on72hr BT,500m Start Ht, 10514 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 3.48 6.79Bext 67.72 111.17PM 8.64 15.06OC 1.63 3.70# Trajs 405 925# Trajs w. Poll 100 259Frequency ProximitySulfate 2.12 4.46Bext 40.84 84.54PM 6.20 11.15OC 1.69 2.43# Trajs 128 1919# Trajs w. Poll 23 513Frequency ProximitySulfate 4.88 3.31Bext 89.86 61.73PM 11.65 8.39OC 2.42 1.15# Trajs 363 588# Trajs w. Poll 107 142Frequency ProximitySulfate 2.74 2.24Bext 63.07 48.68PM 7.95 6.72OC 1.87 1.91# Trajs 261 886# Trajs w. Poll 80 215Frequency ProximitySulfate 3.89 5.53Bext 65.80 98.54PM 8.54 13.18OC 1.44 2.48# Trajs 129 773# Trajs w. Poll 30 198Brigantine All Trajectories 00-04, Best/Worst SulfateModes defined at: R=12, 120hr BT,500mStart ht, 6934 Valid Trajectories, 7374 InvalidReassigned Trajectories Based on72hr BT,500m Start Ht, 10514 Valid TrajectoriesHighest SulfateLowest SulfateSulfate- 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 5.83 6.43Bext 103.11 105.64PM 14.33 14.64OC 3.02 2.93# Trajs 432 801# Trajs w. Poll 128 222Frequency ProximitySulfate 3.48 6.79Bext 67.72 111.17PM 8.64 15.06OC 1.63 3.70# Trajs 405 925# Trajs w. Poll 100 259Frequency ProximitySulfate 4.88 3.31Bext 89.86 61.73PM 11.65 8.39OC 2.42 1.15# Trajs 363 588# Trajs w. Poll 107 142Frequency ProximitySulfate 2.74 2.24Bext 63.07 48.68PM 7.95 6.72OC 1.87 1.91# Trajs 261 886# Trajs w. Poll 80 215Brigantine All Trajectories 00-04, Incremental ProbabilityIP Based on Top10%, 500mSulfate PMOCB-extBrigantine All Trajectories 00-04, Cluster WeightedProbabilityCalculated using Proximity Based Clusters, 500mSulfate PMOCB-extBrigantine All Trajectories 00-04, Cluster WeightedProbabilityCalculated using Frequency Based Clusters, 500mSulfate PMOCB-ext