Appendix A- Great SmokeyMountains SupplementTrajectory analysis results atGreat Smokey Mountains NationalPark.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 5GRSM All Trajectories 00-04, Top 10 ClustersModes defined at: R=12, 120hr BT,500mStart ht, 9827 Valid Trajectories, 4552 InvalidReassigned Trajectories Based on72hr BT,500m Start Ht, 12557 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 5.45 6.08Bext 101.65 112.58PM 13.62 15.08OC 3.23 3.38# Trajs 7141 1648# Trajs w. Poll 2099 494Frequency ProximitySulfate 3.25 4.28Bext 70.48 91.09PM 8.00 11.78OC 2.59 3.22# Trajs 427 1239# Trajs w. Poll 97 367Frequency ProximitySulfate 4.47 6.37Bext 89.30 113.89PM 10.78 14.14OC 2.58 2.96# Trajs 1330 392# Trajs w. Poll 396 130Frequency ProximitySulfate 4.26 4.17Bext 77.11 78.79PM 10.85 10.96OC 2.44 2.38# Trajs 787 1515# Trajs w. Poll 251 476Frequency ProximitySulfate 4.23 4.95Bext 75.88 93.00PM 10.39 12.19OC 2.33 2.70# Trajs 483 1032# Trajs w. Poll 141 260Cluster 6 Cluster 7 Cluster 8 Cluster 9 Cluster 10GRSM All Trajectories 00-04, Top 10 ClustersModes defined at: R=12, 120hr BT,500mStart ht, 9827 Valid Trajectories, 4552 InvalidReassigned Trajectories Based on72hr BT,500m Start Ht, 12557 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 3.05 4.71Bext 71.00 89.15PM 8.74 12.70OC 2.41 3.25# Trajs 396 1168# Trajs w. Poll 122 336Frequency ProximitySulfate 4.00 4.55Bext 70.34 81.73PM 9.69 10.64OC 2.21 2.21# Trajs 130 841# Trajs w. Poll 27 267Frequency ProximitySulfate 1.94 2.70Bext 50.52 62.65PM 6.02 7.48OC 1.56 2.14# Trajs 292 2103# Trajs w. Poll 97 648Frequency ProximitySulfate 6.52 4.52Bext 116.58 80.59PM 15.83 11.60OC 3.06 2.85# Trajs 221 944# Trajs w. Poll 61 259Frequency ProximitySulfate 1.78 6.17Bext 54.67 114.09PM 6.13 14.21OC 1.99 3.08# Trajs 144 1448# Trajs w. Poll 42 362Highest Sulfate(Proximity)Lowest Sulfate(Proximity)GRSM All Trajectories 00-04, Best/Worst SulfateModes defined at: R=12, 120hr BT,500mStart ht, 9827 Valid Trajectories, 4552 InvalidReassigned Trajectories Based on72hr BT,500m Start Ht, 12557 Valid TrajectoriesSulfate- 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 4.47 6.37Bext 89.30 113.89PM 10.78 14.14OC 2.58 2.96# Trajs 1330 392# Trajs w. Poll 396 130Frequency ProximitySulfate 1.78 6.17Bext 54.67 114.09PM 6.13 14.21OC 1.99 3.08# Trajs 144 1448# Trajs w. Poll 42 362Frequency ProximitySulfate 4.26 4.17Bext 77.11 78.79PM 10.85 10.96OC 2.44 2.38# Trajs 787 1515# Trajs w. Poll 251 476Frequency ProximitySulfate 1.94 2.70Bext 50.52 62.65PM 6.02 7.48OC 1.56 2.14# Trajs 292 2103# Trajs w. Poll 97 648GRSM All Trajectories 00-04, Incremental ProbabilityIP Based on Top10%, 500mSulfate PMOCB-extGRSM All Trajectories 00-04, Cluster Weighted ProbabilityCWP calculated using Proximity Based Clusters, 500mSulfate PMOCB-extGRSM All Trajectories 00-04, Cluster Weighted ProbabilityCalculated using Frequency Based Clusters, 500mSulfate PMOCB-ext