Appendix A-Great GulfSupplementTrajectory analysis results atGreat Gulf Wilderness Area.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 1Cluster 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 TrajectoryGreat Gulf All Trajectories 00-04, Top 9 ClustersModes defined at: R = 12, 120hr BT,500mStart Height, 6110 Valid, 8271 Invalid TrajectoriesReassigned Trajectories Based on72hrBT, 500m Start Height, 9352 Valid TrajectoriesFrequency ProximitySulfate 3.48 0.97Bext 54.84 21.48PM 8.11 3.23OC 1.77 1.12# Trajs 560 1309# Trajs w. Poll 142 278Frequency ProximitySulfate 2.29 3.04Bext 40.64 51.94PM 6.09 7.45OC 1.66 1.92# Trajs 4514 1195# Trajs w. Poll 1086 290Frequency ProximitySulfate 1.02 3.94Bext 21.03 58.59PM 2.98 8.77OC 0.89 1.86# Trajs 952 712# Trajs w. Poll 240 171Frequency ProximitySulfate 3.71 1.42Bext 64.02 27.76PM 8.69 4.11OC 1.98 1.22# Trajs 871 2011# Trajs w. Poll 206 513Frequency ProximitySulfate 1.44 2.05Bext 26.61 37.60PM 3.62 5.07OC 1.10 1.38# Trajs 734 738# Trajs w. Poll 205 191Great Gulf All Trajectories 00-04, Top 9 ClustersModes defined at: R = 12, 120hr BT,500mStart Height, 6110 Valid, 8271 Invalid TrajectoriesReassigned Trajectories Based on72hrBT, 500m Start Height, 9352 Valid TrajectoriesCluster 6Cluster 9Cluster 8Cluster 7 Frequency Based Cluster Proximity Based ClusterFrequency Based Cluster Frequency Based Cluster Frequency Based Cluster Frequency Based ClusterProximity Based Cluster Proximity Based Cluster Proximity Based Cluster Proximity Based ClusterCentral Trajectory Central Trajectory Central Trajectory Central TrajectoryFrequency ProximitySulfate 1.58 3.11Bext 31.90 48.28PM 4.42 7.49OC 1.45 1.74# Trajs 346 1379# Trajs w. Poll 96 329Frequency ProximitySulfate 1.25 1.39Bext 25.09 28.95PM 3.43 4.33OC 1.11 1.54# Trajs 171 1134# Trajs w. Poll 59 296Frequency ProximitySulfate 2.25 3.40Bext 42.50 58.13PM 5.79 7.75OC 1.50 1.66# Trajs 223 792# Trajs w. Poll 58 207Frequency ProximitySulfate 1.96 3.28Bext 34.98 58.24PM 5.13 7.81OC 1.42 1.97# Trajs 191 419# Trajs w. Poll 42 101Great Gulf All Trajectories 00-04, Top 9 ClustersModes defined at: R = 12, 120hr BT,500mStart Height, 6110 Valid, 8271 Invalid TrajectoriesReassigned Trajectories Based on72hrBT, 500m Start Height, 9352 Valid TrajectoriesBest/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 IMPROVEsamples taken during the 2000-2004 period).Frequency ProximitySulfate 1.02 3.94Bext 21.03 58.59PM 2.98 8.77OC 0.89 1.86# Trajs 952 712# Trajs w. Poll 240 171Frequency ProximitySulfate 2.25 3.40Bext 42.50 58.13PM 5.79 7.75OC 1.50 1.66# Trajs 223 792# Trajs w. Poll 58 207Frequency ProximitySulfate 3.48 0.97Bext 54.84 21.48PM 8.11 3.23OC 1.77 1.12# Trajs 560 1309# Trajs w. Poll 142 278Frequency ProximitySulfate 1.25 1.39Bext 25.09 28.95PM 3.43 4.33OC 1.11 1.54# Trajs 171 1134# Trajs w. Poll 59 296Great Gulf All Trajectories 00-04, Incremental ProbabilityIP Based on Top10%, 500mSulfate PMOCB-extGreat Gulf All Trajectories 00-04, Cluster WeightedProbabilityCalculated using Proximity Based Clusters, 500mSulfate PMOCB-extGreat Gulf All Trajectories 00-04, Cluster WeightedProbabilityCalculated using Frequency Based Clusters, 500mSulfate PMOCB-ext