Appendix A- Dolly SodsSupplementTrajectory analysis results at DollySods 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.Dolly Sods All Trajectories 00-04, Top 9 ClustersModes defined at: R = 12, 120hr BT,500mStart Height,8954 Valid, 5421 Invalid TrajectoriesReassigned Trajectories Based on72hrBT, 500m Start Height, 12177 Valid TrajectoriesCluster 1 Cluster 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 TrajectoryFrequency ProximitySulfate 5.76 6.21Bext 93.59 100.66PM 12.49 13.65OC 2.37 2.62# Trajs 6263 1820# Trajs w. Poll 1780 505Frequency ProximitySulfate 4.13 5.81Bext 71.82 93.76PM 9.51 12.93OC 2.06 2.33# Trajs 753 712# Trajs w. Poll 241 196Frequency ProximitySulfate 2.86 5.54Bext 54.24 89.60PM 7.05 12.19OC 2.11 2.48# Trajs 1353 834# Trajs w. Poll 420 220Frequency ProximitySulfate 3.58 4.55Bext 63.26 76.80PM 8.25 10.38OC 1.88 2.14# Trajs 880 1208# Trajs w. Poll 222 376Frequency ProximitySulfate 4.09 4.78Bext 70.99 78.82PM 9.12 10.32OC 2.21 2.05# Trajs 759 1686# Trajs w. Poll 214 425Dolly Sods All Trajectories 00-04, Top 9 ClustersModes defined at: R = 12, 120hr BT,500mStart Height,8954 Valid, 5421 Invalid TrajectoriesReassigned Trajectories Based on72hrBT, 500m Start Height, 12177 Valid TrajectoriesCluster 6 Cluster 7 Cluster 8 Cluster 9 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 TrajectoryCentral Trajectory Central Trajectory Central TrajectoryFrequency ProximitySulfate 4.54 5.16Bext 76.59 84.18PM 10.11 10.95OC 1.83 1.89# Trajs 286 1008# Trajs w. Poll 91 278Frequency ProximitySulfate 4.41 4.48Bext 72.35 76.78PM 9.86 9.92OC 1.89 2.10# Trajs 199 2584# Trajs w. Poll 58 721Frequency ProximitySulfate 3.23 4.03Bext 55.31 69.20PM 7.02 9.20OC 1.22 2.07# Trajs 226 1053# Trajs w. Poll 56 303Frequency ProximitySulfate 3.55 2.60Bext 68.90 51.45PM 8.76 6.67OC 2.01 2.09# Trajs 220 1272# Trajs w. Poll 80 438Dolly Sods All Trajectories 00-04, Top 9 ClustersModes defined at: R = 12, 120hr BT,500mStart Height,8954 Valid, 5421 Invalid TrajectoriesReassigned Trajectories Based on72hrBT, 500m Start Height, 12177 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 5.76 6.21Bext 93.59 100.66PM 12.49 13.65OC 2.37 2.62# Trajs 6263 1820# Trajs w. Poll 1780 505Frequency ProximitySulfate 4.13 5.81Bext 71.82 93.76PM 9.51 12.93OC 2.06 2.33# Trajs 753 712# Trajs w. Poll 241 196Frequency ProximitySulfate 3.23 4.03Bext 55.31 69.20PM 7.02 9.20OC 1.22 2.07# Trajs 226 1053# Trajs w. Poll 56 303Frequency ProximitySulfate 3.55 2.60Bext 68.90 51.45PM 8.76 6.67OC 2.01 2.09# Trajs 220 1272# Trajs w. Poll 80 438Dolly Sods All Trajectories 00-04, Incremental ProbabilityIP Based on Top10%, 500mSulfate PMOCB-extDolly Sods All Trajectories 00-04, Cluster WeightedProbabilityCalculated using Proximity Based Clusters, 500mSulfate PMOCB-extDolly Sods All Trajectories 00-04, Cluster WeightedProbabilityCalculated using Frequency Based Clusters, 500mSulfate PMOCB-ext