Appendix A- MohawkMountain SupplementTrajectory analysis results atMohawk Mountain.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 5Mohawk Mt All Trajectories 00-04, Top 9 ClustersModes defined at: R=12, 120hr BT,500mStart ht, 6456 Valid Trajectories, 7743 InvalidReassigned Trajectories Based on72hr BT,500m Start Ht, 10161 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 4.00 4.25Bext 74.59 77.74PM 9.83 10.12OC 2.85 3.03# Trajs 4562 1286# Trajs w. Poll 931 293Frequency ProximitySulfate 1.62 5.10Bext 35.40 91.95PM 4.55 11.78OC 1.41 3.19# Trajs 1318 917# Trajs w. Poll 254 205Frequency ProximitySulfate 4.85 2.01Bext 89.55 41.43PM 10.99 5.35OC 2.87 1.50# Trajs 925 1130# Trajs w. Poll 196 200Frequency ProximitySulfate 5.04 4.84Bext 89.33 83.57PM 12.38 10.98OC 3.31 2.58# Trajs 641 1135# Trajs w. Poll 110 220Frequency ProximitySulfate 1.75 2.65Bext 36.74 49.81PM 5.12 6.45OC 1.66 1.73# Trajs 812 698# Trajs w. Poll 168 141Cluster 6 Cluster 7 Cluster 8 Cluster 9Mohawk Mt All Trajectories 00-04, Top 9 ClustersModes defined at: R=12, 120hr BT,500mStart ht, 6456 Valid Trajectories, 7743 InvalidReassigned Trajectories Based on72hr BT,500m Start Ht, 10161 Valid Trajectories 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 2.34 4.08Bext 45.33 74.60PM 5.49 8.50OC 1.63 2.10# Trajs 188 641# Trajs w. Poll 37 118Frequency ProximitySulfate 1.96 1.53Bext 38.83 40.71PM 5.53 6.44OC 1.62 2.95# Trajs 301 1141# Trajs w. Poll 41 239Frequency ProximitySulfate 2.38 4.62Bext 47.70 83.40PM 6.37 10.99OC 1.69 2.80# Trajs 270 1061# Trajs w. Poll 48 217Frequency ProximitySulfate 2.51 2.26Bext 49.09 47.14PM 6.52 6.32OC 1.60 1.87# Trajs 253 2161# Trajs w. Poll 58 369Mohawk Mt All Trajectories 00-04, Best/Worst SulfateModes defined at: R=12, 120hr BT,500mStart ht, 6456 Valid Trajectories, 7743 InvalidReassigned Trajectories Based on72hr BT,500m Start Ht, 10161 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 1.62 5.10Bext 35.40 91.95PM 4.55 11.78OC 1.41 3.19# Trajs 1318 917# Trajs w. Poll 254 205Frequency ProximitySulfate 5.04 4.84Bext 89.33 83.57PM 12.38 10.98OC 3.31 2.58# Trajs 641 1135# Trajs w. Poll 110 220Frequency ProximitySulfate 4.85 2.01Bext 89.55 41.43PM 10.99 5.35OC 2.87 1.50# Trajs 925 1130# Trajs w. Poll 196 200Frequency ProximitySulfate 1.96 1.53Bext 38.83 40.71PM 5.53 6.44OC 1.62 2.95# Trajs 301 1141# Trajs w. Poll 41 239Mohawk Mt All Trajectories 00-04, Incremental ProbabilityIP Based on Top10%, 500mSulfate PMOCB-extMohawk Mt All Trajectories 00-04, Cluster WeightedProbabilityCalculated using Proximity Based Clusters, 500mSulfate PMOCB-extMohawk Mt All Trajectories 00-04, Cluster WeightedProbabilityCalculated using Frequency Based Clusters. 500mSulfate PMOCB-ext