Appendix A- MoosehornSupplementTrajectory analysis results atMoosehorn National WildlifeRefuge.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.Moosehorn All Trajectories 00-04, Top 10 ClustersModes defined at: R= 12, 120hr BT,500mstart height, 4804 valid trajectories, 9562 invalidReassign Trajectories Based on72hrBT, 500m start height,7894 Valid TrajectoriesCluster 1 Cluster 2Cluster 3Cluster 4Cluster 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 1.26 1.28Bext 26.61 27.63PM 3.70 3.91OC 1.20 1.25# Trajs 378 492# Trajs w. Poll 121 142Frequency ProximitySulfate 2.47 2.55Bext 51.08 53.59PM 6.87 7.21OC 1.98 2.13# Trajs 3666 1106# Trajs w. Poll 1141 299Frequency ProximitySulfate 1.67 3.30Bext 37.55 64.22PM 5.22 8.29OC 1.79 1.73# Trajs 974 434# Trajs w. Poll 273 109Frequency ProximitySulfate 2.86 1.42Bext 55.21 34.94PM 7.05 4.71OC 1.59 1.69# Trajs 742 1052# Trajs w. Poll 208 313Frequency ProximitySulfate 1.63 2.83Bext 36.00 54.84PM 5.15 7.38OC 1.68 1.95# Trajs 508 1382# Trajs w. Poll 166 332Moosehorn All Trajectories 00-04, Top 10 ClustersModes defined at: R= 12, 120hr BT,500mstart height, 4804 valid trajectories, 9562 invalidReassign Trajectories Based on72hrBT, 500m start height,7894 Valid TrajectoriesCluster 6 Cluster 7 Cluster 8 Cluster 9 Cluster 10 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 TrajectoryCentral Trajectory Central Trajectory Central TrajectoryFrequency ProximitySulfate 1.86 2.21Bext 34.52 43.64PM 4.94 5.72OC 1.02 1.55# Trajs 118 528# Trajs w. Poll 36 140Frequency ProximitySulfate 2.91 1.85Bext 58.09 40.18PM 7.65 5.59OC 1.90 1.82# Trajs 301 1547# Trajs w. Poll 88 410Frequency ProximitySulfate 1.12 3.68Bext 27.26 68.86PM 3.74 8.95OC 1.48 2.08# Trajs 257 485# Trajs w. Poll 67 167Frequency ProximitySulfate 0.95 3.32Bext 24.11 64.52PM 3.33 8.44OC 1.31 2.18# Trajs 147 781# Trajs w. Poll 28 243Frequency ProximitySulfate 1.94 2.07Bext 43.02 37.93PM 5.98 5.31OC 1.78 1.04# Trajs 120 318# Trajs w. Poll 39 87Moosehorn All Trajectories 00-04, Top 10 ClustersModes defined at: R= 12, 120hr BT,500mstart height, 4804 valid trajectories, 9562 invalidReassign Trajectories Based on72hrBT, 500m start height,7894 Valid TrajectoriesBest and 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 1.12 3.68Bext 27.26 68.86PM 3.74 8.95OC 1.48 2.08# Trajs 257 485# Trajs w. Poll 67 167Frequency ProximitySulfate 1.26 1.28Bext 26.61 27.63PM 3.70 3.91OC 1.20 1.25# Trajs 378 492# Trajs w. Poll 121 142Frequency ProximitySulfate 2.86 1.42Bext 55.21 34.94PM 7.05 4.71OC 1.59 1.69# Trajs 742 1052# Trajs w. Poll 208 313Frequency ProximitySulfate 0.95 3.32Bext 24.11 64.52PM 3.33 8.44OC 1.31 2.18# Trajs 147 781# Trajs w. Poll 28 243Moosehorn All Trajectories 00-04, Incremental ProbabilityIP Based on Top10%, 500mSulfate PMOCB-extMoosehorn All Trajectories 00-04, Cluster Weighted ProbabilityCalculated using Proximity Based Clusters, 500mSulfate PMOCB-extMoosehorn All Trajectories 00-04, Cluster Weighted ProbabilityCalculated using Frequency Based Clusters, 500mSulfate PMOCB-ext