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, are potentially useful for identifying thesource regions for pollutants measured at a receptor. However, individualtrajectories have uncertainties associated with the resolutionand accuracy of the meteorological data and by any simplifying
assumptions usedinthe trajectorymodel,whichultimatelylimits theirusefulness (Stohl, 1998). To some extent, this may be overcome bycalculating a large number of back trajectories and subjecting themto a cluster analysis. This is a multivariate statistical techniquewhich groups the individual trajectories of an ensemble into a smallernumber of clusters, where the errors in the individual trajectoriestend to average out. In thisway sourceereceptor relationshipsmay bedetermined in a statistical sense, helpful in developing an understandingof the pollution climatology of a location.Cluster analysis of back trajectories has previously been used tosupport the interpretation of precipitation composition (Dorlinget al., 1992a, 1992b), particulate matter (Wang et al., 2004; Abdalmogithand Harrison, 2005; Borge et al., 2007; Cabello et al., 2008)and ozone (Moody et al.,1995; Sirois and Bottenheim, 1995; Brankovet al., 1998; Cape et al., 2000). The majority of such studies use back
trajectories with a timescale E-mail address: j.baker@bham.ac.uk of 3e5 days. This is generallyContents lists available at ScienceDirect
Atmospheric Environmentjournal homepage: www.elsevier.com/locate/atmosenv1352-2310/$ e see front matter
2009 Elsevier Ltd. All rights https://www.51lunwen.org/ygshlw/2011/0708/1203558424.htmlreserved.doi:10.1016/j.atmosenv.2009.10.030Atmospheric Environment 44 (2010) 563e571

other pollutant  monitoring site combination. This indicates theexistence of a significant local source of SO2 at Harwell and in factthere is a coal-fired power station located about 10 km to the northeast(Lee et al., 1999). As shown in Fig. 2, the slow-easterly air masstype contains a significantnorth-easterlycomponent,whichexplainsthe high concentrations associated with this cluster type. Similarlythe northerly Arctic cluster is also affected by it. The seasonal variationcan nowbe interpreted as increased grounding of the SO2 plumefromthe power station during thewarmseason compared to the coolseason, associated with enhanced turbulence and convection in thelower atmosphere during the warm season.
3.4. Comparison with pollutant concentrations: ozone episodes
Table 4 provides information on ozone episodes associated withthe six air mass types. The concentrations can be compared to theUK air quality standard for ozone of 100 mg m3 (50 ppbv). Thesevarious metrics all show that ozone episodes are most significantlyassociated with the slow-easterly air mass, followed next by theslow-southerly air mass. These results are consistent with theconclusions drawn from the analysis of the warm season incrementsin secondary oxidant e see Fig. 6.
4. Conclusion
A novel k-means cluster algorithm was developed and applied tothe analysis of four-day back trajectories for January 1998eDecember2001 arriving mid-afternoon in Birmingham, UK at three differentarrival heights for the identification and description of the mainsynoptic scale air transport patterns associated with this region.Clustering was undertaken on trajectory sets rather than individual
trajectories to account for vertical shear that has affected previousstudies. The clustering analysis revealed a natural break of trajectories
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