Fortyeight hour, 3dimensional kinematic
backtrajectories were calculated from the time and location of every
aircraft
spiral using the NOAA Air Resources Laboratory (ARL) HYbrid
SingleParticle
Lagrangian Integrated Trajectory (HYSPLIT) model (Version 4) (R. R.
Draxler
and G. D. Rolph, 2003, http://www.arl.noaa.gov/ready/hysplit4.html) and
80 km
Eta Data Assimilation System (EDAS) 3hourly archive data. The
latitude,
longitude, and pressure were converted to Cartesian coordinates by
treating the
Earth as a sphere and calculating their position in 3dimensional
space. Vertical
variability along the trajectory paths may have a large impact on
transport and
hence, pollution levels, but the spatial distances described by the
variability
in the vertical wind component are typically less than the horizontal
spatial
distances covered by the air parcels. The spatial coordinates
were
normalized to give the vertical variability similar weighting to the
horizontal
variability. The mean value for each coordinate at every time
step was
calculated. The differences between the individual coordinates
and the
mean value were quantified and normalized by the standard
deviation. This
process gives equal weighting to all three coordinates when performing
the
cluster analysis. The Euclidean
distance between each trajectory pair was then calculated for each hour
of the
48 hour backtrajectory. However, the
first six time steps back from the receptor site were given zero
weighting to
account for the spatial heterogeneity of the aircraft spiral
locations.
To further discount the spatial variability of the receptor locations
and place
the emphasis on the source regions, the trajectory time steps were
weighted
linearly back in time, increasing the weighting for each hour after the
initial
six zeroweighted time steps.
After the distances between individual trajectories were calculated,
the trajectories
were clustered using an agglomerative, hierarchical clustering
algorithm.
The algorithm used an average linkage function to determine the
distance
between the trajectories making up the clusters. After reviewing
the meteorology
and pollutant profiles associated with each cluster, eight was
determined to be
the appropriate number of clusters. In the above link, the
backtrajectory
densities are plotted for each cluster. To determine these densites, a 1^{o} latitude by 1^{o} longitude grid map was made
for each
cluster, and the number of backtrajectory points crossing a grid box
was
divided by the total number of backtrajectory points in a cluster. Densities between the 1^{o} by 1^{o} grid were interpolated
using a linear weighting
scheme.
