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the last recorded positions are not within the boundaries of the destination
airports. Therefore, to refer the flights to their origin and destination airports,
it is necessary to build sufficiently large areas around the airports that would
include the available first and last points. It is not known in advance how large
the areas need to be and what geometrical shapes are appropriate.
Our approach to defining the areas is based on the background knowledge that
airplanes typically land and take off in similar directions, which are determined
by the orientation of the airport runways. We extract the available last positions
of the aircraft that landed and first positions of those that took off and cluster them
by spatial positions and movement directions using a density-based clustering
method, Optics ( Ankerstetal. , 1999 ), with similarity measures designed for
spatio-temporal events ( Andrienko et al. , 2011c ). As a result, points lying outside
or even quite far from the airports are grouped together with the points lying
within the airport boundaries if they correspond to landings or takeoffs with
similar directions. The airport “catchment” areas are built as buffers around these
clusters. The areas can be verified using the known positions of the airports: they
must be within the areas.
Not always do starts and ends of trajectories correspond to takeoffs and
landings. The radar observation data also contain parts of transit trajectories that
just pass over France as well as flights going outside France and those coming
to France from abroad. Real takeoffs and landings must be distilled from the
available starts and ends of the recorded tracks. To extract the landings, we use
the following query condition: the altitude is less than 1 km in the last 5 minutes
of the trajectory. From each trajectory that has such points, we extract the last
point as an m-event representing the landing (Figure 12.6 a). In the second step of
the analysis, we cluster the landing events by the spatial positions and directions
(SD) using the thresholds of 1 km and 30 degrees, respectively. The resulting
SD-clusters are presented in the space-time cube in Figure 12.6 b; the noise
(events not having sufficient counts of SD-neighbors) is excluded. The colors
represent different clusters. The vertical alignments of points correspond to the
airports where multiple landings took place during the day.
An interesting pattern can be observed in the area of Nice in the southeast of
France. There are two SD-clusters of landings, yellow and green; their points
make a column on the right in the cube. The green cluster appears as an intrusion
inside the yellow one. This means that the landing direction changed in this area
twice during the day due to a change of wind direction (aircraft take off and
land facing the wind). The map fragment in Figure 12.6 c shows that the yellow
cluster contains landings from the southwest and the green cluster landings from
the northeast. The blue lines in Figure 12.6 show the last 10-minute fragments
of the respective trajectories and reflect the mandatory landing directions.
The observation of the direction changes gives us an idea that the temporal
patterns of landings should be investigated not by airports only but by airports
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