LOW-ERROR MAP PROJECTIONS FOR PAN-EUROPEAN STATISTICAL
MAPPING
F. Canters
Department of Geography, Vrije Universiteit Brussel
fcanters@vub.ac.be
The
widespread use of geographical information technology and the establishment of
spatial databases at sub-continental to global scales have promoted new
interest in map projection issues. While for most applications at the local up
to the national level the reference system that is used for the official
topographic mapping of a country’s territory can be adopted, the problem of map
projection selection will usually present itself when data from different
countries have to be integrated into a common reference system.
In the 80s
the British cartographer Derek Maling proposed a suitable map projection for
CORINE, the EU environmental database. Using a combination of graphical and
analytical methods, Maling determined the optimal aspect and other projection
parameters for various standard equal-area projections, and compared distortion
characteristics for the limiting extremities on each projection. Based on
Maling’s analysis an azimuthal equal-area projection, with centre at 48°N, 9°E
proved to be the best choice for the mapping of the EU, which at that time
consisted of twelve member states.
With the
reunion of Germany in 1990, and the enlargement of the EU with three new member
states (Austria, Finland and Sweden) in 1993, the borders of the EU changed
considerably, and the distortion pattern of Maling’s azimuthal equal-area
projection no longer matched the shape of the area. The expansion of the EU
with 10 new member states in 2004 led the European Commission to slightly shift
the centre of its azimuthal equal-area projection to the northeast. While this
change of origin resulted in less overall distortion, the variation in error
along the boundaries of the EU is still quite substantial.
In 1997,
Canters and De Genst proposed a series of low-error equal-area map projections
for the EU. Instead of using the traditional least-squares approach, and
optimizing a locally defined distortion criterion, the selection of optimal map
projection parameters was based on reducing the distortion of a large number of
finite distances spread randomly over the area of the EU. A polynomial
transformation was presented transforming the graticule of the azimuthal
equal-area projection so that its distortion pattern better fits the general
outline of the EU. The proposed transformation reduced the average distortion
of distance to less than half the value obtained for the original azimuthal
projection.
In this
paper a similar approach is proposed for developing new, low-error equal-area
map projections for statistical mapping of the EU, using present and
anticipated EU boundary definitions. Distortion properties of the new
projections are described in detail, based on local distortion statistics and
on maps showing the spatial distribution of local scale factors and angular
distortion. The impact of the order of the polynomials used for transforming
the original graticule, as well as the effect of various symmetry conditions
imposed on the transformation, are systematically analyzed.