LOW-ERROR MAP PROJECTIONS FOR PAN-EUROPEAN STATISTICAL MAPPING
Department of Geography, Vrije Universiteit Brussel
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.