Map projection errors in the Weber problem |
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| Authors: | Yoshiaki Ohsawa Hirofumi Kagaya Takeshi Koshizuka |
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| Institution: | (1) Institute of Policy and Planning Sciences, University of Tsukuba, Tsukuba 305-8573, Japan (e-mail: osawa@sk.tsukuba.ac.jp; koshizuk@sk.tsukuba.ac.jp), JP;(2) Tokyo Metropolitan Government, Tokyo, Japan, JP |
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| Abstract: | When demand points are given as a planar map where projection method is explicitly stated, we usually know the latitudes
and longitudes of these points from the map. Then we can solve the Weber problem on the globe, and we do not suffer from errors.
This paper analyses how cylindrical projections cause distortion in the Weber problem when demands are distributed on the
Northern Hemisphere. First, we demonstrate that planar solutions are always located south of the spherical solution if the
Mercator projection, the equirectangular projections with standard parallels near the demands, or the equal-area projection
with the same characteristic is chosen. Second, we verify that this geographical tendency is inclined to hold when the demand
points, are distributed symmetrically, widely or toward the north.
Received: 15 August 2001 / Accepted: 20 April 2002
This paper was partially written while the first author was visiting the Department of Geography at the Catholic University
of Louvain, Louvain-la-Neuve, Belgium 1993–1994]. He is grateful for the hospitality of this department. An earlier version
of this paper was presented in 1994 at the Seventh Meeting of the European Operational Research Working Group on Locational
Analysis in Brussels, and in 1996 at the Fifth World Congress of the Regional Science Association International in Tokyo.
The authors would also like to thank the participants as well as three anonymous referees for their constructive comments. |
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| Keywords: | : Weber problem spherical distance map projection cylindrical projection location error |
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