Resolving Thiessen polygons

Abstract We have developed an automated computer forecast package for Lake Superior, North America, that uses near real-time meteorological data to produce operational outlooks of basin runoff for improving lake-level regulations. The data collection network changes frequently as stations are added or dropped or fail to report from time to time. Therefore, forecasts depend on semi-automatic updating of meteorological data, requiring efficient computations of Thiessen weights. Various methods of computing Thiessen weights either have large computational overheads or provide unacceptable approximations. A new algorithm is presented for quickly computing Thiessen weights for all stations in a collection network for each of several watersheds of interest. The algorithm determines weights by finding first the edges of the Thiessen polygons and then the intersections of the polygons with watershed areas. It makes use of the fact that Thiessen polygons are convex sets of points. Considerable computational savings result by defining polygons by their edges instead of by their areal extent. Although comparisons of methods depend on particular network configurations, an example application to 18 stations covering 22 watersheds, represented on a 760 × 516-km map at 1-km2 resolution (392,160 cells), requires only 10.0 CPU-seconds on a VAX® 11 780 minicomputer (2 CPU-seconds on a CDC® 750). This represents a 93% savings in computational time with no loss of accuracy when compared to conventional computer methods.