Automated Thiessen polygon generation

Data uncertainty research of rain gauge network requires generation of large numbers of Thiessen polygons. Despite its importance in hydrology, few studies on computational Thiessen polygons have been carried out, and there is little published information in the hydrological literature. This paper describes two automated approaches and the ways for their implementation in hydrological applications: triangulation method and grid method. Triangulation is a lossless method but suffers from complications in coding and slow computational speed with small numbers of gauges. Grid method is easy to implement, but a compromise must be made between the computational grid size, accuracy, and speed. This paper describes a procedure to derive the relationship between the catchment area, grid size, and accuracy indicator based on weighted mean error. The computational speed comparison between the two methods has been found to follow a logarithm curve, and the critical number of gauges could be found from this curve for deciding the method choice if the computational speed is the limiting factor in a project.