The Thiessen polygon method estimates average rainfall by giving each rain gauge a weight equal to the area nearest to it.
The Thiessen polygon method estimates average rainfall over an area by weighting each rain gauge according to the area closest to it. Alfred H. Thiessen described it in 1911. The same shapes are known in mathematics as Voronoi polygons. To apply it, join neighbouring gauges with straight lines, draw the perpendicular bisector of each line, and use the bisectors to form a polygon around each gauge. Each gauge's rainfall is multiplied by its polygon's area, the results are added and the total is divided by the catchment area. For example, gauges reading 20, 35 and 10 mm with areas of 30, 50 and 20 km² give (600 + 1,750 + 200) / 100 = 25.5 mm. The method is more accurate than a simple average where gauges are unevenly spaced, and it is objective and easy to automate. Gauges just outside a catchment can be included. Once drawn, the weights can be reused for every storm, unlike isohyets. However, the method assumes rain changes abruptly at polygon edges and ignores the effect of terrain. If a gauge fails, the polygons must be redrawn.