Research on the Application of Constrained Delaunay Triangulation in Precipitation Averaged over China

The properties and algorithm type for applying constrained Delaunay triangulation is studied. Based on the precipitation data from 2200 stations in China from 1980 to 2009, a set of station and boundary points is analyzed using ordinary Delaunay triangulation. Constrained Delaunay triangulation is achieved by deleting the boundary points and the relevant edges, and then calculating the spherical triangle area. After converting the geodetic coordinate system to a direct coordinate system in space, the interior angles of the spherical triangle can be attained. Precipitation averaged over China can then be calculated using a weighting factor based on the triangulation area. Comparing the precipitation averaged over China for different time periods, the mean value standard deviation, when using the triangulation method, is lower than when using the arithmetic method. However, there is a high correlation between the two methods. Results from our statistical analysis and examination of these two methods are as follows: Through normal verification of the Shapiro-Wilk test, the annual mean precipitation from both methods shows a normal distribution. Using a singular variance F-test, the variance of the two methods is different. Applying a t-test, the differences in the annual mean precipitation values for two methods is significant at the 0.05 level. Using the 2009 precipitation forecast data from European and Japanese numerical weather prediction, the authors determined the precipitation values averaged over China using these two methods and analyzed the results. Compared with the traditional arithmetic averaging method, constrained Delaunay triangulation is more complete since it factors in both regional mean precipitation and regional climate.