DOI：

中文关键词: Delaunay三角剖分法, 三角分片线性插值, 反距离权重法, 降水量

英文关键词:Delaunay triangulated networks Triangulated slice linear interpolation algorithm Inverse distance weighting Precipitation

基金项目:中国气象局“精细化要素预报用户支撑环境系统改进与推广应用”、公益性行业（气象）科研专项(GYHY201106010、GYHY201106027)

作者

熊敏诠

单位

1. 中国科学院大气物理研究所，北京，100029; 2. 中国科学院大学，北京,100049; 3. 国家气象中心，北京，10008

中文摘要:

Delaunay三角剖分方法在空间分析中具有重要地位，文中简要介绍了Delaunay三角网特性和常用的3类算法，并对随机增长法实现过程进行了详细阐述。根据三角分片线性插值原理，求得插值系数，实现对任意点的三角分片线性插值。利用2008年中国2200个观测站的08时24 h降水量资料，对全中国范围及划分的8个区域内相应的0.28125°×0.28125°降水量格点场，使用交叉检验方法，对比分析了三角分片线性插值和反距离权重法的估值准确率。结果表明：在各区域，三角分片线性插值法的均方根误差偏小；在站点较密集的区域，均方根误差、平均绝对误差比较中，三角分片线性插值都有一定的优势；在平均误差对比中，三角分片线性插值优势明显，在全中国范围交叉检验中，三角分片线性插值法对应的年平均误差是0.005 mm，而反距离权重法为-0.107 mm，对其可能的原因进行了分析，证明了Delaunay三角剖分法的合理性。同时，从图形上展示了降水量的Delaunay三角网的三维结构图和三角分片线性插值后的格点场， 在直观上，Delaunay三角剖分后得到降水分布和实况保持一致，并有较好的视觉效果；通过三角分片线性插值得到的格点场降水量分布图，克服了反距离权重法的固有缺陷，使获得的降水量格点场趋于合理，提高了插值精度。最后，探讨了Delaunay三角网在气象领域的应用前景。

英文摘要:

Delaunay triangulated method plays an important role in the spatial analysis. The characteristic of Delaunay triangulation and three kinds of generation algorithm are introduced in this article. The stochastic growth algorithm is also discussed in detail. Based on the principle of the triangulated slice linear interpolation the coefficient is attained and thus the value at an arbitrary point can be calculated through the triangulated slice linear interpolation algorithm. By using the daily precipitation data of the 2400 stations over China in 2008, the interpolation cross verification for the precision of interpolation is made between the triangulated slice linear interpolation algorithm and the inverse distance weighting for the whole China and the eight regions divided in China. The results show that the root mean square error of the triangulated slice linear interpolation algorithm is smaller for the various regions, and it has higher accuracy in the root mean square error and the mean absolute error in the concentrated site. For average error, triangulated slice linear interpolation algorithm has a highlighted high precision and the possible cause is discussed. The value of annual mean error is 0.005 mm and -0.107 mm for the triangulated slice linear interpolation and the inverse distance weighting method, respectively. It is also showed that the rationality of the triangulated slice linear interpolation algorithm. In the meanwhile, the three dimensional structure and the grid field on triangulated slice linear interpolating are showed in graph as well. The results showed that the figures calculated by the triangulated slice linear interpolation algorithm maintain consistency with the observation and have good visual effects. The precipitation distribution grid field by the triangulated slice interpolation gets rid of the inherent defect of the inverse distance weighting, thus improving the precision of interpolation. Finally, the application prospect of Delaunay triangulation in meteorology is discussed.