以2009 年全国2203 个气象台站累积降水数据为例，采取逐步抽稀方法，定量分析大样本的数据样本量、样本空间分布、以及不同空间插值方法对插值结果的影响。研究表明：①在随机抽样中，总体而言，平均绝对误差(MAE)、均方根误差(RMSE)随着插值样本量的减小而增加、相关系数递减，特别当抽样比<20%时，MAE、RMSE显著增加，R2显著减少；②以Thiessen 多边形剖分的方式检验随机抽样、等间隔抽样、分区单站点控制面积约束抽样分布的均匀性，经交叉验证后知，样本空间分布对降水空间插值的结果影响比较复杂，并非越均匀越好；③对随机组中抽样比≥ 4%的数据和等间隔组，采用Kriging 方法插值，插值结果优于IDW方法。以等间隔分布的(50%，50%)、(20%，80%)数据为例，采用IDW、Kriging 方法，得到2009 年全国降水空间分布图，降水空间分布规律与中国2009年实际降水量分布吻合。
This paper studies spatial interpolation of precipitation at a national scale, the precipitation data comes from 2203 meteorological stations of China in 2009. The research content includes three parts as follows. At first, this paper divided the stations into different groups by stochastic methods, including 90%, 80%, 70%, 60%, 50%, 40%, 30%, 20%, 10%, 5% and 4% sampling rate groups, and analyzed the impact of sampling data on interpolation result by inverse distances weighting methods. Secondly, the stations with 80%, 50% and 20% of sampling rates were treated by the same sampling interval method, which extracted sampling data with gaps equal 1 or 4 according to ID serial number. By comparing interpolation result with the result by stochastic method in the same sampling rate, this paper analyzed the relationship between sampling methods of data and the result of interpolation. Finally, the paper analyzed the differences of interpolation result by IDW, Kriging and Co-Kriging in the same sampling rate groups. We can draw some conclusions as follows: (1) Using IDW methods, MAE and RMSE decreased gradually as the amount of sampling data increased, while the correlation coefficient decreased at the same time. The increase from 50% to 90% was slow with slight fluctuations, and that from 20% to 50% became obvious. Especially, when the sampling fraction <20%, MAE and RMSE were increased significantly, and the correlation coefficient was significantly reduced. (2) We found that the relationship between uniform of stations distribution and precipitation interpolation results was complex after cross-validation, and sometimes it did not have better interpolation result under more uniform distribution of stations. (3) With not only the random sampling data, but also the same interval sampling data, MAE and RMSE using IDW methods were large than Kriging interpolation method, while R2 was smaller. It is suggested that Kriging interpolation was better than IDW method in this paper. Taking 50% and 20% sampling rate groups as an example, using IDW and Kriging spatial interpolation methods, we obtained the precipitation spatial distribution of China, and the interpolation results were consistent with the actual situation.
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