基于时空变异函数的Kriging插值及实现

Kriging（克里金）算法通常用于对空间变量进行插值，但不能直接应用于时空变量，它需要进行时空扩展。以月平均气温数据为例，运用时空Kriging方法结合R统计语言进行时空插值研究及其实现。通过时序分解去除气温数据中季节变化项，在分别得到空间变异函数和时间变异函数的基础上构建一类积和式时空变异函数来描述变量的时空相关结构，并给出基于R语言的具体实现步骤。将普通Kriging方法进行时空扩展，应用于气温数据的时空插值中。验证结果表明，基于时空变异函数的Kriging方法能提供较高精度的插值效果，这为时空变量的插值预测提供了有效的途径。

Research and realization of Kriging interpolation based on spatial-temporal variogram

The Kriging method is generally used in spatial variable interpolation,but not directly in spatial-temporal variable. It needs to be extended to space-time.The spatial-temporal Kriging,with R language,is applied for the spatial-temporal interpolation research and realization of monthly average temperature.The seasonal part has been removed from original temperature data by time series decomposition.A kind of product-sum variogram in space-time,describing the spatial-temporal correlation,is constructed based on pure spatial variogram and pure temporal one.The realization steps with R software are given. Spatial-temporal Kriging extended from ordinary Kriging is used in the temperature data.The experimental results show that this Kriging method based on spatial-temporal variogram has satisfied accuracy,which supplies an effective approach for interpolation and estimation of spatial-temporal variables.