顾及各向异性的CSRBF空间插值及其在气温场重建中的应用

Anisotropic CSRBF Spatial Interpolation and Its Application in Temperature Field Reconstruction

在地理空间中各种地理现象实际上是一种连续变化的空间场。由于受到观测手段、工具的限制,只能从有限的地点获得有限的观测数据。为了获得连续的空间场,通常采用克吕格插值、反距离权重插值等方法进行重建。但这些方法都是各向同性的,与具有各向异性的真实地理现象分布并不相符。该文以各向同性的紧支撑径向基函数插值模型为基础,对其进行改进,使其能够顾及空间场的各向异性。其方法是利用加权主成分分析对原始数据进行方向性特征分析并进行旋转,再利用半变异函数拟合变换后坐标系下各轴向的变程值,以此为基础构建紧支撑径向基函数插值模型并进行插值,最后将插值结果逆旋转到真实地理空间。以国家气象中心提供的黄淮海平原气温数据与香港天文台提供的香港地区气温数据为例,对该文提出的顾及各向异性紧支撑径向基函数空间插值方法进行验证,并与反距离权重插值、全局径向基函数插值及顾及各向异性的普通克里格插值进行对比,实验表明该方法具有较高的精度且能够对气温场的细节进行准确的重建。

In geographic space,a variety of geographic phenomena actually is continuously changing spatial field.Due to the constraints of means and tools,only observational data can be obtained from limited locations.In order to obtain a continuous spatial field,the Kriging interpolation and the Inverse Distance Weighting （IDW） interpolation are usually used for the reconstruction.However,these methods are isotropic,which do not match the real anisotropic geographical phenomena.In this paper,the isotropic Compactly Supported Radial Basis Function （CSRBF） interpolation model is improved,so that spatial field anisotropy could be taken into account.The method uses the weighted PCA （WPCA） to analysis directional characteristics of the original data and the original data is rotated to the new coordinate system,after that,the semivariogram is used to calculate the variable ranges of each axis.Then CSRBF interpolation model is built.Finally the interpolation results are rotated back to the real geospatial space.With the temperature data of Huanghuaihai Plain provided by the National Meteorological Center and the Hong Kong Observatory,the anisotropic CSRBF spatial interpolation method proposed by this paper is tested.The interpolation results are compared with the IDW interpolation,global Radial Basis Function （RBF） interpolation and the anisotropic Ordinary Kriging （OK） interpolation,which shows that the proposed method has higher precision and is capable of accurate details of the temperature field reconstruction.