自适应的IDW插值方法及其在气温场中的应用

Adaptive IDW interpolation method and its application in the temperature field

反距离权重(Inverse Distance Weighting,IDW)插值通常采用距离搜索策略选择插值参考点,当采样点集分布不均匀时,距离搜索策略使得参考点聚集一侧影响插值精度。自然邻近关系具有良好的自适应分布特性,可有效地解决参考点分布不均匀问题。结合自然邻近关系,提出自适应的反距离权重(Adaptive-IDW,AIDW)插值方法。首先对采样数据构建初始Delaunay三角网,然后采用逐点插入法,将待插值点插入初始Delaunay三角网中,局部调整得到新的Delaunay三角网,以待插值点的一阶邻近点作为IDW插值的参考点,使参考点自适应均匀地分布在待插值点周围,再进行IDW插值计算。利用AIDW插值方法对Franke函数、全国气温观测数据进行插值实验,结果表明此方法具有较高的精度,且减少了"牛眼"现象。

The Inverse Distance Weighting(IDW) interpolation has the advantage of simpleness, convenience for calculation, and high compatibility with Tobler's first law. It is widely used in construction of DEM, weather analysis, hydrological analysis, and so on. Distance search strategy is usually adopted by the IDW interpolation to select referent points. However,referent points gathering in one side may cause the loss of interpolation accuracy when sampling points are unevenly distributed. The natural adjacency spatial relationship with good adaptive characteristics about choosing referent points can effectively solve the problem of reference points' uneven distribution. Based on this, the adaptive inverse distance weighting(AIDW) interpolation method was proposed in this paper. Firstly, the initial Delaunay triangulation was built with the sampling data points. Secondly, interpolative points were inserted one by one, the purpose of which was making the referent points evenly distributed around the interpolative points by taking the first-order neighboring of interpolative points as referent points.At last, IDW was interpolated. In step two, when each point was inserted, the Delaunay triangulation should be reconstructed, which elapseded time a lot. To solve this problem, the spatial grid index was built in order to raise the speed of Delaunay triangulation's reconstruction. Compared with ordinary IDW, there was no need to assign the number of referent points or search radius in the AIDW, because the referent points could be adaptively selected with the natural adjacency spatial relationship of interpolative points. Especially when referent points were too intensive, the problem of superfluous points being inserted could be avoided. Two experiments were conducted in this paper, which were the theoretical surface reconstruction of the Franke and the national surface air temperature field reconstruction respectively. The results were compared with IDW interpolation methods with different search strategies in ArcGIS 10.1, which verify that the proposed method have higher accuracy. Meanwhile, the results of the proposed method show that the 'buphthalmos' phenomenon is reduced. All the outcomes indicate that the proposed method can be applied in the interpolation of geographical phenomenon as a new method.