关键词: IDW, Delaunay, 自然邻近, 插值, 气温

Abstract:

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 patial 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.

Key words: IDW, Delaunay, natural neighbor, interpolation, temperature