三种常用DEM内插模型误差分析

Error analysis of three types of DEM interpolation model

通过给出在测、绘数据上常用的线性、三角形上线性、双一次拟线性3种DEM内插方法的内插误差模型和偶然误差在该逼近函数下的传播模型,对把地面或其局部视为随机曲面的观点以及以随机误差概括DEM误差的流行观点和方法提出明确异议,给出具体的论据和分析;并针对所有DEM生成方法均使用内插方法,却大多避而不谈逼近理论和逼近误差的怪现象,揭示地面观、数据观、逼近观三者之间互相依存的紧密关系;分析DEM主要生产过程的误差及其作用机制,指出符合规范的测、绘数据即能在该分辨率上正确反映地形结构特征;并运用这些模型解释历史实验中若干困惑问题。最后给出具有最小线性内插误差的DEM实例和实验模块网址。

The error models of three types of DEM interpolation methods（linear,triangular linear,double primary quasilinear） usually used in surveying and mapping data and the random-error propagating model in this approximating function is introduced.We argue against the general standpoints and methods which concern the ground or parts of it as random surface or sum up all DEM errors as random errors.At the same time,we offer the detailed evidence and analysis contraposing the amazing phenomenon that all DEM building methods adopt interpolation,but most of them avoid discussing the approximating theory and approximation errors.We also analyze the tight affiliation among the accurate viewpoints about ground,data and approximation.The paper analyzed DEM error and function mechanism during its main production and pointed out that the mapping data matching the criterion could reflect the terrain construction characteristic exactly on that resolution.And then explained several confused problems on history experiments making use of these models.Finally we took an example of DEM which had minimum linear interpolation error and gave a Web address of experiment module.