数字高程模型（DEM）误差分析的逼近论模型

通过对现有地面DEM各种不同观点的分析,阐明地面是多个单元曲面在复杂的地形结构线上拼接而成的确定表面;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,并给出具体论据和分析.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,分析了正确的地面现、数据观、逼近观三者之间互相依存的紧密关系.在此基础上,运用数值逼近理论量化地分析了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能在该分辨率上正确反映地形结构特征;给出了规范数据常用的线性、三角形上线性、双一次拟线性DEM内插方法的内插误差模型,以及偶然误差在该逼近函数下的传播模型,指出并证明了DEM最优线性内插模型及其卓越特性;运用这些模型解释了历史试验中若干引起困惑的问题.

Approximation Theory Model on Error Analysis of a Digital Elevation Model

This paper examined the different views of ground DEM and justified that the ground surface was the mul- tiple cell surface mosaic in complex terrain structure. With specific evidence, it challenged both the popular concept which read the ground wholly or locally as random surfaces and the method that used the mere random error to ge neralize I）EM error. It clarified the interdependent relation of ground view, data view and approximation view and opposed the DEM generation method which depended on interpolation method but mostly evaded approximation the- ory and the approximation error. A quantitative study was conducted on the error analysis and mechanism of action of DEM production process in light of numerical approximation theory. This result shows that the normal mapping data c~m properly reflect the sub-braid rate terrain structural features. The findings give the linear mapping data, the error model of linear DEM interpolation method and the propagation model of accidental errors in approximation function. This study explains some confusing issues in the historical experiments and testifies DEM optimal linear in- terpolation model and its outstanding features.