基于主成分变换模型的DEM格网聚合及其误差分析

摘要

利用主成分分析揭示变量之间关系的特性,进而提出一种既能保证较高精度又能较好地保持地形形态特征的DEM格网聚合方法.首先根据主成分变换模型推导DEM格网聚合数学公式,构建主成分聚合模型;然后以30m分辨率DEM转换为90m分辨率DEM为例,根据格网点属性间的权重关系聚合重构DEM.在此基础上,以均值聚合和双线性重采样聚合方法为比较对象,从聚合前后的检查点高程偏差的统计描述、空间分布与自相关性、地形形态保持程度方面分析3种聚合策略下重构DEM的误差特性.最后运用描述统计、半变异分析和等高线套合方法,定量评价主成分聚合重构DEM的质量效果.试验分析结果表明,同均值聚合和重采样聚合相比较,该方法重构的DEM既能保持较高精度,又能很好地保持地形形态特征.%The object is to present a new DEM aggregation method which not only can ensure high precision of DEM, but also can maintain the terrain morphology better according to the characteristic of principal component analysis which can reveal the relationship between variables.First of all, the mathematical formula deduction and practical calculation procedures about the new DEM grid aggregation method are presented on the basis of principal component transformation model.The principal component aggregation method is applied to get the weights of DEM grid cells in the 3×3 filter window to rebuild new DEM.Then taking converting DEM with 30m resolution into the DEM with 90m resolution as an example, three new DEMs are rebuilt respectively using principal component aggregation, mean aggregation and bilinear resample aggregation.Based on the model, the uncertainty characteristic of the DEM rebuilt with three aggregation methods are analyzed from elevation deviation before and after grid aggregation, the spatial distribution and spatial autocorrelation, and the keeping level of the terrain feature.Finally, the quality of DEM rebuilt with principal component aggregation is evaluated with descriptive statistics, semi variance function and contour overlay method.Experimental analysis results show that the new method can maintain the terrain feature better under keeping the high precision of DEM compared with mean aggregation and bilinear resampling aggregation methods.