基于单个栅格的DEM坡度与分辨率关系研究

Study on the Relationship Between the Resolution and the Slope Derived by DEM Based on Single Grids

在黄土高原选取代表不同地貌类型的延川、绥德、富县3大研究样区108个小样区，以研究样区1：1万地形图所建立的5m分辨率的数字高程模型（DEM）提取的坡度矩阵为标准值，基于单个栅格分析15～75m分辨率的DEM提取的坡度矩阵准确程度．提出了基于栅格的坡度准确程度评价指标：分级正确率指标a和坡度数值误差指标b．在每一大样区随机选取的20个试验样区得到了上述两项误差指标与水平分辨率的函数关系，可以根据函数关系由已知误差求得所需要的水平分辨率范围，并且函数关系在每一大样区16个随机检验样区通过了检验．结论表明：指标a和b可以用于基于单个栅格方式评价DEM所提取坡度的准确程度，所得到的函数关系可望为实际工作选取适宜的水平分辨率提供依据．

108 sub-areas were selected from three major sample areas： Yanchuan, Suide, and Fu County which are different in physiognomy and locate in the Loess Hill and Gully Area. The slope matrix derived by DEM with the resolution at 5 m established according to the map scaled at 1～10 000 was taken as the standard value. The accuracy of the slope matrix with resolutions from 15 m to 75 m based on single grids was analyzed.The slope accuracy evaluating indexes based on grids were proposed as follows： the graded slope accuracy a and slope error b .The function of the above error indexes and the horizontal resolution was obtained in 20 randomly selected experiment areas. According to the function, the range of the needed resolution was calculated when the errors were known. The function has been tested in 16 randomly selected areas. The results show that indexes a and b can be used to evaluate the accuracy of the slope derived by DEM based on single grids.