DEM分辨率与平均坡度的关系分析

由DEM提取坡度时,DEM分辨率的变化会造成局部栅格提取的坡度数值的变化,其变化规律对于深刻理解平均坡度,随DEM分辨率的变化而变化的规律具有现实意义。在黄土高原的研究中,选择了8个典型地貌类型的样区,获得了以1:10 000比例尺地形图为数据源的DEM(分辨率为5 m)。从DEM分辨率对栅格坡度影响规律的分析中,得到如下结论:(1)随着DEM分辨率粗略化,所提取的坡度平均值有可能升高;(2)在所有样区,随DEM分辨率粗略化,负误差的栅格均是正误差的栅格数量的1.13倍以上,保持负误差的栅格是保持正误差的栅格数量的1.81-4.04倍,同时坡度的负误差均值是正误差均值变化幅度的3.1倍以上;(3)结合结论(2)和本文提出的指标,可准确地解释8个样区中坡度平均值随DEM分辨率变化而变化的规律;(4)DEM的分辨率对正负误差的栅格数量没有明显影响,正误差(或负误差)栅格均集中于个别坡度的分级区间,而DEM分辨率对此集中的区间没有明显影响;(5)坡度总体误差可根据本研究所提出的经验公式由DEM分辨率和分辨率为5 m的DEM所提取坡度的平均值计算出来。

Relationship Between DEM Resolution and Average Slope Derived from DEM

At present, slopes are usually derived from discrete DEMs. When deriving slope from DEM, the variation of DEM resolution will cause changes in the slope values which are extracted from the local grids. The variation will be significant in understating the general rule of the variation of average slope with respect to DEM resolution. 8 areas representing the typical geomorphology in Loess Plateau were chosen as the sample areas, and the DEMs with a 5m resolution were established according to the topographic map scaled at 1：10 000. In every sample area, 22 500 sampling points were selected, and the slopes which were derived according to the algorithm of third-order finite difference weighted by reciprocal of squared distance on the sampling points were taken as the research object. The regression analysis, single-factor variance analysis, contrast analysis were adopted to analyze the rule of the influence of DEM resolution on grid slopes. The following conclusions were obtained：（1） the average slope may increase as the resolution of DEM becomes coarser;（2） in all the sample areas, with the resolution becoming coarser, the number of the grids with negative slope error is at least 1.13 times of the grids with positive slope error. The amplitude of average slope of the grids with negative slope error is greater than 3.1 times of the latter. The number of grids with decreasing slopes is 1.81-4.04 times of the grids with increasing slopes;（3） the change of average slope can be explained in this research by combining the author proposed index with the previously mentioned conclusion（2）;（4） the number of grids with varied slope values is not sensitive to the resolution of DEM. The slopes of the grids which have positive slope error or negative slope error are intensively distributed in certain intervals of slopes that derived from the DEMs with 5m resolution.The intervals are not sensitive to the resolutions of DEM;（5） the total slope error can be computed, according to the empirical formula pr