中文摘要：

在黄土高原、福建省选取20个样区为研究区域，以样区1：1万地形图所建立的5m分辨率DEM为研究对象，分析DEM高程误差、提取坡度的不同算法、不同地形对坡度精度的影响。将中误差、互信息、均值和标准差作为分析指标，采用随机噪声模拟DEM的误差。研究结果表明：互信息可以作为衡量原始坡度与加噪DEM提取坡度之间关联程度的指标；6种算法提取的坡度精度由高到低依次为三阶不带权差分算法、三阶反距离权差分算法、三阶反距离平方权差分算法、Frame差分算法、二阶差分算法、简单差分算法；坡度均值较小的区域，其坡度误差较大，坡度均值较大的区域，其坡度误差则稍小，若坡度标准差较大，则需要进一步考虑。

英文摘要：

This study had been carried out in the 20 sample areas selected from Loess Plateau and Fujian Province. using DEM with a resolution of 5 m which obtained from the topographical map with 1：10 000 scale, and the analysis was based on the accuracy of slope which was caused by DEM elevation error, different algorithms to extract different slope and different terrains. The median error, mutual information, mean and standard deviation were used as the indicators of analysis and random noises were used to simulate DEM error. The main contents are summarized as follows ： the mutual information can be used as the index of measuring the degree of association between the original slope and the slope which is extracted from the DEM with noises. A descending order according to the accuracy of slope extracted from 6 kinds of algorithm presents as ： three-order difference algorithm, three-order inverse distance weight difference algorithm, three-order inverse distance square weight difference algorithm, frame difference algorithms, two-order difference algorithms and simple difference algorithms; the smaller the mean of slope is in the area, the larger the error of slope and vice versa. It is concluded that the further consideration should be taken when the standard deviation of slope is larger.