中文摘要：

从DEM中可获取众多地形因子。其中，坡度作为基本的地形因子，其精度对于退耕还林、水土流失评估等研究具有重要影响。但是，由于DEM只能是真实地表形态的近似表达。如何模拟坡度误差的规律成为研究的热点。本文在黄土高原地区选取代表不同地貌类型的神木、绥德、延川、富县和宜君5个研究样区，以1：1万地形图为基本数据源，建立不同分辨率的DEM，用以分析坡度信息损失量随DEM分辨率变化的规律。故此，提出了基于单个栅格方式的坡度信息量损失指标，并在每一样区随机选取的20个子实验样区得到了其与DEM分辨率的函数关系，以及相关的经验公式，据此求得所需的最适宜DEM分辨率，并在每一样区随机地选取16个子样区进行了检验。

英文摘要：

As a fundamental form of spatial data, Digital Elevation Model （DEM） plays a considerable role in many fields, such as surveying and mapping, territorial planning, and national defense. DEM is usually discrete in data structure and is an approximation of the real terrain. Though the technology of obtaining the elevations of sampling points has been improved, the real surface can only be represented by discrete grids. This means that the slope can only be computed by using the elevations of discrete grids. Therefore, thederived slope will have an unavoidable error. However, it is the slope that determines the transfer of matters and energy on the terrain sur- face and its accuracy exerts a great influence on the related researches and applications. 5 areas of Shenmu, Suide, Yanchuan, Fuxian and Yijun in Loess Plateau that represent the typical geomorphology are chosen as the sample areas, in which the DEMs withresolutions of 5 m, 15 m, 25 m, 35 m, 45 m, 55 m, 65 m and 75m are es- tablished according to the topographic map scaled at 1：10000. The slope is derived by using the algorithm of the third-order finite difference weighted by the reciprocal of squared distance. The slope derived from DEM with a resolution of 5m is assumed to be the true value, and the slopes derived from other DEMs are taken as the investi- gated subjects. Each area is divided into 36 subareas. The relationship between the index and the resolutions of DEMs is investigated in 20 subareas selected randomly from the 36 subareas. We proposed an index for the slope information loss based on the single grid, and obtained empirical equations to describe the relationship between the resolutions of DEM and the values of the index. The equations are tested in the otherl6 subareas and proved to be effective. Using the equations, we can get the most suitable resolution for DEM when the index is known. The users, who want to select proper resolutions for DEM to minimize the amount of data and reduce the cost while ensuring the accuracy of the slope