中文摘要：

分析了坡度提取算法的数学模型,并结合实际数据进行了分析和验证,提出了对误差进行敏感性程度分析的方法,得到了根据DEM分辨率或平均坡度计算坡度误差的公式。

英文摘要：

The value of slope of a grid derived from DEM varies with the resolution of DEM. The pattern of the slope variation is meaningful for the deep understanding of the general variation rule of slopes. The mathematical model for deriving slopes was analyzed, and the real data were used to test it. The following conclusions are obtained： as the resolution of DEM becomes rough, the increase and decrease of the slope value depends upon the first order partial derivative, the three partial derivative and the mixed three partial derivative of the function of real surface; as the resolution of DEM is less than 30 meters, （1） the amount of grids with minus sign of slope error is about 7 times more than that of grids with plus sign of slope error, and the absolute value of minus error is over 2 times as much as that of plus error, （2） plus-or-minus sign of slope error is not related to the resolutions of DEM, and （3） it is the absolute value of minus error that is more sensitive to the change of the resolutions of DEM than the value of plus error. The research method was put forward to analyse the sensitivity of error. The researchers have got the formulas for calculating slope errors from the resolutions of DEM or from the averages of slope. The formulas would provide the guidance for the practical application departments.