中文摘要：

论文依据DEM地形描述误差（简称Et）的产生机理，在分析现有Et计算模型的基础上，研究建立了顾及DEM格网布设位置的新型Et计算模型，同时以1：5万黄土丘陵地形为例，采用对比分析法揭示了DEM高程插值模型对Et计算结果准确性的影响。实验测试表明：（1）模型能有效地解算出Et的标准差、平均值、最大值、最小值等指标，准确展示出Et的空间分布特征，有助于实现DEM地形描述质量与应用不确定性的分区评价；（2）与双线性、三次卷积、局部二次多项式等常用DEM插值模型相比，以4x4DEM格网单元为搜索圆的完全规则样条函数插值模型所重构的DEM地表形态，能更为理想地反映Et的量值大小和空间分布。

英文摘要：

The DEM Terrain Description Error （Et） has a basic fact that even if the elevation sampling errors of DEM grid points are equal to zero, a terrain description error will still exist because of DEM simple matrix data format. With the development of earth observation technology, Et has become the main factor affecting the quality of DEM, especially when the DEM grid. resolution is low. Traditional calculation models could not calculate the Et value of random points on terrain surface. A new calculation model of DEM terrain description error is presented in this paper for improving the traditional models. The new Et calculation model of any ground point considers the layout position of DEM grid which is established based on the mechanism of Et production. Statistic indexes of Et based on DEM are firstly presented. Then the layout scheme of DEM grid on different datum mark position is designed. At last, the Et value of any ground point considering the layout position of DEM grid is calculated using the new model of Et. 100 DEMs with 5, 15,25, 50, 75,100 and 150 meters resolution for Loess hilly test area in Shannxi Province. The results show that： （1） the standard deviation, average value, extreme value, extreme difference and other metrics indexes of Et for each ground point in any DEM grid resolution of different physiognomy type areas could be calculated scientifically and effectively; （2） reconstruction methods of terrain surface based on DEM strongly influence the accuracy of Et model. Complete regularized spline function interpolation method based on a 4×4 search circle is tested for the optimal interpolation method.