插值条件下格网DEM坡度计算模型的噪声误差分析

针对目前DEM（Digital Elevation Model, DEM）数字地形分析的精度评价多数不考虑DEM误差的空间自相关性或仅仅采用经验的自相关性模型问题，本文从DEM插值入手，从理论上推导了插值条件下格网DEM邻域窗口内坡度噪声误差的空间自相关性模型以及坡度精度模型，并选取典型的插值方法和坡度差分算法，从实验角度分析了在顾及和不顾及空间自相关性两种情况下的格网DEM坡度计算模型的噪声精度，实验结果表明：坡度精度受DEM噪声误差的空间自相关性影响较大，并与DEM插值方法和坡度计算模型中的差分算法有关。

Noise Error Analysis of Slope Algorithms Based on Grid DEM Derived from Interpolation

The extraction of slope from Grid DEM is generally through difference algorithms using neighbor analysis (NA), its error is subject to 3 factors: DEM error，DEM data structure and slope algorithms. This study will focusing on slope noise error that is caused by DEM noise error component, this paper will deduct the slope error model on the condition of interpolating points to grid DEM, and evaluated how noise error autocorrelation caused by interpolate influence the slope accuracy. In order to find the rules of noise error autocorrelation influences to slope accuracy, we select case experiment that was taken 5 slope difference algorithms and 4 interpolation methods as example, the experimental results show that slope accuracy can be significantly influenced by DEM noise error autocorrelation, and will be slightly changed with the different interpolation methods and slope algorithms.