坡度提取的边缘效应研究

Study on Edge Effect of Derived Slope

坡度一般是从离散的DEM中提取的,所以在坡度矩阵的边缘存在边缘效应。为了找到这种边缘效应的本质规律,应用Taylor展开方法,以3阶反距离平方权差分算法为例,分析了三维地形表面条件下边缘效应对坡度的影响规律,并在此基础上提出了坡度计算误差函数。以5个典型地貌样区以及基于高斯曲面所生成的6种地形为研究对象,分析了DEM提取坡度时的边缘效应问题。通过实际数据的试验证明:坡度计算误差函数可以准确预测边缘效应条件下坡度的变化情况。通过大量统计分析,找到了边缘效应条件下坡度中误差与DEM分辨率的回归方程。同时,研究指出边缘坡度大于真实坡度的格网出现在地形起伏较大、DEM分辨率粗略化的条件下。

At present,slope is usually derived from discrete DEM. This method brings errors on the edge of slope matrix. This study was focused on the essential law of the edge effect taking place in slope derived from DEM. The Taylor expansion method was used to find the regulations of the slope change on the edge of slope matrix,with the slope derived by using the common algorithm,the third-order finite difference weighted by re-ciprocal of squared distance. On the basis of the theoretical analyses,the author put forward the error function of slope computation. Then,five sample areas which represented five typical physiognomies and six surfaces generated by Gauss function were the objectives of the research. IThe er-ror function of slope calculation could be used to predict whether slope on the edge would increase or decrease. On the basis of a great deal of statis-tics analyses,the researchers found the regression equations that could describe the relationship between resolution of DEM and the Mean Square Error of slope under the conditions of the edge effect. These equations can be used as references for the further studies. Similarly,the author has found out that the increasing of slope on the edge region takes place when the topographic relief is great and the resolution of DEM is coarse.