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### DEM分辨率与平均坡度的关系分析

1. 福州大学福建省空间信息工程研究中心,福州大学空间数据挖掘与信息共享教育部重点实验室,福州 350002
• 收稿日期:2013-08-13 修回日期:2013-12-16 出版日期:2014-07-10 发布日期:2014-07-10
• 作者简介:

作者简介：陈 楠(1975-),男,博士,副研究员,研究方向为数字地形分析。E-mail：fjcn99@163.com

• 基金资助:
国家自然科学基金重点项目“基于DEM的黄土高原地貌形态空间格局研究”(40930531);国家自然科学基金项目“基于信息论的地形因子精度研究”(41001254);福建省科技计划重点项目“地形因子精度评价方法的推广和应用”(2014Y0032)

### Relationship Between DEM Resolution and Average Slope Derived from DEM

CHEN Nan*()

1. Spatial Information Research Center, Fuzhou University, Key Lab for Spatial Data Mining and Information sharing of Ministry of Education, Fuzhou University, Fuzhou 350002, China
• Received:2013-08-13 Revised:2013-12-16 Online:2014-07-10 Published:2014-07-10
• About author:

*The author: CHEN Nan, E-mail：fjcn99@163.com

Abstract:

At present, slopes are usually derived from discrete DEMs. When deriving slope from DEM, the variation of DEM resolution will cause changes in the slope values which are extracted from the local grids. The variation will be significant in understating the general rule of the variation of average slope with respect to DEM resolution. 8 areas representing the typical geomorphology in Loess Plateau were chosen as the sample areas, and the DEMs with a 5m resolution were established according to the topographic map scaled at 1:10 000. In every sample area, 22 500 sampling points were selected, and the slopes which were derived according to the algorithm of third-order finite difference weighted by reciprocal of squared distance on the sampling points were taken as the research object. The regression analysis, single-factor variance analysis, contrast analysis were adopted to analyze the rule of the influence of DEM resolution on grid slopes. The following conclusions were obtained: (1) the average slope may increase as the resolution of DEM becomes coarser; (2) in all the sample areas, with the resolution becoming coarser, the number of the grids with negative slope error is at least 1.13 times of the grids with positive slope error. The amplitude of average slope of the grids with negative slope error is greater than 3.1 times of the latter. The number of grids with decreasing slopes is 1.81-4.04 times of the grids with increasing slopes; (3) the change of average slope can be explained in this research by combining the author proposed index with the previously mentioned conclusion (2); (4) the number of grids with varied slope values is not sensitive to the resolution of DEM. The slopes of the grids which have positive slope error or negative slope error are intensively distributed in certain intervals of slopes that derived from the DEMs with 5m resolution. The intervals are not sensitive to the resolutions of DEM; (5) the total slope error can be computed, according to the empirical formula proposed in this research and calculated from the DEM resolution and the average slope of DEM with a 5m resolution.

Key words: DEM, slope, error, resolution