面向DEM地形复杂度分析的分形方法研究

A Fractal Method to Describe the Terrain Complexity Reflected by the Raster DEM

在基于栅格DEM数据的基础上,应用分形几何学方法,采用元分维模型理论,提出一种描述DEM地形复杂度的分形分析方法,并得出分析指标———地形分维指数(TFI)。实验证明,该指标可以有效描述栅格DEM数据反映的地形变化特征,分析窗口由小到大的规律性变化反映出地貌从微观到宏观的变化情况,因此其既可以作为对栅格DEM所描述地形进行评价的坡面因子,又可以作为基于DEM的地貌类型区自动划分的参照依据。

A new analysis method is put forward in this paper,which is guided by the meta- fractal theory and can be applied in de- scribing the terrain complexity of the raster DEMs. According to the theory, an analytical guide line, which is called terrain fractal di mension index （TFI）, is defined. In this experimentation, a group of DENIs of high resolution and high precision whose map scale is 1 ： 10 000 and 1 ： 50 000 in Yao County, Shanxi Province are also selected as the basic data. The result shows that this method can effectively evaluate the terrain complexity of the DENIs data. As an experimental result, the TFI DTMs are homologous to the source data of DENIs pixel by pixel. Because the scale is adopted in the experimentation, it can reflect the variety of terrain from the micro view to the macro view through the regular change of the analysis scale. So it may be considered as a topographical factor, which can be applied for automatic division of landform region.