典型黄土地貌类型区的地形复杂度分形研究

Research on Terrain Complexity of Several Typical Regions of Loess Landform Based on Fractal Method

黄土高原地貌形态与地形复杂度自南向北有序变化,构成了举世瞩目的独特的地理景观。选择陕西省南北剖面六个典型黄土地貌样区为基本实验区,以其1∶1万栅格DEM为数据源,探讨典型黄土地貌类型区的地形复杂度分形与空间分异特征。首先提出的元分维模型方法,以计算得到的DEM元分维值作为特征指标,研究样区的地形复杂度问题。这种通过滑动窗口的扩展分维分析方法,既可以用于分析该区域不同尺度下的地形复杂度变化情况,也可以探讨区域的局部单元复杂程度及其空间分布,从而不再局限于对全区域的单一分维评价。以此为基础,进一步应用元分维谱方法,研究地貌网格单元的元分维分级分布情况。实验结果表明:以绥德和延川为代表的黄土峁状丘陵沟壑区最为复杂,以宜君和甘泉为代表的梁状丘陵沟壑区居中,而以淳化为代表的黄土塬区和以神木为代表的风沙黄土过渡区最为平缓。实验进一步证明了扩展分形方法在黄土地貌研究中的可行性。

From south to north in the loess plateau, the terrain complexities of various regions are as different as the landforms. This paper selected 6 typical loess landform as test areas, employed their raster DEM datasets of with 5 meters resolution as data bases for the experiment. Firstly, a utilized the meta fractal dimension model was put forward based on DEM, by which the terrain complexity could be described. The extended fractal dimension method by means of sliding window may not only analyze the variation of terrain complexities under the different scales, but also discuss the complexity and its spatial distribution of partial cells in the current region. A benefit of the method is it would not be limited to the single fractal dimension analysis for the whole region. Meta fractal dimension spectrum was put forward as well and applied to research the distribution of grid cells in the different grades of meta fractal dimension. The result showed that variation of the terrain complexity was the most acute in the loess hill regions such as Suide and Yanchuan, and relative slight in the loess tableland regions such as Chunhua and the transitional regions between loess and desert such as Shenmu, and moderate in the loess, ridge regions such as Ganchuan and Yijun. The experiment proved that the extended fractal method is effective in the researches for loess landform.