基于分形理论的地形复杂性量化方法

The Quantitative Method of Topographic Complexity Based on Fractal Theory

地形的复杂性是地表崩塌、山体滑坡、泥石流等自然灾害的主要影响因素之一,近年来对地形复杂性的定量研究十分活跃,分形方法是其中主要的研究方法之一,但是目前的研究大多以沟壑分形、等高线分形、元分形等为主,难以对区域地形的整体复杂性进行定量描述;利用基于相对高差的地形分形研究方法,对三个形状和面积基本一致,地形起伏特征各不相同的区域,以相同的网度兼顾特殊地形位置布设样品点,统计样品点及其相对高差信息,并进行分形分析,分析结果表明,样品点的相对高差信息基本包含了其所在区域的地形特征信息,地形的相对高差信息服从分形分布,其分维值的变化趋势与地形复杂性相反,由此提出将其分维值的倒数定义为地形复杂性指数,地形复杂性指数的变化趋势与地形复杂性一致,它很好地拟合了地形的实际特征,定量地刻划了地形的复杂程度。

Topographic complexity is one of the main influence factor of natural disasters such as surface collapse, landslide and debris flow and so on. In recent years, the quantitative research on the topographic complexity is very active, and among them, fractal method is one of the main research method. However, the research mainly focused on gully fratalfractal, contours fractal, unit fractal, etc., and the topographic complexity of whole area is difficult described quantitatively by them. By using research method of topographic fractal based on relative elevation's difference, sample points were deployed on three regions which shapes and areas were basic consistent and characteristics of topographic relief were different according to the same grid considering special topographic position. Sample points and their information of relative elevation's difference were counted and analyzed by fractal method. The results show that information of the relative elevation's difference of the sample points basically contained information of topographic feature of its region;information of the topographic relative elevation's difference obeyed fractal distribution, variation trends of its fractal dimension was contrary to topographic complexity. From this, it was suggested that reciprocal of its fractal dimension was defined as topographic complexity index. Variation trends of topographic complexity index accorded with topographic complexity. It fitted well the topographic actual characteristics, and described the degree of topographic complexity quantitatively.