流域地貌形态特征多重分形算法研究

为研究流域地貌形态特征的量化指标,提出基于高程分布概率的多重分形计算模型,结合大理河岔巴沟流域和大堡岔流域DEM数据进行多重分形计算,对流域地貌形态特征多重分形谱的表征意义进行了探讨。结果表明:流域地貌形态特征多重分形谱可以更加敏感、更加全面地对流域地貌形态的总体特征进行描述;多重分形谱的顶点对应简单分形的容量维,多重分形谱的宽度可以定量表征流域表面的起伏程度,多重分形谱的端点维数的差别可以间接地反映流域峰谷数目的比例;流域地貌形态特征多重分形谱能够分层次地刻画流域内部的精细结构,从而更加突出地表现异常局部地貌变化特征;流域地貌形态特征多重分形谱的无标度区间的合理范围,应该确定为DEM像元尺度到流域最大高程值的1.5倍左右最为合适。

Multifractal arithmethic for watershed topographic feature

In this paper,taking Dali River Chabagou watershed and Dabucha watershed on Loess Plateau as examples,a new multifractal mathematic model for the large region based on the height distribution probability(HDP)is provided and established for describing the topographic characteristics of watershed by using multifractal theory.The meaning of multifractal spectrum of the topographic characteristics is discussed.The results show that:(1)the multifractal spectrum can express the topographic characteristics of a watershed more sensitive and comprehensive than the simple fractal one.The width of the multifractal spectrum can characterize the degree of the undulation of a surface quantitatively.The difference of the fractal dimensions between the maximum and minimum probability subset can give a statistical result of the ratio between the numbers of lowest and highest sites,which reflects the ratio between the peaks and valleys indirectly.(2)The multifractal spectrum can scientifically represent inner fine structure of a watershed and emphasize the abnormity partial variations of a watershed.And(3)the rational range of the non-scale domain should be identified from the cell size to the 1.5 times the height extremum of the watershed.