流域地貌形态分形布朗运动(FBM)分维数研究

Research on the FBM characters of watershed topographic feature

应用分形布朗运动(FBM)理论,建立了流域地貌形态FBM分维数的计算模型.以大理河流域六条子流域为例进行计算,并对各流域地貌形态FBM分维数的特点进行了分析.结果表明:流域地貌形态特征在一定的像元尺度区间内(无标度区间)遵从某种共同的幂律关系,可以用FBM分维数来表述;流域地貌形态FBM分维数能够从综合性与整体性方面对不同像元尺度流域地貌的共同特征进行描述;利用这个方法可以进行不同像元尺度下地貌形态特征的比较与评价.

The theory and method for describing the topographic characteristics of watershed by using Fractional Brownian Motion （FBM） were introduced in this paper. Based on the DEM surface area, a new arithmetic model for calculating fractal dimension is proposed with the theory of FBM, and takes Dali River on the loess plateau as an example. The results show：（1） In certain grid cell size （non-scale range）, the topographic feature has fractal characteristics and can be described by FBM fractal dimension. （2） The watershed fractal technology can synthetically, holistically, scientifically express the watershed topographic feature. （3） The arithmetic for calculation fractal dimension could be easily used to compare and estimate the topographic feature from different grid cell sizes.